EP1815401A1 - Procede de classification automatique de formes - Google Patents

Procede de classification automatique de formes

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Publication number
EP1815401A1
EP1815401A1 EP05826508A EP05826508A EP1815401A1 EP 1815401 A1 EP1815401 A1 EP 1815401A1 EP 05826508 A EP05826508 A EP 05826508A EP 05826508 A EP05826508 A EP 05826508A EP 1815401 A1 EP1815401 A1 EP 1815401A1
Authority
EP
European Patent Office
Prior art keywords
shape
shapes
average
group
similar
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP05826508A
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German (de)
English (en)
Inventor
Hui Luo
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Carestream Health Inc
Original Assignee
Eastman Kodak Co
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Eastman Kodak Co filed Critical Eastman Kodak Co
Priority claimed from PCT/US2005/042595 external-priority patent/WO2006058154A1/fr
Publication of EP1815401A1 publication Critical patent/EP1815401A1/fr
Withdrawn legal-status Critical Current

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Definitions

  • This invention relates generally to techniques for shape analysis, and more particularly to techniques for automatically classifying 2D shapes in images.
  • the first technique requires the projection of shape instances into a common space and then the implementation of classification on the projection space.
  • Fourier descriptors E. Persoon, et al. "shape discrimination using Fourier descriptors” IEEE Trans. Syst. Man. Cybern, vol.7, ⁇ l70-179, 1977
  • invariant moments F. Zakaria, et. al "Fast algorithm for computation of moment invariants” Pattern Recognition, vol . 20, p 639-643, 1987
  • autoregressive models S .R. Dubois, et. al "An autoregressive model approach to two-dimensional shape classification", IEEE Trans.
  • the second technique comprises locating a set of landmark points along shape boundaries, specifying a distance measure between corresponding landmarks, and performing a distance-based clustering.
  • shape classification is reduced to the general clustering problem for which numerous solutions have been proposed.
  • M. Duta et. al. present a method using Mean Alignment Error(MAE) as a distance to measure the difference of shapes and classify shapes based on MAE.
  • MAE Mean Alignment Error
  • U.S. Patent No. 6,611,630 entitled METHOD AND APPARATUS FOR AUTOMATIC SHAPE CHARACTERIZATION and U.S. Patent No. 6,009,212 entitled METHOD AND APPARATUS FOR IMAGE REGISTRATION are directed to a method to classify shapes based on a best match probability with an average shape of a characterizing population group.
  • the limitation of this technique is that pair wise correspondence between the landmarks of shapes is difficult to achieve in practice because of the noise and variation among individuals. Given the drawbacks and limitation of the prior art, there exists a need for a method to find a simple, efficient and highly accurate method for shape classification.
  • An objective of the present invention is to provide an automated method for 2D shape classification.
  • this objective is achieved by providing an automated method for classifying 2D shapes.
  • the method includes several steps.
  • a training dataset is created for the shape under study.
  • the training set includes two groups of data: a similar shape group and a dissimilar shape group.
  • a polygonal approximation for each shape in the training dataset is generated, and an average shape from the similar shape group is computed.
  • the shapes in the database are aligned to the average shape and their similarity distances is outputted.
  • the distribution of similarity distances is obtained and the shapes are classified into two clusters based on their distances.
  • the present invention is viewed as having some advantages.
  • the method characterizes the study shape by an average shape and a threshold related to the similarity distances.
  • the shape classification is efficient, since its computation complexity is controlled under O(mnlog(mn)), where m is the number of landmarks on the average shape and n is the number of landmarks on a shape instance.
  • the shape classification is robust, since no pairwise correspondence of landmarks is required during shape alignment, and even the number of landmarks can be different. Further, the orientation correction becomes easier since the rotation angle of a shape instance to the average shape can be provided after shape alignment.
  • FIGS. IA and IB are flow charts illustrating the automated methods for shape classification.
  • FIGS. 2A-2U are diagrammatic views showing exemplary shapes extracted from the training database of cistern shape.
  • FIGS. 2A-2K depict the shapes belonging to the similar shape group
  • FIGS. 2L-2U depict the shapes from the dissimilar shape group.
  • FIGS. 3 A and 3 B are graphical views which demonstrates a polygonal approximation of a shape boundary.
  • FIG. 3 A depicts a polygonal approximation generated by equal angle sampling.
  • FIG. 3 B illustrates a polygonal approximation created by filling a number of equidistance points.
  • FIGS. 4A-4F are diagrammatic views illustrating the shape alignment by using the turning functions.
  • FIGS. 4 A and 4B display the turning functions of the template shape.
  • FIGS. 4C and 4D show the turning functions of a shape instance.
  • FIGS.4E and 4F demonstrate the alignment result of these two shapes and their best matched turning functions.
  • FIG. 5 is a flow char showing a way to compute an average shape from the similar shape group.
  • FIG. 6A-6C illustrate a method to obtain a mean point from each segment of the aligned turning functions.
  • FIG. 6A is a graphical view which shows the aligned turning functions.
  • FIG. 6B illustrates an example to compute a mean point from a segment.
  • FIG. 6C is the average shape computed from the similar shape group.
  • FIG. 7 is a diagrammatic view which shows a distance distribution of the training dataset for the study shape and illustrate the way to find a threshold.
  • the present invention discloses a method for automatically classifying 2-dimensional (2D) shapes in images.
  • a flow chart of a method in accordance with the present invention is generally shown in Figure IA.
  • the method includes four steps. First, a training dataset/database of study shape is created, which includes two group data: a similar shape group and a dissimilar shape group (step 10). Then, an average shape to characterize the similar shape group is computed (step 11). Next, the shapes in the database are aligned to the average shape and their similarity distances are calculated (step 12).
  • step 13 the distribution of the similarity distances is obtained and used to classify the shapes into two clusters: similar and dissimilar (step 13).
  • an additional step can be applied prior to the computation of an average shape (step 11).
  • the additional step is the generation of a polygonal approximation for each shape in the training dataset, and will be more particularly described below.
  • Figure 2 shows an exemplary training dataset, in which the study shape (i.e., a target shape) is the shape of cistern extracted from brain images.
  • the training dataset is created by manually selecting two types of shapes: the similar shapes and the dissimilar shapes.
  • the similar shapes represent the same object type, therefore they appear to have a high degree of similarity.
  • all shapes from the similarity group are extracted from cisterns in brain images, as shown in Figures 2A-2K.
  • there may exist a shape variation among them because of noise, pose, and segmentation error as well as nature variation between individuals.
  • the dissimilar shapes are extracted from totally different objects types, for example ventricles, foot, skull, hand, and the like, as shown in Figures 2L-2U.
  • a polygonal approximation of the boundary is generated to represent a shape.
  • the polygonal approximation can be generated by connecting a set of signature points and sampled points extracted from shape.
  • the signature points are the points representing the salient features of shape, such as points with high curvature or at specified location.
  • the sampled points are points located between the signature points based on a certain criteria.
  • One criterion is to find the gravity center of the shape, draw an arbitrary radius from the gravity center to the shape boundary, and then place a set of sampled points along the boundary by moving the radius clockwise with the regular interval of 360/n degrees.
  • the resulting shape can be represented as:
  • FIG. 3 A depicts the polygonal approximation generated by this criterion.
  • Another criterion is to select sampled points by filling a number of equidistance points (v ⁇ ) between signature points.
  • the shape can be given by:
  • Figure 3 B demonstrates the result polygonal approximation.
  • the present invention is not limited to using the above methods to generate the polygonal approximation of shape boundary.
  • Other known algorithms can be used wherein the resultant polygon correctly approximates a shape without losing the salient information.
  • a method using turning functions as a basis for the similarity measure of shapes is provided. Given the polygonal approximations of two shapes, their distance is computed from the turning functions ⁇ (s) of the two polygons.
  • a turning function, or a cumulative angle function represents a polygon by measuring the angle of the counter clockwise tangent as a function of the arc-length s from a reference point O on the shape approximation. It tracks the turning that takes place, for example, increasing with left hand turns, and decreasing with right hand turns.
  • the perimeter length of each polygon can be rescaled to 1.
  • ⁇ (s) starts at ⁇ (O) (assuming that the reference point O is placed at differential point along the contour) and increases to ⁇ (l) — ⁇ (O) + 2 ⁇ .
  • the turning function is piecewise constant for polygons, making computations particularly easy and fast.
  • the function ⁇ (s) is invariant under translation and scaling of the polygon according to the definition.
  • rotation of the polygon over an angle ⁇ corresponds to a vertical shift of the function with an amount ⁇ , while changing the location of the reference point O by an amount tefOJJ along the perimeter of polygon results in a circular shift of the function ⁇ (s).
  • T p and S p be polygonal approximations of the template shape T and a shape instance S.
  • Figures 4B and 4D display the turning functions of the two shapes shown in Figures 4A and 4C, respectively.
  • the X-axis corresponds to the perimeter of shape and the Y-axis represents to the turning angle.
  • the degree to which Tp and S p are similar can be measured by taking the minimal ⁇ 2 distance between the turning functions ⁇ p (s) and ⁇ s p (s), as defined by:
  • ⁇ * is the optimal orientation for any fixed t and is given by: ⁇ * S p ( s ) ds - J 0 V, i s ) ds - 2 ⁇ t (3 ) From these two equations, two matrices are obtained. One is D2 matrix from Equation 2 and the other is 0 matrix from Equation 3. The correct (i.e., best matched) orientation of the shape instance can be determined by searching the minimal L 2 distance in D 2 matrix and its corresponding element in ⁇ c matrix.
  • Figures 4E and 4F demonstrate the alignment result of these two shapes and their best matched turning functions.
  • the rotation angle ⁇ * from the best matched turning functions represents the orientation difference between two shapes, and can be used for orientation correction if needed.
  • the computation complexity for aligning two turning functions is O(mnlog(mn)), where m is the number of landmarks on the template shape and n is the number of landmarks on a shape instance. This is also the computation complexity of the entire shape classification process, since shape alignment takes most time needed for shape classification comparing to the polygon approximation generation and distance classification as will be discussed below. Thus by choosing an appropriate number of landmarks, the shape classification can be made efficient.
  • Another advantage of using the turning function (for example, rather than the distance between the corresponding landmark points) is that the requirement of one-to-one correspondence is no longer necessary, and even the number of landmarks can be different. This can promote shape classification robustness.
  • Each shape in the similar shape group contributes to an average shape which characterizes the feature of shape under study.
  • Figure 5 illustrates a suitable method to achieve this. The method first creates a template shape by randomly selecting a shape from the similar shape group (step 50). Then, the shapes in the similar shape group are aligned to the template shape with the best matched turning functions (step 51).
  • Figure 6k provides an illustration.
  • the aligned turning functions are divided into n equidistance segments along the X-axis, which corresponds the perimeter length of a shape.
  • a mean point is determined from the first points on the turning functions. This is shown in Figure 6B.
  • an average shape can be constructed (step 52).
  • this average shape may not best represent the shape characteristics of the similar shape group, since it highly depends on the selection of the template shape.
  • the average shape is then set as the template shape, and the above processes are repeated until the average shape reaches the minimal distance cross all shapes in the group (step 53), as given by:
  • FIG. 6C illustrates the average shape computed from the similar shape group of Figures 6 A and 6B.
  • the average shape step 54/step 11
  • the shapes in the training dataset are aligned to it and their similarity distances D 2 are computed (step 12).
  • D 2 the similarity distances
  • Combining the distances together forms a distribution of the similarity distances of the training dataset, as shown in Figure 7.
  • the X-axis in Figure 7 represents the distance value, and the Y-axis corresponds to the frequency of the distance.
  • the origin of the coordinate is associated with the average shape. An observation of the distribution shows the difference between the similar shape group and the dissimilar shape group.
  • the shapes are classified into two groups based on their distances. Since the distance distribution is one dimension, the classification problem can be simplified as determining an appropriate threshold to obtain a
  • the classification of study shape is dependent upon an average shape together with its classification threshold extracted from the training dataset.
  • new shapes are input, they are compared against the average shape of the study shape. If a match is found and its distance is less than the threshold, the new shape is classified as a member of the similar shape group.
  • the characteristic average shape and classification threshold are refined to reflect the addition of new members, which can be accomplished by updating the average shape and classification threshold (e.g., every time) when the new shapes accumulate to a certain amount.
  • the disclosed method focuses on one shape type, and the classification result is either YES or NO ( eg. 1 or 0). If a more complicated system is needed to classify several different shape types in the database, the disclosed method can be extended by creating a training dataset for each shape type, then studying the average shape and the classification threshold for each type, and finally performing classification by finding a shape type with the minimal similarity distance.
  • the present invention may be implemented for example in a computer program product.
  • a computer program product may include one or more storage media, for example; magnetic storage media such as magnetic disk (such as a floppy disk) or magnetic tape; optical storage media such as optical disk, optical tape, or machine readable bar code; solid-state electronic storage devices such as random access memory (RAM), or read-only memory (ROM); or any other physical device or media employed to store a computer program having instructions for controlling one or more computers to practice the method according to the present invention.
  • magnetic storage media such as magnetic disk (such as a floppy disk) or magnetic tape
  • optical storage media such as optical disk, optical tape, or machine readable bar code
  • solid-state electronic storage devices such as random access memory (RAM), or read-only memory (ROM); or any other physical device or media employed to store a computer program having instructions for controlling one or more computers to practice the method according to the present invention.
  • the system of the invention can include a programmable computer having a microprocessor, computer memory, and a computer program stored in said computer memory for performing the steps of the method.
  • the computer has a memory interface operatively connected to the microprocessor. This can be a port, such as a USB port, over a drive that accepts removable memory, or some other device that allows access to camera memory.
  • the system includes a digital camera that has memory that is compatible with the memory interface. A photographic film camera and scanner can be used in place of the digital camera, if desired.
  • a graphical user interface (GUI) and user input unit, such as a mouse and keyboard can be provided as part of the computer.
  • GUI graphical user interface

Abstract

L'invention concerne un procédé permettant de classifier des formes 2D, comprenant les étapes suivantes: créer un jeu de données d'apprentissage pour la forme concernée, par étude du groupe de formes similaires et du groupe de formes dissemblables, calculer une forme moyenne sur la base du groupe de formes similaires, aligner toutes les formes dans la base de données sur la forme moyenne et classifier les formes en deux groupes sur la base de leurs distances.
EP05826508A 2004-11-23 2005-11-22 Procede de classification automatique de formes Withdrawn EP1815401A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US63027004P 2004-11-23 2004-11-23
PCT/US2005/042595 WO2006058154A1 (fr) 2004-11-23 2005-11-22 Procede de classification automatique de formes

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EP1815401A1 true EP1815401A1 (fr) 2007-08-08

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CN109300150B (zh) * 2018-10-16 2021-10-29 杭州电子科技大学 一种用于骨龄评估的手骨x光图像纹理特征提取方法

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