JP2012504003A - Fault detection method and apparatus executed using computer - Google Patents

Abstract

A method for automatically detecting normal and abnormal faults from image data is shown. This method is based on local intensity analysis of variance and can be used in many medical computer aided detection (CAD) systems. Although a complete description is presented for a colon CAD system, the present invention can be utilized in other imaging techniques and can be extended to other CAD applications as well. Conventional CTC colon CAD fault detectors are often based on simple shape-specific methods and may therefore miss some deformed faults that are complex in shape. Embodiments of the present invention use a fast and robust method based on the local intensity variance information given by the Hessian at each voxel, using a very probable obstacle that has certain shapes but is not limited to them. To extract. Furthermore, processing requirements are minimal and implementation is simple compared to other known techniques.

Description

  The present invention relates to medical imaging and analysis. In particular, the invention relates to a method for detecting faults in medical digital images.

Medical Imaging An example of a medical digital image is a CT scan image. A CT scan image is a digital image having one or a series of CT image slices obtained from a CT scan of an area of a human or animal patient. Each slice is a two-dimensional digital grayscale image representing the x-ray absorption of the scanned area. The slice characteristics depend on the CT scanner used. For example, a high resolution multi-slice CT scanner can generate an image with a resolution of 0.5 to 1.0 mm / pixel in the x and y directions (ie, the plane of the slice). Each pixel can be displayed in 16-bit gray scale. The intensity value of each pixel may be expressed in Hounsfield units (HU). Consecutive slices may be separated at a constant distance along the z-direction (ie, scan separation axis), for example, a distance of 0.5 to 2.5 mm. Therefore, the scanned image may be a three-dimensional (3D) grayscale image having an overall size according to the scanned area and the number of scanned slices. Therefore, each pixel may be a voxel in a three-dimensional space. Alternatively, the scanned image may have a single slice and thus may be a single two-dimensional (2D) grayscale image.

  CT scans can be obtained by any CT scan technique, such as electron beam computed tomography (EBCT), multiple detectors, swirl scan, or any technique that produces 2D or 3D images representing x-ray absorption as output. May be.

CAD
Computer-aided detection (CAD) is a computerized medical method that helps medical teams interpret and make decisions. CAD uses information from medical imaging techniques such as CT, SPECT, PET, MRI, ultrasound, electron microscopy, fluoroscopy or optical tomography to detect suspicious lesions and masses.

  Over the last decade, the evolution and development of computer performance in computerized image analysis has influenced the interpretation stage of medical imaging examinations by giving radiologists a valuable second opinion. Has led to improved detection and early diagnosis of aggressive disease. Recently, computer-aided detection has been used in many medical screening applications for various anatomies such as colon, lung, breast, liver, prostate and brain.

  In general, a CAD system is composed of three main parts: a scanner 1, software 2 and a viewer 3 (see FIG. 1). The scanner 1 is used for acquisition and digitization. Almost all scanners already have electronic devices that can provide digital acquisition data. Software 2 has a high-performance computer program that analyzes the captured data and prompts the radiologist to review areas that may indicate a failure. The viewer 3 is a graphic user interface (GUI) for image visualization and processing that supports medical diagnosis.

  CAD software uses an automatic or semi-automatic algorithm to determine and basically consists of five stages: preprocessing, segmentation, detection, feature extraction and classification (see FIG. 2). The preprocessing step S1 usually consists of artifact correction and noise removal. The dividing step S2 divides the target organ (for example, lung or colon [4]) from the data. The detection step S3 is intended to reduce the amount of data to be processed by selecting only candidate regions with high probability in the segmented organ by extracting and grouping geometric features characterizing the fault. Therefore, it is the core of CAD (see Fig. 3). Methods developed for this detection step include the use of volumetric shape index and curvature, surface curvature with rule-based filters, Hough transform and spherical fitting (references [4] and [4]). It is out. The feature extraction step S4 characterizes the candidate regions by evaluating which values are very similar to regions of the same category and very different from regions of different categories. The last classification step S5 is based on supervised classification or neural network statistical methods and aims to identify invariant features.

European Patent Application No. 0060922

CAD for CTC
Colorectal cancer is a global problem with a global increase in the number of cases and deaths due to the expanding and aging population in both developing and developed countries. Computed tomography colonoscopy (CTC), or virtual colonoscopy, is a promising screening tool for colon cancer. CTC is a non-invasive imaging technique intended to image the colon and intestines, including polyps, diverticulitis and cancer. CTC uses X-rays to generate 2D and 3D images of the entire colon. CAD for CTC can detect the location of suspicious obstacles in CTC and help the radiologist make decisions. Colorectal cancer is thought to arise from raised polyps that are potentially visible on CTC. It has been estimated that removal of such raised polyps will prevent most of the cancer. However, there is widespread recognition that some important polyps of the colon have complex structures or are not raised. Detection of this type of polyp is very difficult. Over the last few years, CAD systems have had a highly sophisticated CTC and a mechanism for detecting polyps has been established. However, CAD for CTC is still unable to detect some complex structures and further improves the technology to achieve clinically sufficient detection with high sensitivity and low false positive rate. Is required.

Traditional CAD mechanism for CTC
The CAD mechanism for CTC mainly consists of the following four steps.
1. Pretreatment step S1 that may include noise removal, minimization of fecal tagging effects or electronic colon cleaning (ECC)
2. Division of colon S2 from extra colonic structures such as small intestine, lungs or stomach
3. Detection S3 and segmentation of polyp candidates. Several methods have been developed including the use of volumetric shape index and curvature, surface curvature with rule-based filters, spherical fitting or overlapping surface normals. All of these methods use shape-specific analysis that distinguishes polyps from other structures. Unfortunately, as mentioned above, polyps do not have a unique shape and potential obstacles may be overlooked.
4). Characterization and differentiation of false positives using various internal features such as volumetric tissue or CT intensity S4
5. Classification step S5 for selecting candidates belonging to polyps and reporting the candidates as polyps detected by CAD

  According to one aspect of the present invention, in a computer-implemented method for identifying an object of a medical digital image having intensities at a plurality of points, receiving medical image data representing the image, the intensity Is provided at each point, and the local variance is analyzed along a minimum change direction to identify the object.

  According to another aspect of the present invention, in a computer-implemented method for identifying an object of a medical digital image having intensity at a plurality of points, receiving medical image data representing said image, Calculating the Hessian matrix at each point, determining the positive definiteness and negative definiteness of the Hessian matrix at each point, and analyzing the positive definiteness and negative definiteness of the Hessian matrix to identify the object Is provided.

  In one embodiment, a method for automatically detecting normal and abnormal faults from image data is shown. This method is based on local intensity analysis of variance and can be used in many medical computer aided detection (CAD) systems. A complete description is presented for the colon CAD system. Conventional CTC colon CAD fault detectors are often based on simple shape-specific methods and may therefore miss some deformed faults that are complex in shape.

  Embodiments of the present invention extract sufficiently reliable obstacles that have certain shapes, but are not limited to these. Said embodiment may comprise a fast and robust method based on the local intensity distribution information given by the Hessian at each voxel. Further, the processing requirements may be minimal and can be easily implemented as compared to other known methods in the art.

  Embodiments of the present invention include CAD mechanisms associated with volumetric digital images, and in particular, methods that can be used to detect normal and abnormal faults. Instead of using shape analysis and distinction between shapes, or instead of using a matching method for specific shapes, three-dimensional local intensity variance analysis is used to extract normal and abnormal obstacles. Local intensity variance information is given by the characteristics of the Hessian matrix at each voxel. Information derived from the Hessian matrix allows the location of normal and abnormal faults that can characterize brighter areas with darker backgrounds.

  Other extensions and advantages of the present invention will become apparent to those skilled in the art from the following detailed description, the accompanying drawings, and the appended claims. The present invention is not limited to CT scan images but may be applied to other medical digital images such as MRI, ultrasound or X-ray images. Conventional X-ray images may be developed with X-ray film before being digitized.

It is a figure which shows a CAD system. It is a flowchart which shows a well-known CAD mechanism. It is a figure which shows a well-known detection mechanism. It is a flowchart which shows calculation of the eigenvalue in embodiment of this invention. It is a figure which shows the example with two possibilities for the fault control in this embodiment. It is a figure which shows the characterization of the critical point in this embodiment. It is the schematic which shows a medical imaging device and the remote computer for processing the image data from a medical imaging device. FIG. 2 illustrates a remote computer in more detail.

  Embodiments of the present invention will be described below with reference to the accompanying drawings.

  For clarity, the following description focuses on the use of the proposed methodology for colorectal cancer cases in the form of colonic disorders (polyps). Similarly, particular embodiments are specifically illustrated with respect to data generated by computed tomography colonoscopy (CTC). The present invention is not limited to one application or one medical form. The present invention, as will be apparent, can be extended to other CAD applications as well, and any other medical form including data generated by PET / SPECT, MRI, OT, US, EM, etc. Can be adapted.

CAD mechanism for CTC The CAD mechanism of this embodiment is fully associated with CTC, in particular with the division and detection steps. Instead of using shape analysis to identify each shape, local intensity variance analysis is used to extract normal and abnormal faults. Local intensity variance uses information only from the largest eigenvalue of the Hessian matrix. If the data is processed without ECC, two eigenvalues are required: the largest eigenvalue and the smallest eigenvalue as will be seen in the following description.

  First, a reliable technique is shown that can be used to detect normal and abnormal anatomy in the colon. The CT value of the three-dimensional CTC image can be regarded as a three-dimensional intensity function I (x, y, z). The Hessian matrix at each point of image I can be used. The Hessian, denoted as H, is a matrix of second derivatives of the intensity function I with respect to the geometric arrangement. The Hessian matrix H is a 3 × 3 symmetric matrix describing the secondary structure of the local intensity change of the original intensity I at each point. The Hessian matrix H is an excellent structural descriptor that can provide local intensity variance information through simple partial derivative testing.

  The calculation of the second derivative of the intensity function I is important for the quality of the Hessian. In practice, the image is usually accompanied by high frequency noise, and therefore a filter that removes the noise is required. There are many ways to reduce noise and get an accurate Hessian. These methods can be categorized into various filtering types: isotropic diffusion and anisotropic diffusion [2,3] (see references in [2,3]). The use of robust statistics in anisotropic diffusion [3] is very promising and has not been used in the CAD field. For convenience, only isotropic diffusion is shown because it is the most commonly used method in the field. Isotropic diffusion filtering can be considered a Gaussian filter.

  One method of calculating the derivative for the Hessian using isotropic diffusion for high-speed execution is a serial cascade causal Gaussian filter and anti-causal Gaussian filter [1]. This method is usually less expensive than other alternative methods. This recursive Gaussian filter is also called the infinite impulse response (IIR) approximation of Gaussian filtering.

  Since the Hessian has 3 × 3 symmetry, only six elements are calculated. It is further important to note that the Gaussian function is separable. Thus, the multidimensional Gaussian filter can be separated into a one-dimensional Gaussian function along the principal axis and is calculated more efficiently. The one-dimensional Gaussian function and its first and second derivatives can be expressed by the following equation (1).

Here, the derivative g ′ is related to t 1, and σ is a noise measure that causes the detector to ignore details less than 0 (σ), also called high frequency. Since the Gaussian function is separable, the three-dimensional Gaussian filter mask consists of a one-dimensional Gaussian function multiplication in each direction. Gaussian filter masks corresponding to g, g ′, g ″ are denoted by G ₀ , G ₁ and G ₂ . The calculation of the second derivative may be expressed by the following equation (2).
I ^σ _xx = I * (G ₂ (x) ・ G ₀ (y) ・ G ₀ (z))
I ^σ _yy = I * (G ₀ (x) ・ G ₂ (y) ・ G ₀ (z))
I ^σ _zz = I * (G ₀ (x), G ₀ (y), G ₂ (z)) (2)
I ^σ _xy = I * (G ₁ (x) ・ G ₁ (y) ・ G ₀ (z))
I ^σ _xz = I * (G ₁ (x) ・ G ₀ (y) ・ G ₁ (z))
I ^σ _yz = I * (G ₀ (x) ・ G ₁ (y) ・ G ₁ (z))
An asterisk “*” represents a convolution operator. The subscript notation represents the partial derivative with respect to the spatial coordinates x, y, z.

  Therefore, a symmetric Hessian matrix is given by the following equation (3).

This matrix is symmetric and thus has multiple real eigenvalues. Each eigenvalue describes the local intensity variance in the corresponding eigendirection (directed by its eigenvector). Applying element-related convolutions using Gaussian G _ρ to obtain reliable direction estimates for these three-way fluidity structures and focus only on the study of size-appropriate regions It is possible to average the direction, where ρ is an integral measure. Convolution can be performed using a recursive method as described above.

  Here, the index ρ and the index σ are omitted from the elements of the Hessian matrix for the sake of clarity.

The eigenvalue (λ ₁ ≦ λ ₂ ≦ λ ₃ ) of the Hessian matrix H integrates the amount of change in intensity within the vicinity of the magnitude 0 (ρ). The eigenvalue describes the average contrast in the corresponding eigendirection. The integral scale ρ reflects the characteristic size of the tissue. λ ₁ ≦ λ ₂ ≦ λ ₃ is invariant under orthonormal transformation. A multidimensional space can be defined, and the axes of the multidimensional space correspond to these invariant measurements.

A fast and robust way to calculate the eigenvalues of the Hessian matrix H is to solve a cubic equation that arises analytically [6] from the characteristic matrix equation.
| H−λI | = 0 (5)

In the vicinity of the steady point h ₀ = (x _0, y _0, z ₀ ) (minimum point, maximum point or saddle point), the intensity function I (h = (x, y, z)) is expressed by the following equation (6) Can be approximated by
I ≒ I ₀ + 1 / 2h ^T Hh (6)

Since the Hessian matrix H is a symmetric matrix, it can be shown that all of its eigenvalues are real and the eigenvectors associated with the various eigenvalues are orthogonal. It is possible to construct an orthonormal coordinate system from the eigenvectors of the Hessian H, called the principal axis. By the principal axis theorem, it is possible to construct an orthogonal matrix P whose columns are eigenvectors of the Hessian matrix H and a diagonal matrix PHP ^T = D whose diagonal is an eigenvalue of the Hessian matrix H. Therefore, Expression (6) becomes the following Expression (7).
I ≒ I ₀ +1/2 (Ph) ^T D (Ph) ≒ I ₀ +1/2 (λ ₁ κ ₁ ² + λ ₂ κ ₂ ² + λ ₃ κ ₃ ² ) (7)
Here, k _i = (Ph) _i , i = 1,2,3.

Therefore, it is possible to characterize the local structure by the corresponding critical point characteristics using the eigenvalues of the Hessian matrix H (see also FIG. 6).
• If all eigenvalues of the Hessian H are completely positive (H positive definite), the critical point is the relative (or local) minimum.
• If all eigenvalues of the Hessian matrix H are completely negative (H negative definite), the critical point is the relative (or local) maximum point.
• If the Hessian matrix H has both positive and negative eigenvalues (H indefinite values), the critical point is a saddle point.
-Further analysis is necessary when the Hessian H is positive or negative semidefinite.

An alternative to characterize the critical point, using an eigenvalue-based method, is to examine the Sylvester condition for determining the positive or negative of the real symmetric Hessian matrix H 1.
If the Hessian matrix H is positive definite, the critical point is the relative (or local) minimum point.
If the Hessian matrix H is negative definite, the critical point is the relative (or local) maximum point.
-Further analysis is necessary when the Hessian H is positive or negative semidefinite.

The Sylvester condition for determining the positive of the real symmetric Hessian matrix H is defined as follows.
The real symmetric Hessian matrix H is positive definite if and only if all the determinants (Δ _i , i = 1,2,3) of the sub-matrix at the upper left corner of the Hessian matrix H are positive.

  The Sylvester condition for determining the negative of the real symmetric Hessian matrix H is given by replacing the symbol “>” with the symbol “<” in equation (8).

Using decision characteristics and Sylvester conditions, it is possible to develop practical and fast criteria based on Gaussian elimination type algorithms. This algorithm uses the sign-preserving line operation property of the decision element and can be derived as follows [7].
The Hessian matrix H is positive definite if and only if all diagonal components can be reduced to an upper triangular matrix by using only the inner code storage row operation.

  The conversion of the Hessian matrix H to an upper triangular matrix is given by

Here, r _i , i = 1, 2, 3 represent the i th row of the original matrix or the resulting matrix.

Another way to study the local properties of an analytical shape uses its local Gaussian and the mean curvature (κ ₁ and κ ₂ ) from the differential geometry framework [5]. This technique is based on the following two-dimensional formulation, also called the Monge representation of the surface patch.
z (u, v) ≒ κ ₁ u ² + κ ₂ v ² (9)

  This method is based on the display of the surface shape, and in the present embodiment, information from the entire three-dimensional volume image is used, so it is different from the proposed method.

  It should be noted that the proposed methodology is not limited to 3D digital images but can be extended to any dimension. For example, in some applications, detection of normal or abnormal tissue (obstacles or objects) can be identified from a two-dimensional input digital image. In these applications, the proposed methodology can be easily implemented. The eigenvalue criterion, the Sylvester criterion method and the Gaussian elimination type criterion can be applied using the same principles described in the three-dimensional case.

  In the case of CAD for the colon, the disorder (also called colorectal polyp) is a fleshy growth that occurs in the lining of the colon or rectum. A polyp is a sac composed of a layer of cells, pedicled (attached to the intestinal wall by an axis) or sessile (growing directly from the intestinal wall), and having various shapes Good. Colorectal polyps can be recognized by CTC scans due to their shape, and are also recognized by the appearance of soft tissue masses with high Hounsfield units (with bright intensity) compared to air or other surrounding tissue Can be done. Therefore, colorectal polyps can be extracted by local intensity variance analysis.

An important step of embodiments of the present invention is a detection algorithm for extracting potential polyp candidates. Since the polyp is a soft tissue mass, it is sufficient to find an area that is compact and has a brighter contrast compared to the surrounding tissue (colon wall) to recognize the polyp on a CTC scan. Thus, regions where λ ₃ << 0 are potential polyp candidates in the colon wall. Since the lesion is the only mass of soft tissue in the colon wall, there is no need to characterize the structural shape of the lesion. Note that λ ₃ << 0 is the maximum eigenvalue (λ ₁ ≦ λ ₂ ≦ λ ₃ << 0), and is also the minimum absolute eigenvalue. This condition prevents detection of a saddle-like structure such as a fold line (in the case of a saddle point) in which the amount of change in one direction is smaller than usual and mathematically the Hessian matrix is indefinite. In some cases, colon polyps appear in fluids that are tagged with contrast agents brighter than soft tissue. In this example, the condition can be specified in the same way for the case where the contrast is inverted, ie λ ₁ >> 0 (see FIG. 5).

  Two non-limiting mechanisms illustrate the use of algorithms for polyp detection.

Mechanism 1: With ECC pretreatment Pretreatment step: electronic colon washing Segmentation: Extraction of colon strips with inner and outer colon walls Lumen segmentation: Luminal binary mask Application of morphological dilation to the lumen to produce an inflated lumen mask Morphologically 2. Remove the lumen from the inflated mask. Detection of potential polyps of soft tissue in the luminal strip: A local intensity variance analysis is performed along the largest eigendirection corresponding to λ ₃ << 0 (eg, λ ₃ ≦ T, where T is Only the regions within the soft tissue in Hounsfield units (HU) are considered.
4). Reduce false positives:
• Apply conditional erosion and expansion to the potential region to remove all small regions without changing the soft tissue voxels. • Remove regions that are not in contact with air. Classification of detected polyps and reporting to CAD

Mechanism 2: No ECC pretreatment Segmentation: Extraction of colon strips, as described above. Detection of potential polyps of soft tissue in the luminal strip: Local intensity variance analysis is performed with maximum and minimum eigendirections corresponding to λ ₃ << 0 and λ ₁ >> 0 (eg, λ ₃ ≦ T , Where T is the threshold), only regions within the soft tissue range in units of Hounsfield are considered. 3. Reduction of false positives: treatment like the above mechanism Classification of detected polyps and reporting to CAD

Computer System As shown in FIG. 7, a scan image may be generated by a computer 104 that receives scan data from a scanner 102 and constructs a scan image. The scanned image is stored as an electronic file or a series of files, and the electronic file or series of files is stored in a storage medium 106 such as a fixed disk or a removable disk. The scanned image may include metadata associated with the scanned image. The scanned image may be analyzed by the computer 104, or the scanned image may be transferred to another computer 108 that executes software for processing the scanned image, for example, as described below. The software may be stored on a carrier such as a removable disk or solid-state memory, or via a network such as a local area network (LAN), a wide area network (WAN), and a broad or narrow Internet. May be downloaded.

  The computer described herein may be a computer system 200 as shown in FIG. Embodiments of the invention may be implemented as programmable code for execution by computer system 200. Various embodiments of the present invention are described with respect to the example computer system 200. After reading this description, it will become apparent to a person skilled in the art how to implement the invention using other computer systems and / or computer structures.

  Computer system 200 includes one or more processors, such as processor 204. The processor 204 may be any type of processor including but not limited to a dedicated or general purpose digital signal processor. The processor 204 is connected to a communication infrastructure 206 (eg, a bus or network). Various software implementations are described in terms of this exemplary computer system. After reading this description, it will become apparent to a person skilled in the art how to implement the invention using other computer systems and / or computer structures.

  The computer system 200 further comprises a main memory 208, preferably random access memory (RAM), and may further comprise a secondary memory 210. The secondary memory 210 may include, for example, a hard disk drive 212 and / or a removable storage drive 214 corresponding to a floppy disk drive, magnetic tape drive, optical disk drive, or the like. The removable storage drive 214 reads / writes data to / from the removable storage unit 218 by a known method. The removable storage unit 218 corresponds to a flexible disk, a magnetic tape, an optical disk, or the like that is read and written by the removable storage drive 214. The detachable storage unit 218 has a storage medium that can be used by a computer, as well understood, and computer software and / or data are stored in the storage medium.

  In alternative implementations, secondary memory 210 may have other similar means for loading computer programs or other instructions into computer system 200. Such means may include, for example, a removable storage unit 222 and an interface 220. Examples of such means include program cartridges and cartridge interfaces (as already found in video game devices), removable memory chips (such as EPROM, PROM or flash memory) and associated sockets, and other There is a removable storage unit 222 and an interface 220 for transferring software and data from the removable storage unit 222 to the computer system 200. Alternatively, the program may be executed using the processor 204 of the computer system 200 and / or data may be accessed from the removable storage 222.

  The computer system 200 may further include a communication interface 224. The communication interface 224 allows software and data to be transferred between the computer system 200 and external devices. Examples of the communication interface 224 include a modem, a network interface (such as an Ethernet card), a communication port, a personal computer memory card international association (PCMCIA) slot, and a card. Software and data transferred via the communication interface 224 are in the form of a signal 228, which can be an electronic signal, an electromagnetic signal, an optical signal, or other signal that can be received by the communication interface 224. Such a signal 228 is provided to the communication interface 224 via the communication path 226. Communication path 226 carries signal 228 and may be implemented using wire or cable, fiber optic, telephone line, wireless link, cellular telephone link, radio frequency link, or any other suitable communication channel. For example, the communication path 226 may be implemented using a combination of channels.

  In this application, the terms “computer program medium” and “computer usable medium” refer to media such as removable storage drive 214, hard disk attached to hard disk drive 212, and signal 228. Commonly used. Such a computer program product is a means for providing software to the computer system 200.

  Computer programs (also called computer control logic) are stored in main memory 208 and / or secondary memory 210. A computer program may be received via the communication interface 224. When such a computer program is executed, the computer system 200 can implement the invention described herein. Therefore, such a computer program corresponds to a control unit of the computer system 200. When the present invention is implemented using software, the software may be stored in a computer program product using a removable storage drive 214, hard disk drive 212, or communication interface 224 to provide multiple embodiments. It may be loaded into computer system 200.

  In other embodiments, the present invention may be implemented as control logic in hardware, firmware, software, or any combination thereof.

  It is well understood that the methods described herein may be implemented in software of a computer system, such as computer system 200, unless otherwise specified. The expression “automatically” performed may encompass the meaning of execution by such software, preferably without user intervention.

Other Embodiments The present invention may be applied to different types of disorders such as lung nodules, liver disorders, mammary masses, brain disorders. A segmentation technique appropriate to the desired fault type may be used.

  Application of the present invention is not limited to CT scans, for example, aspects of the present invention may be applied to MRI, PET or X-ray images.

  Although the above embodiments have been described with respect to medical images having intensity values, the images can be preprocessed such that each pixel or voxel does not represent the intensity measured by the scan that generated the image. For example, preprocessing can change the local or global contrast of the image. Alternatively or additionally, the image can be pre-processed to generate spatial data representing other characteristics such as connectivity.

  Other embodiments of the invention will be apparent upon reading the above description. However, such other embodiments are included within the scope of the present invention.

References
[1] Eye. tea. IT Young and L. Jay. LJ van Vliet, “Recursive implementation of the Gaussian filter, Signal Proc.”, 1995, 44 (2), pages 139-151.
[2] Tee. T. Chan et al., “High-order total variation-based image restoration (SIAM J. Sci. Comput.),” Siam Journal on Science and Computing. 2000, 22 (2), 503-516
[3] A. A. Douiri et al., “Local diffusion regularization method for optical tomography reconstruction by using robust statistics, Opt. Lett.), 2005, 30, pages 2439-2441
[4] H. Yoshida (H. Yoshida) and Jay. J. Nappi, “CAD in CT colonography with and without oral contrast agents: development and challenges, CAD in CT colonography without and with oral contrast agents: Progress and challenges, Comp. Med. Imag. And Graphics), 2007, pp. 267-284
[5] Jay. Jay. By JJKoenderink, "Solid Shape", MIT press, Massachusetts (MA), Cambridge, 1990
[6] G. By G. Cardano, "Ars Magna or The Rules of Algebra, 1545"
[7] Double. W. Li, “Practical criteria for positive-definite matrix, M-matrix and Hurwitz matrix, Practical criteria for positive-definite matrix, M-matrix and Hurwitz matrix , App. Math. And Comput.), 2007, 185 (1), pages 397-401.
[8] US Pat. No. 6,345,112, by Summers et al.
[9] U.S. Pat. No. 7236620, by Gurcan

Claims (42)

In a computer-implemented method for identifying an object in a medical digital image having values at multiple points,
a. Receiving medical image data representing the image;
b. Determining a local variance of the values at each of the points;
c. Analyzing the local variance along a minimum direction of change to identify the object.   The method of claim 1, wherein the identified object has an area within a predetermined range.   The method according to claim 1 or 2, wherein the determination of the variance is performed using a Hessian matrix.   4. The method of claim 3, wherein a plurality of eigenvalues are derived from the Hessian matrix.   5. The method of claim 4, wherein the eigenvalue is derived by an analysis method.   6. The method according to claim 4, wherein the analysis of variance is performed using only the maximum value of the eigenvalues.   The method of claim 6, wherein the identification is determined by taking a maximum eigenvalue as a threshold value.   The method of claim 4, wherein the identification is determined using a minimum eigenvalue.   9. The method of claim 8, wherein the identification is determined by taking a minimum eigenvalue as a threshold. In a computer-implemented method for identifying an object in a medical digital image having values at multiple points,
a. Receiving medical image data representing the image;
b. Calculate the Hessian of the image at each point,
c. Determine the positive definiteness and negative definiteness of the Hessian matrix at each point,
d. Analyzing the positive definiteness and negative definiteness of the Hessian matrix to identify the object.   11. The method of claim 10, wherein the positive definiteness and the negative definiteness are determined using Sylvester conditions.   11. The method according to claim 10, wherein the positive definiteness and the negative definiteness are determined using a Gaussian elimination criterion.   13. The method according to claim 10, wherein the identification is applied to a negative definite Hessian.   14. The method according to claim 10, wherein the identification is determined by using a positive definiteness value and a negative definiteness value of the Hessian matrix as threshold values.   15. A method as claimed in any preceding claim, wherein the image is preprocessed.   16. The method of claim 15, wherein the image is preprocessed to remove noise.   17. A method according to claim 15 or 16, characterized in that the preprocessing enhances the local structure of the image.   18. The method according to claim 15, wherein the preprocessing is performed using an isotropic noise removing filter.   19. The derivative of an image is determined by convolution with a derivative of a Gaussian filter with a standard deviation corresponding to the size of the object to be identified. The method described.   20. A method according to any preceding claim, wherein the identification comprises a reduction in false positives.   21. The method of claim 20, wherein the false positive reduction is performed using a conditional form.   21. The method of claim 20, wherein the false positive reduction is achieved using a classifier.   23. A method according to any preceding claim, wherein the medical image comprises an image of at least a portion of the colon.   24. The method of claim 23, wherein the object is a disorder in the colon.   25. A method according to claim 23 or 24, wherein the image is preprocessed to electronically wash away fecal tagging agent from the colon.   26. A method according to any of claims 23 to 25, wherein the points correspond to a band around the colon lumen.   27. The method of claim 26, wherein the band is a region that is offset from a divided colon.   23. A method according to any one of claims 20 to 22, wherein the false positive reduction removes areas that do not contact air.   The method according to any one of claims 1 to 22, wherein the medical image includes an image of at least a part of the brain, lungs, liver, or breast.   30. A method according to any preceding claim, wherein the image is two dimensional.   29. A method as claimed in any preceding claim, wherein the image is three dimensional.   32. A method according to any preceding claim, wherein the value is an image intensity value.   The method according to any one of claims 1 to 32, wherein the medical image is a CT image.   The method according to any one of claims 1 to 32, wherein the medical image is an MR image.   The method according to any one of claims 1 to 32, wherein the medical image is an X-ray image.   The method according to any one of claims 1 to 32, wherein the medical image is an ultrasound image.   The method according to any one of claims 1 to 32, wherein the medical image is a microscopic image.   38. A computer program comprising program code means arranged to perform the method according to any of claims 1-37 when executed by a suitably arranged processor.   40. A computer program product comprising the computer program according to claim 38.   38. Apparatus arranged to perform the method according to any of claims 1-37.   A method fully described herein with reference to the accompanying drawings.   Apparatus fully described herein with reference to the accompanying drawings.

Images