WO2021011581A1 - Image-based predictive model for lung cancer - Google Patents

Abstract

Systems and methods for detecting malignant pulmonary nodules can include a computing device conformally mapping a surface corresponding to a pulmonary nodule into a spherical surface. The device may evaluate, at a plurality of points of the surface, an area distortion metric representing distortion in area due to mapping. The device may identify, using values of the area distortion metric, one or more spikes associated with the surface corresponding to the pulmonary nodule. The device may compute a cumulative sharpness score and a cumulative irregularity score of the one or more spikes, and use the computed scores to determine whether the pulmonary nodule is benign or malignant.

Description

IMAGE-BASED PREDICTIVE MODEL FOR LUNG CANCER

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application claims the benefit of, and priority to, the U.S. Provisional

Application No. 62/874,470 filed on July 15, 2019, and entitled“IMAGE-BASED

PREDICTIVE MODEL FOR LUNG CANCER” which is incorporated herein by reference in its entirety.

FIELD OF THE DISCLOSURE

[0002] The present application relates generally to systems and methods for an image-based predictive model for lung cancer. Specifically, the present application relates to systems and methods for lung cancer screening based on nodule spiculation quantification.

BACKGROUND OF THE DISCLOSURE

[0003] Lung cancer is the most common cause of cancer related death in the United States and worldwide. Similar to other types of cancer, diagnosis of lung cancer at an early stage increases the chance of cure for patients. Screening using low-dose computed tomography (CT) scans allows for early diagnosis of lung cancer. In fact, lung cancer screening with a low-dose CT for current and former smokers was shown to lead to clear increase in survival rate.

[0004] When performing lung cancer screening using low-dose computed tomography (CT) scans, radiologists or physicians usually look for lung nodules, which are potential indicators of lung cancer. Pulmonary nodules are typically small (e.g., smaller than three centimeters in diameter) abnormal growth areas in the lung having a round or oval shape. However, not all pulmonary nodules are cancerous. In fact, most pulmonary nodules discovered in chest CT scans are benign. For instance, old infections, scar tissue, among other causes, can be the source of benign pulmonary nodules. Distinguishing between benign and malignant pulmonary nodules allows for early diagnosis of lung cancer, and helps save the lives of many lung cancer patients.

SUMMARY

[0005] According to at least one aspect, a method can include one or more processors transforming a first triangular mesh representing a surface of a volumetric image region corresponding to a pulmonary nodule into a second triangular mesh representing a spherical surface while preserving angles of the first triangular mesh. The method can include the one or more processors computing, for a plurality of points of the surface of the volumetric image region a respective plurality of values of an area distortion metric. The plurality of values can include, for each point of the plurality of points, a corresponding area distortion value representing distortion in area at the point due to transforming the first triangular mesh into the second triangular mesh. The method can include the one or more processors identifying, using the respective plurality of area distortion values, one or more spikes associated with the surface of the volumetric image region. The method can include the one or more processors computing a cumulative sharpness score and a cumulative irregularity score of the one or more spikes. The method can include the one or more processors determining whether the pulmonary nodule is benign or malignant using a plurality of radiomic features of the pulmonary nodule including the cumulative sharpness score and the cumulative irregularity score.

[0006] According to at least one other aspect, a system can include one or more processors and a memory storing computer instructions. The computer instructions when executed by the one or more processors cause the one or more processors to transform a first triangular mesh representing a surface of a volumetric image region corresponding to a pulmonary nodule into a second triangular mesh representing a spherical surface while preserving angles of the first triangular mesh. The one or more processors can compute for a plurality of points of the surface of the volumetric image region a respective plurality of values of an area distortion metric. The plurality of values can include, for each point of the plurality of points, a corresponding area distortion value representing distortion in area at the point due to transforming the first triangular mesh into the second triangular mesh. The one or more processors can identify, using the respective plurality of area distortion values, one or more spikes associated with the surface of the volumetric image region. The one or more processors can compute a cumulative sharpness score and a cumulative irregularity score of the one or more spikes. The one or more processors can determine whether the pulmonary nodule is benign or malignant using a plurality of radiomic features of the pulmonary nodule including the cumulative sharpness score and the cumulative irregularity score.

[0007] According to at least one other aspect, a non-transitory computer-readable medium can store computer instructions. The computer instructions when executed by one or more processors can cause the one or more processors to transform a first triangular mesh representing a surface of a volumetric image region corresponding to a pulmonary nodule into a second triangular mesh representing a spherical surface while preserving angles of the first triangular mesh. The one or more processors can compute for a plurality of points of the surface of the volumetric image region a respective plurality of values of an area distortion metric. The plurality of values can include, for each point of the plurality of points, a corresponding area distortion value representing distortion in area at the point due to transforming the first triangular mesh into the second triangular mesh. The one or more processors can identify, using the respective plurality of area distortion values, one or more spikes associated with the surface of the volumetric image region. The one or more processors can compute a cumulative sharpness score and a cumulative irregularity score of the one or more spikes. The one or more processors can determine whether the pulmonary nodule is benign or malignant using a plurality of radiomic features of the pulmonary nodule including the cumulative sharpness score and the cumulative irregularity score.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The foregoing and other objects, aspects, features, and advantages of the disclosure will become more apparent and better understood by referring to the following description taken in conjunction with the accompanying drawings, in which:

[0009] FIG. l is a flow chart illustrating a method of distinguishing between benign and malignant anatomical regions, according to an example embodiment;

[0010] FIG. 2 shows an example triangular mesh approximating a 3-D surface corresponding to a pulmonary nodule;

[0011] FIG. 3 shows a flow diagram illustrating various processes for performing conformal (or angle-preserving) mapping of a Riemann surface into a spherical surface, according to an example embodiment;

[0012] FIGS. 4A and 4B show color maps for the first non-trivial eigenfunction of the Laplace-Beltrami operator for the mesh in FIG. 2;

[0013] FIGS. 5A-5D show simulation results illustrating the iterative transformation of the surface of FIG. 2 into a spherical surface; [0014] FIG. 6 shows a color map of the area distortion metric overlaid on the triangular mesh 200 of FIG. 2 representing a surface corresponding to a pulmonary nodule;

[0015] FIGS. 7A and 7B show segmentation results for different pulmonary nodules;

[0016] FIG. 8 shows an example flow diagram for building and validating the malignancy prediction model, according to an example embodiment.

[0017] FIG. 9A is a block diagram depicting an embodiment of a network environment comprising client devices in communication with server devices;

[0018] FIG. 9B is a block diagram depicting a cloud computing environment comprising client devices in communication with a cloud service provider; and

[0019] FIGS. 9C and 9D are block diagrams depicting embodiments of computing devices useful in connection with the methods and systems described herein.

DETAILED DESCRIPTION

[0020] Following below are more detailed descriptions of various concepts related to, and embodiments of, inventive systems and methods for an image-based predictive model for lung cancer. It should be appreciated that various concepts introduced above and discussed in greater detail below may be implemented in any of numerous ways, as the disclosed concepts are not limited to any particular manner of implementation. Examples of specific

implementations and applications are provided primarily for illustrative purposes.

[0021] A relatively large number of radiomic features, e.g., about or greater than a hundred, can be extracted from CT images (or other medical images) of anatomical regions, for example, for diagnosis or treatment purposes. Such features can include intensity features, texture features, shape features, and statistical features among others. A key challenge in radiomics is identifying the best radiomic features to use for a specific purpose. For instance, in the case of lung cancer screening, a technical challenge is to determine the best radiomic features to distinguish between benign and malignant pulmonary nodules, and therefore, help diagnosing lung cancer at an early stage. Specifically, using the“proper” image features or characteristics of pulmonary nodules allows for reliable prediction or identification of malignant pulmonary nodules, and therefore, reliable lung cancer screening.

[0022] CT scans of lungs can show spiculations on the surface of pulmonary nodules. Spiculations are thin sharp spikes around the core of a pulmonary nodule. The spiculations or spikes and respective characteristics are relevant biological features and important predictors of lung cancer malignancy. Lung-RADS^®, which is a tool designed to standardize lung cancer CT-based screening and reduce confusion in lung cancer CT scans employ a qualitative score for spiculations or spikes associated with pulmonary nodules. Such score is a binary score subjectively produced by radiologists. Using a binary score, e.g., compared to fmer-scale scores, does not reflect the various biological and geometrical characteristics of spiculations associated with pulmonary nodules and their relevancy in terms of predicting malignancy of pulmonary nodules. Also, quantifying spiculations or spikes in an objective and automatic way, instead of a subjective way, leads to more reliable radiomic features for identification of malignant growth regions.

[0023] In the current disclosure, systems, devices and methods use a reproducible and interpretable parameter-free technique to quantify spiculations associated with abnormal growth regions, such as pulmonary nodules, and use obtained spiculation quantification features to distinguish between benign and malignant growth regions or areas. Specifically, the systems, devices and methods employ a comprehensive pipeline to quantify spiculations, lobulations, and vessel/wall attachments, and evaluate their importance in malignancy prediction. The systems, devices and methods described herein determine the spiculation quantification features using an area distortion metric that is obtained from a conformal (angle-preserving) spherical parameterization.

[0024] When mapping a given compact surface (e.g., a surface representing a pulmonary nodule or other abnormal growth region) to a sphere, there is a trade-off between angle distortion and area distortion. For instance, restricting or lowering angle distortion during the mapping increases the corresponding area distortion. Considering an angle-preserving (or conformal) spherical mapping or transformation of a given pulmonary nodule, the corresponding negative area distortion due to the mapping or transformation precisely characterizes the spiculations on that pulmonary nodule. The systems, devices and methods described herein exploit this fact by using an area distortion metric defined based on the conformal (angle-preserving) spherical parameterization to accurately quantify spiculations on a given pulmonary nodule (or other abnormal growth region). Specifically, negative peaks of the area distortion metric can be indicative of spiculations or spikes of the pulmonary nodule. [0025] The systems, devices and methods described herein can identify spiculations or spikes associated with an abnormal growth region, such as a pulmonary nodule, using the area distortion metric, and determine quantitative features of the identified spiculations. The systems, devices and methods described herein can use one or more spiculations scores defined based on the quantitative features, and use the spiculation scores to determine whether the pulmonary nodule (or other growth region) is malignant or benign.

[0026] Referring to FIG. 1, a flow chart illustrating a method 100 of distinguishing between benign and malignant anatomical regions is shown, according to an example embodiment.

The method 100 can include applying a conformal mapping to transform a surface of a volumetric image region corresponding to an abnormal growth region into a spherical surface (STEP 102), and computing values of an area distortion metric at a plurality of points of the surface of the volumetric image region (STEP 104). The method 100 can include identifying one or more spiculations or spikes associated with the surface of the volumetric image region using the values of the area distortion metric (STEP 106). The method 100 can include computing a cumulative sharpness score and a cumulative irregularity score of the one or more spiculations or spikes (STEP 108), and determining whether the abnormal anatomical growth is benign or malignant using the cumulative sharpness score and the cumulative irregularity score (STEP 110).

[0027] The method 100 can be performed or executed by a computing device or a computing system including one or more computing devices. In some implementations, the method 100 can be performed by one or more hardware processors, one or more electronic circuits, or a combination thereof associated with a computer device or system. For instance, the method 100 can be performed by an X-ray scanner, other medical imaging device, a laptop, a desktop, a handheld device, a computer server or a combination thereof. The method 100 can be implemented as hardware, firmware, software or a combination thereof.

[0028] The method 100 can include one or more processors applying a conformal mapping to transform a surface of a volumetric image region corresponding to an abnormal growth region into a spherical surface (STEP 102). The one or more processors can obtain or generate a volumetric image region or a corresponding surface representing an abnormal anatomical growth region, such as a pulmonary nodule. For example, the one or more processors can segment one or more CT images (or other medical images) to reconstruct the volumetric image region. The CT images can represent chest or lung scans, and the one or more processors can perform the segmentation to identify or construct the image region or corresponding surface representing a pulmonary nodule. The CT images can include three- dimensional (3-D) CT images or a collection of two-dimensional CT images. The one or more processors can perform 2-D image segmentation, 3-D image segmentation or a combination of both to reconstruct the volumetric image region or the corresponding 3-D surface representing the pulmonary nodule. In some implementations, the one or more processors can obtain the volumetric region or the corresponding 3-D surface from a memory, another computing device, or another system.

[0029] The one or more processors can generate a mesh, such a triangular mesh, to model the 3-D surface representing the pulmonary nodule. The mesh represents a triangulated polyhedral surface that approximates the 3-D surface representing the pulmonary nodule. Conformal mapping of the 3-D surface into a spherical surface can include the one or more processors mapping or transforming the mesh into a second mesh, e.g., a second triangular mesh, representing a spherical surface while preserving angles of the mesh. In other words, the conformal mapping can be viewed as a distortion of the areas or sizes of the triangles forming the mesh while preserving the angles of each triangle of the mesh.

[0030] As a theoretical overview, let be a genus zero Riemannian surface and let S² be the unit sphere. Gauss’s Theorema Egregium states that there exists no diffeomorphism from S to S², with non-constant Gaussian curvature, which preserves both the areas and angles of the triangles of the mesh. Furthermore, by a general result in complex analysis (uniformization), S and S² are conformally equivalent. That is, there exists a diffeomorphism <p: S— > S² that preserves the angles of the mesh. The mapping f is unique up to Mobius transformation on S², which can be viewed as an angle preserving spherical parameterization of the compact genus zero surface. As discussed in further detail below, the one or more processors can measure the area distortion due to the mapping ø, and use the measured area distortion to localize or identify spiculations or spikes of the 3-D surface representing the pulmonary nodule.

[0031] Let go be the Riemannian metric on the 3-D surface S with corresponding Gaussian curvature Ko. Let K„ be the curvature on the conformally equivalent surface S² with metric 9_u = ^e2udo- The parameter u is the conformal distortion factor, and the function e²" represents the area distortion between the surface S and the sphere S². The distortion in any spherical parameterization satisfies: Dΐί + K_ue^2u = K₀. (1)

For a unit sphere, such as the surface S², K„ = 1, and thus the conformal distortion factor u satisfies the Poisson equation:

Au = K₀ - e^2u. (2)

By examining the Poisson equation (2), one can see that the more the Gaussian curvature Ko(x) varies, the greater is the variation in the conformal distortion factor u. Also, from the maximum principle, spiculations or spikes may be identified by the greatest negative variation in area distortion.

[0032] Let = (V , E, F) be a triangular mesh representing a triangulated polyhedral surface approximating the genus zero Riemannian surface S , where V denotes the vertices, E denotes the edges, and F denotes the faces of the triangles forming the mesh M. FIG. 2 shows an example triangular mesh 200 approximating a 3-D surface corresponding to a pulmonary nodule.

[0033] A discrete Riemannian metric (or function) can be defined as the edge length function l E — > M⁺, which satisfies the triangle inequality on each face. That is, on each face or triangle of the mesh M, the three comer angles are determined by the Euclidean cosine law using the edge lengths. Also, the discrete Gaussian curvature is defined as angle deficit. That is, the Gaussian curvature for an interior vertex of a mesh representing a volumetric region is 2p minus the surrounding corner angles, and for a boundary vertex, its geodesic curvature is p minus the surrounding comer angles. Specifically, given a vertex v_; of the triangular mesh M with a discrete Riemannian metric, the curvature for the vertex v_; is defined as:

where dM is the boundary of the triangulated polyhedral surface M, and q( i fc represents the angle that the vertex v_; forms with the vertices v ,· and vk.

[0034] It can be shown that the total curvature equals 2p multiplied by the Euler characteristic number c(L /) of the mesh M,

The Euler characteristic number of A / i s defined as c(M^') = V— E + F . Also, given the triangle mesh , with the discrete Riemannian metric / and conformal factor iv. V— > M, for an edge e e E having end vertices v_; and v ,· and an original length 4, the deformation in length is defined as:

The discrete Ricci flow (or discrete Yamabe flow) for the mesh M having an initial discrete metric and a target curvature K is given by:

[0035] The corresponding convex discrete Ricci energy is defined as:

where u = , !½)· One computational algorithm is to optimize the convex Ricci energy using Newton’s method. The gradient of the energy is equal to the curvature difference n£·(ΐί) = (K— K), and the Hessian matrix of the energy is defined as:

The algorithm for solving the discrete Yamabe flow is given as Algorithm 1 below in pseudo code form.

Algorithm 1. Discrete Yamabe Flow

(1) The user determines the target curvature such that for each

vertex v_; e V, K(V_j) < 2p the total curvature satisfies the Gauss-Bonnet condition,

(2) Initialize the conformal factor as zeros ut = 0, for all vertices.

(3) Compute the current edge length using equation l_tj =

compute the corner angles using Euclidean cosine law and compute the vertex curvatures using equation (3).

(4) Compute the gradient of the entropy energy as

(5) Compute the Hessian matrix of the entropy energy using equation (7).

(6) Solve linear system VE = Hx.

(7) Update the conformal factor

dc, where d is a step length.

(8) Repeat step 4 through 8 until where s is a threshold.

[0036] To perform the conformal (angle preserving) mapping, the one or more processors can divide the surface S, or the corresponding mesh , into two segments Si and & with boundary curve given by g. The one or more processors can determine the Si, & and g via the zeroth level set of the eigenfunction corresponding to the smallest positive eigenvalue of the (discrete) Laplacian (the so-called Fiedler vector). The one or more processors can employ a discretization of the 2D Ricci flow (Yamabe flow), e.g., using Algorithm 1, to conformally flatten or map the segments Si and & onto the planar (unit) discs Di and D2.

[0037] The one or more processors can conformally weld together the planar discs Di and D2 into a plane. The one or more processors can stereographically project the plane representing the conformally welded planar discs Di and D2 onto the sphere S² to get a conformal mapping to the Riemann sphere S². Details of the conformal welding and the stereographical projection can be found in“Spherical parameterization balancing angle and area distortions,” IEEE Transactions on Visualization and Computer Graphics 23 (6) (2017) 1663-1676.

[0038] FIG. 3 shows a flow diagram illustrating the various processes for performing conformal (or angle-preserving) mapping of surface S into spherical surface S², according to an example embodiment. As discussed above, these processes include dividing the surface S into two segments and mapping each of the segments to a corresponding planar disc using discrete Ricci flow, as indicated by process (a) of FIG. 3. The process (b) of FIG. 3 illustrates the conformal welding of the planar discs into an extended plane. Finally, process (c) of FIG. 3 illustrates the stereographical projection of the extended plane onto a spherical surface, such as spherical surface S².

[0039] FIGS. 4A and 4B show color maps for the first non-trivial eigenfunction of the Laplace- Beltrami operator for mesh 200 of FIG. 2. is computed. The curve 302 represents the zeroth- level set of the eigenfunction. The one or more processors can compute the first non-trivial eigenfunction of the Laplace-Beltrami operator, and determine the zeroth-level set 302 of the eigenfunction. The one or more processors can divide the mesh into two topological segments along the zeroth-level set 302 of the eigenfunction. The one or more processors can conformally weld the two segments into an extended plane and stereographically project the extended plane to the spherical surface shown in FIG. 3B by applying angle-preserving spherical parameterization. The curve 304 represents the zeroth-level set of the eigenfunction on the spherical surface. [0040] FIGS. 5A-5D show simulation results illustrating the iterative transformation of the surface S of FIG. 2 into the spherical surface S². FIG. 5A shows the initial surface S, or corresponding mesh M, as depicted in FIG. 2. FIGS, 5B and 5C show intermediate transformation of the surface S at intermediate iterations of the iterative algorithm implementing the conformal mapping F . Finally, FIG. 5D shows the final conformal mapping of the surface S, which is a spherical surface. The conformal mapping or transformation can be viewed as a transformation of the mesh A/into another mesh representing the spherical surface S² where the angles of the mesh Mare preserved and the areas of the triangles can be distorted.

[0041] Referring back to FIG. 1, the method 100 can include the one or more processors computing values of an area distortion metric at a plurality of points of the surface of the volumetric image region (STEP 104). The area distortion metric can be a normalized area distortion metric defined as;

where [v_;, vy, vk\ is the triangle formed by the vertices v_i, v _/, vk and A() represents the area of a triangle. The one or more processors can evaluate (or compute a corresponding value of) the area distortion metric at each vertex v_; of the meshM The triangle area

represents the mapping of the triangle [v_;, v _/, vk\ on the spherical surface S² (or a corresponding mesh M2 approximating S²), and area term represents the area of the

triangle

[0042] The method 100 can include identifying one or more spiculations or spikes associated with the surface of the volumetric image region using the values of the area distortion metric (STEP 106). As discussed above, spiculations correspond to negative peaks of the area distortion metric (or function) e(. ). Hence, in identifying the spiculations or spikes on the surface S, the one or more processors can identify or determine the negative peaks (or negative minima) of the area distortion metric (or function) e(. ). Algorithm 2 below is an example pseudocode for negative peak detection of the area distortion metric (or function) e(. )·

2: Tn _* T

3: for each node t E T do

4: Initialize (St, a) subset of S and e when e < min(e(t, b))

5: B <— FindBoundariesfS'_/, a) Next level boundaries

6: if B is empty then

7: Tn <— ί T U node(nil, t)} Terminal node (apex)

8: else

9: T_t ^<— i Ί) U node(b, t)} for each b cB

10: Tn ^< (G u RecursePeakContoursfV, et, T)}

return G«

11 : function PeakDetectionfV, c)

12: Initialize (S_b, eb) subset of S and e when e £ 0

13: B <— FindBoundaries(Sb, eb) Baseline detection

14: T_{t <—} {Tt U node(b, nil)} for each b c B Generate root nodes

15: T <— RecursePeakContours(S_b, eb, T)

Ensure: a peak p is a stack consisting of nodes from each individual terminal node (apex) to a root node (baseline) of the tree T.

[0043] In Algorithm 2, T represents a tree formed by recursively adding closed curves of the continuous-valued area distortion metric or function e(. ) starting from baselines B having a zero area distortion. The one or more processors can find all the baselines B where area distortion is zero (Line 13 in Algorithm 2). The one or more processors can recursively search closed curves from the baseline (zero area distortion) to the apex (the smallest area distortion) using the level-set method. During the search, the closed curves can break into multiple closed curves and move towards different apexes. Each pair of the apex (a terminal node) and its corresponding closed curves define a peak, and the one or more processors assign unique IDs to the pairs of apex and corresponding curves to track their progression and for height and width computations in the next step. (Line 1-10 in Algorithm 2). The one or more processors can compute the sum of the distances between the successive centroids of the closed curves to obtain the peak height. The one or more processors can compute the peak width on the area distortion map of the peak using a full width half maximum concept. To exclude lobulation (curved peak) from spiculation (sharp peak), the one or more processors can apply thresholding for the height (e.g., Th ³ 3mm) and solid angle (To £ 0.65sr). The one or more processors can apply a full width half maximum concept for more robust width measures of a peak, using the peak surface and its area distortion. The one or more processors can measure the peak width on an iso-contour at half minimum area distortions (all negative values).

[0044] FIG. 6 shows a color map of the area distortion metric e(. ) overlaid on the triangular mesh 200 of FIG. 2 representing a surface corresponding to a pulmonary nodule. Darker colors represent more negative values of the area distortion metric or function e(. ). The results shown in FIG. 6 illustrate that the negative peaks of the area distortion metric e(. ), shown with“X”, perfectly match or overlap on spikes of the mesh 200.

[0045] The method 100 can include computing a cumulative sharpness score and a cumulative irregularity score of the one or more spiculations or spikes (STEP 108). The one or more processors can determine various features of the pulmonary nodule, such as the number of all peaks N_P, the number of spiculations Ns, the number of lobulations Ni, the number of attachments Na, and the surface area ratio of attached regions ra =

A(S_a) / A(S_nodule) . The one or more processors can compute (or determine) cumulative sharpness score as:

where p(i) is spike i, h_P(i) is height of spike p(i). The term {mean(e_p(i))) represents the mean of the area distortion at a detected spike p(i). The one or more processors can compute (or determine) the cumulative irregularity score S2 as:

The term (var(e_p(i))) represents the variation of the area distortion at spike p(i).

[0046] In determining (or computing) features of the surface S, or the corresponding pulmonary nodule, the one or more processors can employ a semi-automatic segmentation approach to precisely segment or quantify the identified spiculations and accurately extract radiomic features. The semi-automatic segmentation approach described herein leads to more accurate spiculation quantification because it excludes the attachments from spikes on the pulmonary nodule surface. The semi-automatic segmentation approach can be viewed as a combination of two segmentations methods; the GrowCut segmentation method (or algorithm) described in“Toward understanding the size dependence of shape features for predicting spiculation in lung nodules for computer-aided diagnosis,” Journal of Digital Imaging 28, 704-717, 2015, and the chest imaging platform (CIP) segmentation method (or algorithm) described in“Cancer statistics,” CA: A Cancer Journal for Clinicians 66, 7-30, 2016.

[0047] The GrowCut segmentation method is a cellular automata-based region growing approach that starts from two input sets of seed points for foreground and background.

According to the GrowCut segmentation approach, the one or more processors can grow or expand various starting from the two input sets of seed points until convergence is achieved. When applying the GrowCut approach to segment spikes, a common drawback is that the segmented foreground region can leak into surrounding structures, such as the chest wall, airway walls, and vessel-like structures. The segmentation inaccuracy can result in errors in the spiculation quantification or the generated radiomic features. The CIP segmentation method is a level-set based approach that uses a front propagation approach from a seed point placed within the image region corresponding to pulmonary nodule. The propagation (or segmentation) is constrained by feature maps of the structures to prevent leakage into surrounding structures. However, the CIP segmentation approach might ignore or miss some regions or portions of the spiculation or spike, for example, due to inaccurate vessel and wall feature maps.

[0048] The one or more processors can employ a combination of the GrowCut segmentation approach and the CIP segmentation approach to accurately reconstruct and quantify the spiculations or spikes. In some implementations, the one or more processors can combine the GrowCut and CIP segmentation methods in the sense of morphological intersection of output segmentation masks from the two segmentation techniques. On one hand, the CIP

segmentation technique gives a more constrained output segmentation mask since it takes into account neighborhood vesselness (blood vessels impinging on the tumor) heuristics. On the other hand, the GrowCut segmentation technique is more freeform. Hence, the combination of the two techniques can give a better consensus and help in identifying vessel/mediastinum/chest wall attachment regions, which is potentially another interesting predictive biomarker. The combined segmentation compensates for the limitations of the GrowCut segmentation approach and the CIP segmentation approach and allows for attachment detection. In some implementations, the one or more processors can execute the GrowCut segmentation algorithm and the CIP segmentation algorithm separately, e.g., sequentially or simultaneously in a multithreaded framework, and determine the morphological intersection of the output segmentations provided by both algorithms. The one or more processors can provide, for each of the identified spiculations or spikes, the morphological intersection of the corresponding output segmentations provided by both algorithms as the final segmentation the spiculation or spike.

[0049] FIGS. 7 A and 7B show segmentation results for different pulmonary nodules. FIG.

7A shows two-dimensional segmentation results using the GrowCut segmentation approach, the CIP segmentation approach, and the combined segmentation approach discussed above. The dashed gray lines illustrate the GrowCut segmentations, and the continuous black lines illustrate the corresponding CIP segmentations. The white lines illustrate the final segmentations provided by the combined segmentation approach discussed above. The regions 402 represent the attachment detection on axial slice. FIG. 7B shows the final segmentations and attached surfaces for the various pulmonary nodules of FIG. 7 A. The final segmentations and attached surfaces of the identified spiculations or spikes are shown in dark gray in FIG. 7B.

[0050] Finally, the method 100 can include the one or more processors determining whether the abnormal anatomical growth is benign or malignant using the cumulative sharpness score and the cumulative irregularity score (STEP 110). The one or more processors can employ a prediction model to predict the malignancy of pulmonary nodules using features quantifying spiculations of the pulmonary nodules, such as at least the cumulative sharpness score, the cumulative irregularity score, the number of all peaks N_P, the number of spiculations Ns, the number of lobulations N_I , the number of attachments Na, the surface area ratio of attached regions ra, other speculation quantifying features or a combination thereof. The prediction model can also use other features of the pulmonary nodule. The prediction model can use any combination of the features listed in Table 2 below. For instance, the prediction model or the one or more processors can use statistical parameters (or features) of the area distortion metric e(. ), such as the minimum, maximum, mean, median or variance of e(. ) or a combination thereof. The prediction model or the one or more processors can use the minimum, maximum, mean, median or variance of hp_(i) and/or ra, or any combination thereof.

[0051] The prediction model can include a support vector machine (SVM) classifier model. The prediction model can include a SVM classifier coupled with a least absolute shrinkage and selection operator (LASSO), such as the SVM-LASSO model described in“Radiomics analysis of pulmonary nodules in low-dose CT for early detection of lung cancer,” Medical Physics-doi: 10.1002/mp.12820. The prediction model can include other types of feature classifiers. In some implementations, the one or more processors can construct the predictive model.

[0052] To evaluate the spiculation quantification measures and radiomic features for classifying pathological malignant nodules and benign nodules, the spiculation quantification features were added to the SVM-LASSO model. A total of 103 radiomic features were extracted from each pulmonary nodule to quantify its intensity, shape, and texture. Intensity features are first order statistical measures that quantify the level and distribution of CT attenuations in a nodule (e.g., Minimum, Mean, Median, Maximum, Standard deviation (SD), Skewness, and Kurtosis). Shape features describe geometric characteristics (e.g., volume, diameter, elongation, roundness, and flatness) for voxels. Texture features quantify tissue density patterns. We used Graylevel co-occurrence matrix (GLCM): Energy, Entropy, Correlation, Inertia, Cluster prominence (CP), Cluster shade (CS), Haralicks correlation (HC), Inverse difference moment (IDM); and Graylevel runlength matrix (GLRM):

Runlength non-uniformity (RNU), Gray-level non-uniformity (GNU), Long-run emphasis (LRE), Short-run emphasis (SRE), High gray-level run emphasis (HGRE), Low graylevel run emphasis (LGRE), Long-run high gray-level emphasis (LRHGE), Long-run low gray-level emphasis (LRLGE), Short-run high gray-level emphasis (SRHGE), Short-run low gray-level emphasis (SRLGE). The mean (average) and SD values of each texture feature were computed over 13 directions to obtain rotationally invariant features.

[0053] Moreover, other features were extracted from the triangular mesh model, such as shape features (size, volume, average of longest and its perpendicular diameters, equivalent volume sphere’s diameter, and roundness) and statistical features (median, mean, minimum, maximum, variance, skewness, and kurtosis) of the area distortion metric e. Univariate analysis was performed to evaluate the significance of each feature to classify spiculation using the area under the receiver operating characteristic curve (AUC), Wilcoxon rank-sum test, and Spearman’s correlation coefficient p. Bonferroni correction was applied to the original p-values to counteract the problem of multiple comparisons since the multiple features were tested for a single outcome.

[0054] The SVM-LASSO model was then applied to predict the malignancy of nodules. The model uses size (BB AP) and texture (SD IDM) features. The performance of the original SVM-LASSO model was compared the performance of SVM-LASSO models using other feature combinations of the scores si and S2, other spiculation features, or radiologist’s spiculation score (RS), respectively. The same data set and evaluation method was used to evaluate the new radiomics model with spiculation quantification features.

[0055] Also, a model building process using weak-labeled data (radiological malignancy score, RM) to predict pathological malignancy (PM) was evaluated. The model building process allows more data to be used despite missing pathological malignancy. FIG. 8 shows an example flow diagram illustrating a process for building and validating the malignancy prediction model. In some implementations, the method 100 can include the one or more processors constructing and building the prediction model according to the flow diagram in FIG. 8. The model building process includes applying semi-auto segmentation to nodules in both LIDC and LUNGx datasets, and extracting features using the segmentations of the spiculations. The extracted features from LIDC dataset are used for model building. The model was evaluated on pathological malignancy subset and the LUNGx test set after model calibration using the LUNGx calibration set (Model’).

[0056] In some implementations, the output of the method 100 can be used for lung cancer screening, for treatment purposes (e.g., to identify which nodules or areas to be radiated in a radio therapy procedure) or a combination of both.

[0057] Experimental Results

[0058] The Lung Image Database Consortium image collection (LIDC-IDRI) and LUNGx datasets were applied to evaluate the proposed method 100, and the data flow is shown in FIG. 8. LIDC contains 1018 cases with low-dose screening thoracic CT scans and markedup annotated lesions. Four experienced thoracic radiologists annotated nodules, including delineation, malignancy (RM), spiculation (RS), margin, texture, and lobulation. Eight hundred eighty -three cases in the dataset have nodules with contours. For the biggest nodules in each case, we applied semi-auto segmentation for more reproducible spiculation quantification and also calculated consensus segmentation using STAPLE to combine multiple contours by the radiologists. The accuracy of our semi auto-segmentation compared to the consensus contour was 0.71 0.13 in terms of the dice coefficient. LUNGx consists of 10 cases for calibration set (10 nodules) and 60 cases for the test set (73 nodules). We applied the same semi-auto segmentation to nodules in the LUNGx dataset. [0059] For more rigorous data analysis, we divided the LIDC dataset into two subsets depending on whether pathological malignancy (LIDC PM, N=72) or radiological malignancy (LIDC RM, N=811) was available. The radiological malignancy scores are 1 - highly unlikely, 2 - moderately unlikely, 3 - indeterminate likelihood, 4 - moderately suspicious, and 5 - highly suspicious for cancer. The case where RM ³ 3 (moderately suspicious to highly suspicious) was considered radiological malignancy. RS in the dataset ranged between 1 (non-spiculated) and 5 (highly spiculated). The RS can be binarized (or discretized) using three different cutoffs (1,2, and 3) because the current clinical standard uses binary classification, non-spiculated (NS) and spiculated (S), as shown in Table 1 below (the cutoff at four is shown for reference).

Table 1.

[0060] To optimize spiculation height and solid angle thresholds, Th and To, for filtering out false positives such as small peaks and lobulations, the Phantom FDA layout #4 was used. The thresholds were tuned to clearly differentiate the spiculations from lobulations

(annotations available in Phantom FDA) and to detect as many spiculations as possible without false positives. The final selected thresholds were Th ³ 3mm and To £ 0.65sr. The results showed that the optimal thresholds excluded lobulations and elliptical shape corners from final spiculations.

[0061] Since we evaluated the malignancy prediction model on LIDC PM, we performed univariate analysis on LIDC RM to avoid the selection bias in malignancy prediction model building. In the univariate analysis, 84 features were identified as significant features (adjusted p-value £0.05) for spiculation quantification. Among these, 56 features were highly correlated with size features (p ³ 0:75); size is one of the main criteria for diagnosing malignancy. Thus, we removed all the size-related features, including Dhara’s spiculation s_a and Np, to provide complementary information. After applying the size-related feature removal, 28 significant features remained, and we picked 20 highly correlated features with RS. Half of these were texture or intensity statistics features, which are not interpretable. Almost all of our spiculation measures were significant and ranked in the top 20. Table 2 below shows the univariate analysis results of the top 20 features using semi-auto

segmentation. None of Dhara’s spiculation scores (s_a and sb) were selected in the top 20 features even though they were significant features. Dhara’s spiculation score s_a was excluded by its high correlation with size (p = 0:87), and Dhara’s spiculation score sb was not ranked among the top 20.

[0062] We built models using feature combinations of the features (Size: BB AP and

Texture: SD IDM) selected (or used) in“Radiomics analysis of pulmonary nodules in low- dose CT for early detection of lung cancer,” Medical Physics-doi: 10.1002/mp.12820, and the spiculation features Ns, N_a, N₁, N_p;, ra, si and S2. As shown in FIG. 8, the model trained by LIDC was then externally validated by LUNGx dataset, which was collected for a lung cancer screening competition (LUNGx Challenge) and provides a calibration set (size- matched ten nodules, five benign and five malignant) and a test set (73 nodules, 37 benign and 36 malignant). For the external validation, the model evaluation process of the LUNGx Challenge was followed. The model was calibrated by the calibration set of LUNGx (Model’) and finally evaluated by the test set (73 cases) of LUNGx. We used zero value instead of missing variable RS in the external validation because LUNGx does not provide it. Since pathological malignancy (PM) was only available for the 72 cases, we used weak-labeled data (LIDC RM, N=811) based on the radiological malignancy score (RM). We divided the weak-labeled data into two groups (training 80% and validation 20%) for training and optimizing the model. Then, the best model was evaluated on strong -labeled data (LIDC PM, N=72). We repeated the analysis 100 times to measure the statistical variance of the models.

[0063] Table 3 shows the classification results of each model, and their external validation. The model using Size and our spiculation features (Size+Spiculations) showed comparable performance (accuracy =75.2% and AUC=0.80) to the previous model (Size+Texture, accuracy =73.7% and AUC=0.82) in the validation on LIDC PM, but the performance of Size+Spiculations was much higher (accuracy =71.8% and AUC=0.76) than Size+Texture (accuracy =57.8% and AUC=0.61) in the external validation.

[0064] Table 4 below shows the comparisons with the top 3 participants and 6 radiologists in LUNGx Challenge. The model trained using the weak-labeled data showed an AUC of 0.76, which was better than the best model and two radiologists in the LUNGx challenge. The model trained by the strong-labeled data showed an AUC=0.69. The radiomics model (Size+Texture) showed comparable performance (strong-labeled: AUC=0.67 and weak- labeled: AUC=0.68) with the best model in the LUNGx Challenge (AUC=0.68). Weak- labeled data training generated more robust and flexible models due to the larger volume of data available (about ten times larger than the strong-labeled data) even though the outcomes were not pathologically proven, they were correlated with the real outcome.

[0065] The number of spiculations feature (N_s) achieved higher correlation with RS than other features, as shown in Table 2. Many texture features were selected in the top 20, but since it is hard to interpret the correlation between these texture features and spiculations, these can be excluded to avoid the un-interpretability of the final models. Moreover, just using the spiculation features proposed herein, one can avoid the mandatory image/feature harmonization in the preprocessing step for any new given dataset (repository). Roundness features showed good correlations with spiculation as well as good accuracy in the malignancy prediction because they quantify the irregularity of the target shape. However, these cannot filter out lobulation or attachments from spiculations.

Table 4. Comparison with the top 3 participants and 6 radiologists in LUNGx Challenge

[0066] The radiomics models using semi-auto segmentation showed relatively lower performance than manual segmentation. The models using size (BB AP) and texture (SD IDM) showed a big difference between manual segmentation (79.2% accuracy) and semi auto segmentation (73.7% accuracy). However, it is difficult to normalize the texture feature. Thus, the models using SD IDM were less stable, and the performance was significantly degraded in the weak-labeled data training and external validation.

[0067] Adding the radiologist’s spiculation score into previously used radiomics model using size and texture (Size+Texture, 74.9% accuracy) could improve the performance

(Size+Texture+RS, 77.4% accuracy). Similarly, combining Size and RS without Texture (Size+RS, 76.5% accuracy) showed better performance. A prediction model combining the spiculation features and Size without texture (Size+Spiculations, 75.2% accuracy) was slightly better than Size+Texture. In essence, the texture feature SD IDM could be replaced by the spiculation features discussed herein.

[0068] The weak-labeled data (LIDC RM) was employed to train the malignancy prediction model because of the lack of pathological malignancy data. These models showed

comparable performance to the model trained by strong-labeled data (LIDC PM). In the case of strong-labeled data training, it was difficult to avoid bias and over-fitting due to the lack of training data, while building accurate prediction models for malignant nodules. Hence, these models were more susceptible to failure because of the lack of adaptability to out-of-training unlabeled data. In contrast, weak-labeled data training can help build models that mimic conventional lung cancer screening by radiologists in the clinic using correlation with pathological malignancy. Moreover, a large amount of weak-labeled training data is usually accessible, thus allowing the creation of a more robust model and better performance than the strong-labeled data in external validation.

[0069] Embodiments described herein provide guidelines for a radiomics workflow to overcome the limitations of conventional radiomics studies using weak-labeled data and interpretable and reproducible features. Specifically, if the number of strong-labeled datasets is insufficient to build a good model, the abandoned weak-labeled data can be utilized in further analysis, as in the current study. Leveraging weak-labeled data in the clinic enables continuous tuning of radiomics models training using diagnosis (weak-labeled) followed by evaluation using the clinical outcomes (strong-labeled). Also, while the embodiments herein are described in relation with pulmonary nodules, it is to be noted that methods described herein can be applied to other types of abnormal or normal anatomical growth regions where respective spiculations or spikes are relevant in diagnosing or treating a disease (e.g., other types of cancer other than lung cancer).

[0070] Computing and Network Environment

[0071] It may be helpful to describe aspects of the operating environment as well as associated system components (e.g., hardware elements) in connection with the methods and systems described in above. The methods described herein, such as method 100, can be implemented or executed by any of the devices, or any combination thereof, described in relation to FIGS. 9A-9D. Referring to FIG. 9A, an embodiment of a network environment is depicted. In brief overview, the illustrated exploring network environment includes one or more clients 902a-902n (also generally referred to as local machine(s) 902, client(s) 902, client node(s) 902, client machine(s) 902, client computer(s) 902, client device(s) 902, endpoint(s) 902, or endpoint node(s) 902) in communication with one or more servers 906a- 906n (also generally referred to as server(s) 906, node 906, or remote machine(s) 906) via one or more networks 904. In some embodiments, a client 902 has the capacity to function as both a client node seeking access to resources provided by a server and as a server providing access to hosted resources for other clients 902a-902n.

[0072] Although FIG. 9A shows a network 904 between the clients 902 and the servers 906, the clients 902 and the servers 906 may be on the same network 904. In some embodiments, there are multiple networks 904 between the clients 902 and the servers 906. In one of these embodiments, a network 904’ (not shown) may be a private network and a network 904 may be a public network. In another of these embodiments, a network 904 may be a private network and a network 904’ a public network. In still another of these embodiments, networks 904 and 904’ may both be private networks.

[0073] The network 904 may be connected via wired or wireless links. Wired links may include Digital Subscriber Line (DSL), coaxial cable lines, or optical fiber lines. The wireless links may include BLUETOOTH, Wi-Fi, NFC, RFID Worldwide Interoperability for Microwave Access (WiMAX), an infrared channel or satellite band. The wireless links may also include any cellular network standards used to communicate among mobile devices, including standards that qualify as 1G, 2G, 3G, or 4G. The network standards may qualify as one or more generation of mobile telecommunication standards by fulfilling a specification or standards such as the specifications maintained by International Telecommunication Union. The 3G standards, for example, may correspond to the International Mobile Telecommunications-2000 (IMT-2000) specification, and the 4G standards may correspond to the International Mobile Telecommunications Advanced (IMT- Advanced) specification. Examples of cellular network standards include AMPS, GSM, GPRS, UMTS, LTE, LTE Advanced, Mobile WiMAX, and WiMAX-Advanced. Cellular network standards may use various channel access methods e.g. FDMA, TDMA, CDMA, or SDMA. In some

embodiments, different types of data may be transmitted via different links and standards. In other embodiments, the same types of data may be transmitted via different links and standards.

[0074] The network 904 may be any type and/or form of network. The geographical scope of the network 904 may vary widely and the network 904 can be a body area network (BAN), a personal area network (PAN), a local-area network (LAN), e.g. Intranet, a metropolitan area network (MAN), a wide area network (WAN), or the Internet. The topology of the network 904 may be of any form and may include, e.g., any of the following: point-to-point, bus, star, ring, mesh, or tree. The network 904 may be an overlay network, which is virtual and sits on top of one or more layers of other networks 904’. The network 904 may be of any such network topology as known to those ordinarily skilled in the art capable of supporting the operations described herein. The network 904 may utilize different techniques and layers or stacks of protocols, including, e.g., the Ethernet protocol, the internet protocol suite (TCP/IP), the ATM (Asynchronous Transfer Mode) technique, the SONET (Synchronous Optical Networking) protocol, or the SDH (Synchronous Digital Hierarchy) protocol. The TCP/IP internet protocol suite may include application layer, transport layer, internet layer (including, e.g., IPv6), or the link layer. The network 904 may be a type of a broadcast network, a telecommunications network, a data communication network, or a computer network.

[0075] In some embodiments, the system may include multiple, logically-grouped servers 906. In one of these embodiments, the logical group of servers may be referred to as a server farm 907 or a machine farm 907. In another of these embodiments, the servers 906 may be geographically dispersed. In other embodiments, a machine farm 907 may be administered as a single entity. In still other embodiments, the machine farm 907 includes a plurality of machine farms 38. The servers 906 within each machine farm 907 can be heterogeneous - one or more of the servers 906 or machines 906 can operate according to one type of operating system platform (e.g., WINDOWS NT, manufactured by Microsoft Corp. of Redmond, Washington), while one or more of the other servers 906 can operate on according to another type of operating system platform (e.g., Unix, Linux, or Mac OS X).

[0076] In one embodiment, servers 906 in the machine farm 907 may be stored in high- density rack systems, along with associated storage systems, and located in an enterprise data center. In this embodiment, consolidating the servers 906 in this way may improve system manageability, data security, the physical security of the system, and system performance by locating servers 906 and high performance storage systems on localized high performance networks. Centralizing the servers 906 and storage systems and coupling them with advanced system management tools allows more efficient use of server resources.

[0077] The servers 906 of each machine farm 907 do not need to be physically proximate to another server 906 in the same machine farm 907. Thus, the group of servers 906 logically grouped as a machine farm 907 may be interconnected using a wide-area network (WAN) connection or a metropolitan-area network (MAN) connection. For example, a machine farm 907 may include servers 906 physically located in different continents or different regions of a continent, country, state, city, campus, or room. Data transmission speeds between servers 906 in the machine farm 907 can be increased if the servers 906 are connected using a local- area network (LAN) connection or some form of direct connection. Additionally, a heterogeneous machine farm 907 may include one or more servers 906 operating according to a type of operating system, while one or more other servers 906 execute one or more types of hypervisors rather than operating systems. In these embodiments, hypervisors may be used to emulate virtual hardware, partition physical hardware, virtualized physical hardware, and execute virtual machines that provide access to computing environments, allowing multiple operating systems to run concurrently on a host computer. Native hypervisors may run directly on the host computer. Hypervisors may include VMware ESX/ESXi, manufactured by VMWare, Inc., of Palo Alto, California; the Xen hypervisor, an open source product whose development is overseen by Citrix Systems, Inc.; the HYPER-V hypervisors provided by Microsoft or others. Hosted hypervisors may run within an operating system on a second software level. Examples of hosted hypervisors may include VMware Workstation and VIRTUALBOX.

[0078] Management of the machine farm 907 may be de-centralized. For example, one or more servers 906 may comprise components, subsystems and modules to support one or more management services for the machine farm 907. In one of these embodiments, one or more servers 906 provide functionality for management of dynamic data, including techniques for handling failover, data replication, and increasing the robustness of the machine farm 907. Each server 906 may communicate with a persistent store and, in some embodiments, with a dynamic store.

[0079] Server 906 may be a file server, application server, web server, proxy server, appliance, network appliance, gateway, gateway server, virtualization server, deployment server, SSL VPN server, or firewall. In one embodiment, the server 906 may be referred to as a remote machine or a node. In another embodiment, a plurality of nodes may be in the path between any two communicating servers.

[0080] Referring to FIG. 9B, a cloud computing environment is depicted. A cloud computing environment may provide client 902 with one or more resources provided by a network environment. The cloud computing environment may include one or more clients 902a-902n, in communication with the cloud 908 over one or more networks 904. Clients 902 may include, e.g., thick clients, thin clients, and zero clients. A thick client may provide at least some functionality even when disconnected from the cloud 908 or servers 906. A thin client or a zero client may depend on the connection to the cloud 908 or server 906 to provide functionality. A zero client may depend on the cloud 908 or other networks 904 or servers 906 to retrieve operating system data for the client device. The cloud 908 may include back end platforms, e.g., servers 906, storage, server farms or data centers.

[0081] The cloud 908 may be public, private, or hybrid. Public clouds may include public servers 906 that are maintained by third parties to the clients 902 or the owners of the clients. The servers 906 may be located off-site in remote geographical locations as disclosed above or otherwise. Public clouds may be connected to the servers 906 over a public network. Private clouds may include private servers 906 that are physically maintained by clients 902 or owners of clients. Private clouds may be connected to the servers 906 over a private network 904. Hybrid clouds 908 may include both the private and public networks 904 and servers 906.

[0082] The cloud 908 may also include a cloud based delivery, e.g. Software as a Service (SaaS) 910, Platform as a Service (PaaS) 912, and Infrastructure as a Service (IaaS) 914.

IaaS may refer to a user renting the use of infrastructure resources that are needed during a specified time period. IaaS providers may offer storage, networking, servers or virtualization resources from large pools, allowing the users to quickly scale up by accessing more resources as needed. PaaS providers may offer functionality provided by IaaS, including, e.g., storage, networking, servers or virtualization, as well as additional resources such as, e.g., the operating system, middleware, or runtime resources. Examples of PaaS include WINDOWS AZURE provided by Microsoft Corporation of Redmond, Washington, Google App Engine provided by Google Inc., and HEROKU provided by Heroku, Inc. of San Francisco, California. SaaS providers may offer the resources that PaaS provides, including storage, networking, servers, virtualization, operating system, middleware, or runtime resources. In some embodiments, SaaS providers may offer additional resources including, e.g., data and application resources.

[0083] Clients 902 may access IaaS resources with one or more IaaS standards, including, e.g., Amazon Elastic Compute Cloud (EC2), Open Cloud Computing Interface (OCCI), Cloud Infrastructure Management Interface (CIMI), or OpenStack standards. Some IaaS standards may allow clients access to resources over HTTP, and may use Representational State Transfer (REST) protocol or Simple Object Access Protocol (SOAP). Clients 902 may access PaaS resources with different PaaS interfaces. Some PaaS interfaces use HTTP packages, standard Java APIs, JavaMail API, Java Data Objects (IDO), Java Persistence API (JPA), Python APIs, web integration APIs for different programming languages including, e.g., Rack for Ruby, WSGI for Python, or PSGI for Perl, or other APIs that may be built on REST, HTTP, XML, or other protocols. Clients 902 may access SaaS resources through the use of web-based user interfaces, provided by a web browser. Clients 902 may also access SaaS resources through smartphone or tablet applications, including. Clients 902 may also access SaaS resources through the client operating system.

[0084] In some embodiments, access to IaaS, PaaS, or SaaS resources may be authenticated. For example, a server or authentication server may authenticate a user via security certificates, HTTPS, or API keys. API keys may include various encryption standards such as, e.g., Advanced Encryption Standard (AES). Data resources may be sent over Transport Layer Security (TLS) or Secure Sockets Layer (SSL).

[0085] The client 902 and server 906 may be deployed as and/or executed on any type and form of computing device, e.g. a computer, network device or appliance capable of communicating on any type and form of network and performing the operations described herein. FIGS. 9C and 9D depict block diagrams of a computing device 900 useful for practicing an embodiment of the client 902 or a server 906. As shown in FIGS. 9C and 9D, each computing device 900 includes a central processing unit 921, and a main memory unit 922. As shown in FIG. 9C, a computing device 900 may include a storage device 928, an installation device 916, a network interface 918, an I/O controller 923, display devices 924a- 924n, a keyboard 926 and a pointing device 927, e.g. a mouse. The storage device 928 may include, without limitation, an operating system, and/or software 920. As shown in FIG. 9D, each computing device 900 may also include additional optional elements, e.g. a memory port 903, a bridge 970, one or more input/output devices 930a-930n (generally referred to using reference numeral 930), and a cache memory 940 in communication with the central processing unit 921.

[0086] The central processing unit 921 is any logic circuitry that responds to and processes instructions fetched from the main memory unit 922. In many embodiments, the central processing unit 921 is provided by a microprocessor unit. The computing device 900 may be based on any of these processors, or any other processor capable of operating as described herein. The central processing unit 921 may utilize instruction level parallelism, thread level parallelism, different levels of cache, and multi-core processors. A multi-core processor may include two or more processing units on a single computing component.

[0087] Main memory unit 922 may include one or more memory chips capable of storing data and allowing any storage location to be directly accessed by the microprocessor 921. Main memory unit 922 may be volatile and faster than storage 928 memory. Main memory units 922 may be Dynamic random access memory (DRAM) or any variants, including static random access memory (SRAM), Burst SRAM or SynchBurst SRAM (BSRAM), Fast Page Mode DRAM (FPM DRAM), Enhanced DRAM (EDRAM), Extended Data Output RAM (EDO RAM), Extended Data Output DRAM (EDO DRAM), Burst Extended Data Output DRAM (BEDO DRAM), Single Data Rate Synchronous DRAM (SDR SDRAM), Double Data Rate SDRAM (DDR SDRAM), Direct Rambus DRAM (DRDRAM), or Extreme Data Rate DRAM (XDR DRAM). In some embodiments, the main memory 922 or the storage 928 may be non-volatile; e.g., non-volatile read access memory (NVRAM), flash memory non-volatile static RAM (nvSRAM), Ferroelectric RAM (FeRAM), Magnetoresistive RAM (MRAM), Phase-change memory (PRAM), conductive-bridging RAM (CBRAM), Silicon- Oxide-Nitride-Oxide-Silicon (SONOS), Resistive RAM (RRAM), Racetrack, Nano-RAM (NRAM), or Millipede memory. The main memory 922 may be based on any of the above described memory chips, or any other available memory chips capable of operating as described herein. In the embodiment shown in FIG. 9C, the processor 921 communicates with main memory 922 via a system bus 950 (described in more detail below). FIG. 9D depicts an embodiment of a computing device 900 in which the processor communicates directly with main memory 922 via a memory port 903. For example, in FIG. 9D the main memory 922 may be DRDRAM.

[0088] FIG. 9D depicts an embodiment in which the main processor 921 communicates directly with cache memory 940 via a secondary bus, sometimes referred to as a backside bus. In other embodiments, the main processor 921 communicates with cache memory 940 using the system bus 950. Cache memory 940 typically has a faster response time than main memory 922 and is typically provided by SRAM, BSRAM, or EDRAM. In the embodiment shown in FIG. 9D, the processor 921 communicates with various EO devices 930 via a local system bus 950. Various buses may be used to connect the central processing unit 921 to any of the EO devices 930, including a PCI bus, a PCI-X bus, or a PCI-Express bus, or a NuBus. For embodiments in which the I/O device is a video display 924, the processor 921 may use an Advanced Graphics Port (AGP) to communicate with the display 924 or the I/O controller 923 for the display 924. FIG. 9D depicts an embodiment of a computer 900 in which the main processor 921 communicates directly with I/O device 930b or other processors 921’ via HYPERTRANSPORT, RAPIDIO, or INFINIBAND communications technology. FIG. 9D also depicts an embodiment in which local busses and direct communication are mixed: the processor 921 communicates with I/O device 930a using a local interconnect bus while communicating with I/O device 930b directly.

[0089] A wide variety of EO devices 930a-930n may be present in the computing device 900. Input devices may include keyboards, mice, trackpads, trackballs, touchpads, touch mice, multi-touch touchpads and touch mice, microphones, multi-array microphones, drawing tablets, cameras, single-lens reflex camera (SLR), digital SLR (DSLR), CMOS sensors, accelerometers, infrared optical sensors, pressure sensors, magnetometer sensors, angular rate sensors, depth sensors, proximity sensors, ambient light sensors, gyroscopic sensors, or other sensors. Output devices may include video displays, graphical displays, speakers, headphones, inkjet printers, laser printers, and 3D printers.

[0090] Devices 930a-930n may include a combination of multiple input or output devices, including. Some devices 930a-930n allow gesture recognition inputs through combining some of the inputs and outputs. Some devices 930a-930n provides for facial recognition which may be utilized as an input for different purposes including authentication and other commands. Some devices 930a-930n provides for voice recognition and inputs. Additional devices 930a-930n have both input and output capabilities, including, e.g., haptic feedback devices, touchscreen displays, or multi-touch displays. Touchscreen, multi-touch displays, touchpads, touch mice, or other touch sensing devices may use different technologies to sense touch, including, e.g., capacitive, surface capacitive, projected capacitive touch (PCT), in-cell capacitive, resistive, infrared, waveguide, dispersive signal touch (DST), in-cell optical, surface acoustic wave (SAW), bending wave touch (BWT), or force-based sensing technologies. Some multi-touch devices may allow two or more contact points with the surface, allowing advanced functionality including, e.g., pinch, spread, rotate, scroll, or other gestures. Some touchscreen devices, including, such as on a table-top or on a wall, and may also interact with other electronic devices. Some I/O devices 930a-930n, display devices 924a-924n or group of devices may be augment reality devices. The I/O devices may be controlled by an I/O controller 923 as shown in FIG. 9C. The I/O controller may control one or more I/O devices, such as, e.g., a keyboard 926 and a pointing device 927, e.g., a mouse or optical pen. Furthermore, an I/O device may also provide storage and/or an installation medium 916 for the computing device 900. In still other embodiments, the computing device 900 may provide USB connections (not shown) to receive handheld USB storage devices. In further embodiments, an I/O device 930 may be a bridge between the system bus 950 and an external communication bus, e.g. a USB bus, a SCSI bus, a FireWire bus, an Ethernet bus, a Gigabit Ethernet bus, a Fibre Channel bus, or a Thunderbolt bus.

[0091] In some embodiments, display devices 924a-924n may be connected to I/O controller 923. Display devices may include, e.g., liquid crystal displays (LCD), thin film transistor LCD (TFT-LCD), blue phase LCD, electronic papers (e-ink) displays, flexile displays, light emitting diode displays (LED), digital light processing (DLP) displays, liquid crystal on silicon (LCOS) displays, organic light-emitting diode (OLED) displays, active-matrix organic light-emitting diode (AMOLED) displays, liquid crystal laser displays, time-multiplexed optical shutter (TMOS) displays, or 3D displays. Examples of 3D displays may use, e.g. stereoscopy, polarization filters, active shutters, or autostereoscopy. Display devices 924a- 924n may also be a head-mounted display (HMD). In some embodiments, display devices 924a-924n or the corresponding EO controllers 923 may be controlled through or have hardware support for OPENGL or DIRECTX API or other graphics libraries. [0092] In some embodiments, the computing device 900 may include or connect to multiple display devices 924a-924n, which each may be of the same or different type and/or form. As such, any of the I/O devices 930a-930n and/or the I/O controller 923 may include any type and/or form of suitable hardware, software, or combination of hardware and software to support, enable or provide for the connection and use of multiple display devices 924a-924n by the computing device 900. For example, the computing device 900 may include any type and/or form of video adapter, video card, driver, and/or library to interface, communicate, connect or otherwise use the display devices 924a-924n. In one embodiment, a video adapter may include multiple connectors to interface to multiple display devices 924a- 924n. In other embodiments, the computing device 900 may include multiple video adapters, with each video adapter connected to one or more of the display devices 924a-924n. In some embodiments, any portion of the operating system of the computing device 900 may be configured for using multiple displays 924a-924n. In other embodiments, one or more of the display devices 924a-924n may be provided by one or more other computing devices 900a or 900b connected to the computing device 900, via the network 904. In some embodiments software may be designed and constructed to use another computer’s display device as a second display device 924a for the computing device 900.

[0093] Referring again to FIG. 9C, the computing device 900 may comprise a storage device 928 (e.g. one or more hard disk drives or redundant arrays of independent disks) for storing an operating system or other related software, and for storing application software programs such as any program related to the software 920. Examples of storage device 928 include, e.g., hard disk drive (HDD); optical drive; solid-state drive (SSD); USB flash drive; or any other device suitable for storing data. Some storage devices may include multiple volatile and non-volatile memories, including, e.g., solid state hybrid drives that combine hard disks with solid state cache. Some storage device 928 may be non-volatile, mutable, or read-only. Some storage device 928 may be internal and connect to the computing device 900 via a bus 950. Some storage device 928 may be external and connect to the computing device 900 via an EO device 930 that provides an external bus. Some storage device 928 may connect to the computing device 900 via the network interface 918 over a network 904. Some client devices 900 may not require a non-volatile storage device 828 and may be thin clients or zero clients 902. Some storage device 928 may also be used as an installation device 916, and may be suitable for installing software and programs. [0094] Client device 900 may also install software or application from an application distribution platform. An application distribution platform may facilitate installation of software on a client device 902. An application distribution platform may include a repository of applications on a server 906 or a cloud 908, which the clients 902a-902n may access over a network 904. An application distribution platform may include application developed and provided by various developers. A user of a client device 902 may select, purchase and/or download an application via the application distribution platform.

[0095] Furthermore, the computing device 900 may include a network interface 918 to interface to the network 904 through a variety of connections including, but not limited to, standard telephone lines LAN or WAN links (e.g., 802.11, Tl, T3, Gigabit Ethernet,

Infmiband), broadband connections (e.g., ISDN, Frame Relay, ATM, Gigabit Ethernet, Ethemet-over-SONET, ADSL, VDSL, BPON, GPON, fiber optical including FiOS), wireless connections, or some combination of any or all of the above. Connections can be established using a variety of communication protocols (e.g., TCP/IP, Ethernet, ARCNET, SONET,

SDH, Fiber Distributed Data Interface (FDDI), IEEE 802.1 la/b/g/n/ac CDMA, GSM,

WiMax and direct asynchronous connections). In one embodiment, the computing device 900 communicates with other computing devices 900’ via any type and/or form of gateway or tunneling protocol e.g. Secure Socket Layer (SSL) or Transport Layer Security (TLS). The network interface 918 may comprise a built-in network adapter, network interface card, PCMCIA network card, EXPRESSCARD network card, card bus network adapter, wireless network adapter, USB network adapter, modem or any other device suitable for interfacing the computing device 900 to any type of network capable of communication and performing the operations described herein.

[0096] A computing device 900 of the sort depicted in FIGS. 9B and 9C may operate under the control of an operating system, which controls scheduling of tasks and access to system resources. The computing device 900 can be running any operating system such as any of the versions of the MICROSOFT WINDOWS operating systems, the different releases of the Unix and Linux operating systems, any version of the MAC OS for Macintosh computers, any embedded operating system, any real-time operating system, any open source operating system, any proprietary operating system, any operating systems for mobile computing devices, or any other operating system capable of running on the computing device and performing the operations described herein. Typical operating systems include, but are not limited to: WINDOWS 2000, WINDOWS Server 2012, WINDOWS CE, WINDOWS Phone, WINDOWS XP, WINDOWS VISTA, and WINDOWS 7, WINDOWS RT, and WINDOWS 8 all of which are manufactured by Microsoft Corporation of Redmond, Washington; MAC OS and iOS, manufactured by Apple, Inc. of Cupertino, California; and Linux, a freely- available operating system, e.g. Linux Mint distribution (“distro”) or Ubuntu, distributed by Canonical Ltd. of London, United Kingdom; or Unix or other Unix-like derivative operating systems; and Android, designed by Google, of Mountain View, California, among others. Some operating systems, including, e.g., the CHROME OS by Google, may be used on zero clients or thin clients, including, e.g., CHROMEBOOKS.

[0097] The computer system 900 can be any workstation, telephone, desktop computer, laptop or notebook computer, netbook, tablet, server, handheld computer, mobile telephone, smartphone or other portable telecommunications device, media playing device, a gaming system, mobile computing device, or any other type and/or form of computing,

telecommunications or media device that is capable of communication. The computer system 900 has sufficient processor power and memory capacity to perform the operations described herein. In some embodiments, the computing device 900 may have different processors, operating systems, and input devices consistent with the device.

[0098] In some embodiments, the computing device 900 is a gaming system. In some embodiments, the computing device 900 is a digital audio player. Some digital audio players may have other functionality, including, e.g., a gaming system or any functionality made available by an application from a digital application distribution platform. In some embodiments, the computing device 900 is a portable media player or digital audio player supporting file formats including. In some embodiments, the computing device 900 is a tablet. In other embodiments, the computing device 900 is an eBook reader. In some embodiments, the communications device 902 includes a combination of devices, e.g. a smartphone combined with a digital audio player or portable media player. For example, one of these embodiments is a smartphone. In yet another embodiment, the communications device 902 is a laptop or desktop computer equipped with a web browser and a microphone and speaker system, e.g. a telephony headset. In these embodiments, the communications devices 902 are web-enabled and can receive and initiate phone calls. In some embodiments, a laptop or desktop computer is also equipped with a webcam or other video capture device that enables video chat and video call. In some embodiments, the communication device 902 is a wearable mobile computing device.

[0099] In some embodiments, the status of one or more machines 902, 906 in the network 904 is monitored, generally as part of network management. In one of these embodiments, the status of a machine may include an identification of load information (e.g., the number of processes on the machine, CPU and memory utilization), of port information (e.g., the number of available communication ports and the port addresses), or of session status (e.g., the duration and type of processes, and whether a process is active or idle). In another of these embodiments, this information may be identified by a plurality of metrics, and the plurality of metrics can be applied at least in part towards decisions in load distribution, network traffic management, and network failure recovery as well as any aspects of operations of the present solution described herein. Aspects of the operating environments and components described above will become apparent in the context of the systems and methods disclosed herein.

[00100] The description herein including modules emphasizes the structural independence of the aspects of the detection of malignancy of pulmonary nodules or other anatomical growth regions, and illustrates one grouping of operations and responsibilities related to speculation quantification and malignancy detection. Other groupings that execute similar overall operations are understood within the scope of the present application. Modules may be implemented in hardware and/or as computer instructions on a non-transient computer readable storage medium, and modules may be distributed across various hardware or computer based components.

[00101] Example and non-limiting module implementation elements include sensors providing any value determined herein, sensors providing any value that is a precursor to a value determined herein, datalink and/or network hardware including communication chips, oscillating crystals, communication links, cables, twisted pair wiring, coaxial wiring, shielded wiring, transmitters, receivers, and/or transceivers, logic circuits, hard-wired logic circuits, reconfigurable logic circuits in a particular non-transient state configured according to the module specification, any actuator including at least an electrical, hydraulic, or pneumatic actuator, a solenoid, an op-amp, analog control elements (springs, filters, integrators, adders, dividers, gain elements), and/or digital control elements.

[00102] Non-limiting examples of various embodiments are disclosed herein. Features from one embodiments disclosed herein may be combined with features of another embodiment disclosed herein as someone of ordinary skill in the art would understand.

[00103] As utilized herein, the terms“approximately,”“about,”“substantially” and similar terms are intended to have a broad meaning in harmony with the common and accepted usage by those of ordinary skill in the art to which the subject matter of this disclosure pertains. It should be understood by those of skill in the art who review this disclosure that these terms are intended to allow a description of certain features described without restricting the scope of these features to the precise numerical ranges provided. Accordingly, these terms should be interpreted as indicating that insubstantial or inconsequential modifications or alterations of the subject matter described and are considered to be within the scope of the disclosure.

[00104] For the purpose of this disclosure, the term“coupled” means the joining of two members directly or indirectly to one another. Such joining may be stationary or moveable in nature. Such joining may be achieved with the two members or the two members and any additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another. Such joining may be permanent in nature or may be removable or releasable in nature.

[00105] It should be noted that the orientation of various elements may differ according to other exemplary embodiments, and that such variations are intended to be encompassed by the present disclosure. It is recognized that features of the disclosed embodiments can be incorporated into other disclosed embodiments.

[00106] It is important to note that the constructions and arrangements of apparatuses or the components thereof as shown in the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter disclosed. For example, elements shown as integrally formed may be constructed of multiple parts or elements, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes and omissions may also be made in the design, operating conditions and arrangement of the various exemplary embodiments without departing from the scope of the present disclosure.

[00107] While various inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other mechanisms and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that, unless otherwise noted, any parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the inventive teachings is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein.

It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure.

[00108] Also, the technology described herein may be embodied as a method, of which at least one example has been provided. The acts performed as part of the method may be ordered in any suitable way unless otherwise specifically noted. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.

[00109] The indefinite articles“a” and“an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean“at least one.” As used herein in the specification and in the claims,“or” should be understood to have the same meaning as“and/or” as defined above. For example, when separating items in a list, “or” or“and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as“only one of’ or“exactly one of’ will refer to the inclusion of exactly one element of a number or list of elements. In general, the term“or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e.“one or the other but not both”) when preceded by terms of exclusivity, such as“either,”“one of,”“only one of,” or“exactly one of.”

[00110] As used herein in the specification and in the claims, the phrase“at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase“at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example,“at least one of A and B” (or, equivalently,“at least one of A or B,” or, equivalently“at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another

embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one,

B (and optionally including other elements); etc.

Claims

What is claimed is:

1. A method comprising:

transforming, by one or more processors, a first triangular mesh representing a surface of a volumetric image region corresponding to a pulmonary nodule into a second triangular mesh representing a spherical surface while preserving angles of the first triangular mesh; computing, by the one or more processors, for a plurality of points of the surface of the volumetric image region a respective plurality of values of an area distortion metric, the plurality of values including, for each point of the plurality of points, a corresponding area distortion value representing distortion in area at the point due to transforming the first triangular mesh into the second triangular mesh;

identifying, by the one or more processors and using the respective plurality of area distortion values, one or more spikes associated with the surface of the volumetric image region;

computing, by the one or more processors, a cumulative sharpness score and a cumulative irregularity score of the one or more spikes; and

determining, by the one or more processors, whether the pulmonary nodule is benign or malignant using a plurality of radiomic features of the pulmonary nodule including the cumulative sharpness score and the cumulative irregularity score.

2. The method of claim 1, wherein the cumulative sharpness score of the one or more spikes is defined as represent a mean of area

distortion e at i^th spike p(i) and height of i^th spike p(i ), respectively, and

the cumulative irregularity score of the one or more spikes is defined as s₂ = represents variance of area distortion e at i^th spike p(i).

3. The method of claim 2, further comprising determining the height hp_(i) for each spike p(i).

4. The method of claim 1, wherein the plurality of radiomic features of the pulmonary nodule includes one or more statistical parameters of the plurality of values of the area distortion metric.

5. The method of claim 4, wherein the one or more statistical parameters of the plurality values of the area distortion metric include at least one of:

a mean of the respective plurality of area distortion values,

a median of the respective plurality of area distortion values,

a variance of the respective plurality of area distortion values,

a minimum of the respective plurality of area distortion values, or

a maximum of the respective plurality of area distortion values.

6. The method of claim 1, wherein the plurality of radiomic features of the pulmonary nodule includes a number of the one or more spikes associated with the surface of the volumetric image region.

7. The method of claim 1, wherein determining whether the pulmonary nodule is benign or malignant includes:

using a support vector machine (SVM) classifier, the SVM classifier configured to determine whether the pulmonary nodule is benign or malignant based on the plurality of radiomic features.

8. The method of claim 7, further comprising constructing the SVM classifier using training data.

9. The method of claim 1, further comprising:

segmenting, by the one or more processors, the volumetric image region representing the pulmonary nodule.

10. The method of claim 1, wherein transforming the first triangular mesh into the second triangular mesh includes:

dividing the surface of the volumetric image region into two separate segments;

conformally mapping each of the two separate segments onto a respective planar disc; conformally welding the respective planer discs into a complex plane; and

stereographically projecting the complex plane to the spherical surface.

11. A system comprising:

one or more processors; and a memory storing computer instructions, the computer instructions when executed by the one or more processors cause the one or more processors to:

transform a first triangular mesh representing a surface of a volumetric image region corresponding to a pulmonary nodule into a second triangular mesh representing a spherical surface while preserving angles of the first triangular mesh;

compute for a plurality of points of the surface of the volumetric image region a respective plurality of values of an area distortion metric, the plurality of values including, for each point of the plurality of points, a corresponding area distortion value representing distortion in area at the point due to transforming the first triangular mesh into the second triangular mesh;

identify, using the respective plurality of area distortion values, one or more spikes associated with the surface of the volumetric image region;

compute a cumulative sharpness score and a cumulative irregularity score of the one or more spikes; and

determine whether the pulmonary nodule is benign or malignant using a plurality of radiomic features of the pulmonary nodule including the cumulative sharpness score and the cumulative irregularity score.

12. The system of claim 11, wherein the computer instructions when executed by the one or more processors cause the one or more processors to:

compute the cumulative sharpness score of the one or more spikes as s_t =

i_1pn represent a mean of area distortion e at i^tb

spike p(i) and height of /^th spike p(i ), respectively; and

compute the cumulative irregularity score of the one or more spikes as s₂ =

represents variance of area distortion e at i^th spike p(i)_.

13. The system of claim 12, wherein the computer instructions when executed by the one or more processors further cause the one or more processors to determine the height h_P(i) for each spike p(i).

14. The system of claim 11, wherein the plurality of radiomic features of the pulmonary nodule includes one or more statistical parameters of the plurality of values of the area distortion metric.

15. The system of claim 14, wherein the one or more statistical parameters of the plurality of values of the area distortion metric include at least one of:

a mean of the respective plurality of area distortion values,

a median of the respective plurality of area distortion values,

a variance of the respective plurality of area distortion values,

a minimum of the respective plurality of area distortion values, or

a maximum of the respective plurality of area distortion values.

16. The system of claim 11, wherein the plurality of radiomic features of the pulmonary nodule includes a number of the one or more spikes associated with the surface of the volumetric image region.

17. The system of claim 11, wherein in determining whether the pulmonary nodule is benign or malignant the one or more processors are configured to use a support vector machine (SVM) classifier, the SVM classifier configured to determine whether the pulmonary nodule is benign or malignant based on the plurality of radiomic features.

18. The system of claim 11, wherein the computer instructions when executed by the one or more processors cause the one or more processors to segment the volumetric image region representing the pulmonary nodule.

19. The system of claim 11, wherein transforming the first triangular mesh into the second triangular mesh includes:

dividing the surface of the volumetric image region into two separate segments;

conformally mapping each of the two separate segments onto a respective planar disc; conformally welding the respective planer discs into a complex plane; and

stereographically projecting the complex plane to the spherical surface.

20. A non-transitory computer-readable medium storing computer instructions, the computer instructions when executed by one or more processors cause the one or more processors to: transform a first triangular mesh representing a surface of a volumetric image region corresponding to a pulmonary nodule into a second triangular mesh representing a spherical surface while preserving angles of the first triangular mesh;

compute for a plurality of points of the surface of the volumetric image region a respective plurality of values of an area distortion metric, the plurality of values including, for each point of the plurality of points, a corresponding area distortion value representing distortion in area at the point due to transforming the first triangular mesh into the second triangular mesh;

identify, using the respective plurality of area distortion values, one or more spikes associated with the surface of the volumetric image region;

compute a cumulative sharpness score and a cumulative irregularity score of the one or more spikes; and

determine whether the pulmonary nodule is benign or malignant using a plurality of radiomic features of the pulmonary nodule including the cumulative sharpness score and the cumulative irregularity score.