Abstract:
Methods and apparatuses detect features. The method according to one embodiment accesses digital image data representing an object; accesses reference data including a shape model relating to shape variation from a baseline object, and a probabilistic atlas comprising probability for a feature in the baseline object; performs shape registration for the object by representing a shape of the object using the shape model, to obtain a registered shape; and determines probability for the feature in the object by generating a correspondence between a geometric element associated with the probabilistic atlas and a geometric element associated with the registered shape.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This non-provisional application is related to co-pending non-provisional applications titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique” and “Method and Apparatus of Using Probabilistic Atlas for Feature Removal/Positioning” filed concurrently herewith, the entire contents of which are hereby incorporated by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to a digital image processing technique, and more particularly to a method and apparatus for processing breast images and detecting cancer in breast images. 
         [0004]    2. Description of the Related Art 
         [0005]    Mammography images and identification of abnormal structures in mammography images are important tools for diagnosis of medical problems of breasts. For example, identification of cancer structures in mammography images is important and useful for prompt treatment and prognosis. 
         [0006]    Reliable cancer detection, however, is difficult to achieve because of variations in anatomical shapes of breasts and medical imaging conditions. Such variations include: 1) anatomical shape variations between breasts of various people or between breasts of the same person; 2) lighting variations in breast images taken at different times; 3) pose and view changes in mammograms; 4) change in anatomical structure of breasts due to aging of people; etc. Such medical imaging variations pose challenges for both manual identification and computer-aided detection of cancer in breasts. 
         [0007]    Breast shapes, and structures inside breasts are important features in mammography images. Accurate breast shapes may convey significant information relating to breast deformation, size, and shape evolution. Inaccurate breast shapes, on the other hand, may obscure abnormal breast growth and deformation. Mammography images with unusual or abnormal breast shapes pose challenges when used in software applications that process and compare breast images. Non-uniform background regions, tags, labels, or scratches present in mammography images may also obscure or change the breast shapes and create problems for detection of cancer in breasts. 
         [0008]    Disclosed embodiments of this application address these and other issues by using methods and apparatuses for cancer detection based on a shape modeling technique for breasts and using a probabilistic atlas for cancer locations in breasts. The methods and apparatuses generate an image for probability of cancer in a breast image using a probabilistic atlas. The methods and apparatuses detect cancer in breasts by representing shapes of breasts using a shape model, and comparing shape modeled breasts. The methods and apparatuses can be used for detection of other abnormal structures in breasts using a probabilistic atlas for locations of abnormal structures in breasts. The methods and apparatuses can be used for detection of abnormal structures or cancer in other anatomical parts besides breasts, by using probabilistic atlases for locations of abnormal structures or cancer formation in anatomical parts. 
       SUMMARY OF THE INVENTION 
       [0009]    The present invention is directed to methods and apparatuses for detecting features. According to a first aspect of the present invention, a feature detection method comprises: accessing digital image data representing an object; accessing reference data including a shape model relating to shape variation from a baseline object, and a probabilistic atlas comprising probability for a feature in the baseline object; performing shape registration for the object by representing a shape of the object using the shape model, to obtain a registered shape; and determining probability for the feature in the object by generating a correspondence between a geometric element associated with the probabilistic atlas and a geometric element associated with the registered shape. 
         [0010]    According to a second aspect of the present invention, a feature detection method comprises: accessing digital image data representing a plurality of images including a plurality of objects; accessing reference data including a shape model relating to shape variation from a baseline object; performing shape registration for the plurality of objects by representing shapes of the plurality of objects using the shape model, to obtain a plurality of registered shapes for the plurality of objects; and determining presence of a feature in a first object from the plurality of objects, the determining step including warping the plurality of registered shapes to the baseline object, to obtain a plurality of warped shapes, and determining differences between a warped shape associated with the first object and a second warped shape from the plurality of warped shapes. 
         [0011]    According to a third aspect of the present invention, a feature detection apparatus comprises: an image data input unit for providing digital image data representing an object; a reference data unit for providing reference data including a shape model relating to shape variation from a baseline object, and a probabilistic atlas comprising probability for a feature in the baseline object; a shape registration unit for performing shape registration for the object by representing a shape of the object using the shape model, to obtain a registered shape; and a feature analysis unit for determining probability for the feature in the object by generating a correspondence between a geometric element associated with the probabilistic atlas and a geometric element associated with the registered shape. 
         [0012]    According to a fourth aspect of the present invention, a feature detection apparatus comprises: an image data input unit for providing digital image data representing a plurality of images including a plurality of objects; a reference data unit for providing reference data including a shape model relating to shape variation from a baseline object; a shape registration unit for performing shape registration for the plurality of objects by representing shapes of the plurality of objects using the shape model, to obtain a plurality of registered shapes for the plurality of objects; and a feature analysis unit for determining presence of a feature in a first object from the plurality of objects, the feature analysis unit determining presence of the feature by warping the plurality of registered shapes to the baseline object, to obtain a plurality of warped shapes, and determining differences between a warped shape associated with the first object and a second warped shape from the plurality of warped shapes. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    Further aspects and advantages of the present invention will become apparent upon reading the following detailed description in conjunction with the accompanying drawings, in which: 
           [0014]      FIG. 1  is a general block diagram of a system including an image processing unit for cancer detection using a probabilistic atlas according to an embodiment of the present invention; 
           [0015]      FIG. 2  is a block diagram of an image processing unit for cancer detection using a probabilistic atlas according to an embodiment of the present invention; 
           [0016]      FIG. 3  is a flow diagram illustrating operations performed by an image processing unit for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 2 ; 
           [0017]      FIG. 4  is a block diagram of an image processing unit for cancer detection using a probabilistic atlas to obtain a cancer probability image according to an embodiment of the present invention illustrated in  FIG. 2 ; 
           [0018]      FIG. 5  is a flow diagram illustrating operations performed by an image F operations unit included in an image processing unit for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 4 ; 
           [0019]      FIG. 6  is a flow diagram illustrating operations performed by a shape registration unit included in an image processing unit for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 4 ; 
           [0020]      FIG. 7  is a flow diagram illustrating exemplary operations performed by a cancer detection unit included in an image processing unit for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 4 ; 
           [0021]      FIG. 8A  illustrates an exemplary baseline breast atlas shape for the ML view for a shape model stored in a probabilistic atlas reference unit; 
           [0022]      FIG. 8B  illustrates exemplary deformation modes for a shape model stored in a probabilistic atlas reference unit; 
           [0023]      FIG. 8C  illustrates another set of exemplary deformation modes for a shape model stored in a probabilistic atlas reference unit; 
           [0024]      FIG. 8D  illustrates exemplary aspects of the operation of calculating a cost function by a shape registration unit for a registered shape according to an embodiment of the present invention illustrated in  FIG. 6 ; 
           [0025]      FIG. 8E  illustrates exemplary results of the operation of performing shape registration for breast masks by a shape registration unit according to an embodiment of the present invention illustrated in  FIG. 6 ; 
           [0026]      FIG. 8F  illustrates an exemplary ML view probabilistic atlas for probability of cancer in breasts stored in a probabilistic atlas reference unit; 
           [0027]      FIG. 8G  illustrates an exemplary CC view probabilistic atlas for probability of cancer in breasts stored in a probabilistic atlas reference unit; 
           [0028]      FIG. 8H  illustrates exemplary aspects of the operation of generating a cancer probability image for a breast image by an image processing unit for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 4 ; 
           [0029]      FIG. 8I  illustrates exemplary aspects of the operation of warping a breast mask to an atlas using triangulation by a cancer detection unit according to an embodiment of the present invention illustrated in  FIG. 7 ; 
           [0030]      FIG. 8J  illustrates exemplary aspects of the operation of bilinear interpolation according to an embodiment of the present invention illustrated in  FIG. 7 ; 
           [0031]      FIG. 9  is a block diagram of an image processing unit for cancer detection using comparative breast analysis according to a second embodiment of the present invention illustrated in  FIG. 2 ; 
           [0032]      FIG. 10A  illustrates aspects of the operation of warping a cancer formation to an atlas for comparative breast analysis according to a second embodiment of the present invention illustrated in  FIG. 9 ; 
           [0033]      FIG. 10B  illustrates aspects of the operation of cancer detection using comparative breast analysis according to a second embodiment of the present invention illustrated in  FIG. 9 ; 
           [0034]      FIG. 11  is a block diagram of an image processing unit for cancer detection using a probabilistic atlas to obtain a cancer probability image according to a third embodiment of the present invention illustrated in  FIG. 2 ; and 
           [0035]      FIG. 12  is a block diagram of an image processing unit for cancer detection using comparative breast analysis according to a fourth embodiment of the present invention illustrated in  FIG. 2 . 
       
    
    
     DETAILED DESCRIPTION 
       [0036]    Aspects of the invention are more specifically set forth in the accompanying description with reference to the appended figures.  FIG. 1  is a general block diagram of a system including an image processing unit for cancer detection using a probabilistic atlas according to an embodiment of the present invention. The system  95  illustrated in  FIG. 1  includes the following components: an image input unit  25 ; an image processing unit  35 ; a display  65 ; an image output unit  55 ; a user input unit  75 ; and a printing unit  45 . Operation of the system  95  in  FIG. 1  will become apparent from the following discussion. 
         [0037]    The image input unit  25  provides digital image data. Digital image data may be medical images such as mammogram images, brain scan images, X-ray images, etc. Image input unit  25  may be one or more of any number of devices providing digital image data derived from a radiological film, a diagnostic image, a digital system, etc. Such an input device may be, for example, a scanner for scanning images recorded on a film; a digital camera; a digital mammography machine; a recording medium such as a CD-R, a floppy disk, a USB drive, etc.; a database system which stores images; a network connection; an image processing system that outputs digital data, such as a computer application that processes images; etc. 
         [0038]    The image processing unit  35  receives digital image data from the image input unit  25  and performs cancer detection using a probabilistic atlas in a manner discussed in detail below. A user, e.g., a radiology specialist at a medical facility, may view the output of image processing unit  35 , via display  65  and may input commands to the image processing unit  35  via the user input unit  75 . In the embodiment illustrated in  FIG. 1 , the user input unit  75  includes a keyboard  85  and a mouse  87 , but other conventional input devices could also be used. 
         [0039]    In addition to performing cancer detection using a probabilistic atlas in accordance with embodiments of the present invention, the image processing unit  35  may perform additional image processing functions in accordance with commands received from the user input unit  75 . The printing unit  45  receives the output of the image processing unit  35  and generates a hard copy of the processed image data. In addition or as an alternative to generating a hard copy of the output of the image processing unit  35 , the processed image data may be returned as an image file, e.g., via a portable recording medium or via a network (not shown). The output of image processing unit  35  may also be sent to image output unit  55  that performs further operations on image data for various purposes. The image output unit  55  may be a module that performs further processing of the image data; a database that collects and compares images; a database that stores and uses cancer detection results received from image processing unit  35 ; etc. 
         [0040]      FIG. 2  is a block diagram of an image processing unit  35  for cancer detection using a probabilistic atlas according to an embodiment of the present invention. As shown in  FIG. 2 , the image processing unit  35  according to this embodiment includes: an image operations unit  125 ; a shape registration unit  135 ; a cancer detection unit  145 ; and a probabilistic atlas reference unit  155 . Although various components of  FIG. 2  are illustrated as discrete elements, such an illustration is for ease of explanation and it should be recognized that certain operations of the various components may be performed by the same physical device, e.g., by one or more microprocessors. 
         [0041]    Generally, the arrangement of elements for the image processing unit  35  illustrated in  FIG. 2  performs preprocessing and preparation of digital image data, registration of shapes of anatomical objects from digital image data, and detection of cancer formations in anatomical objects in digital image data. Image operations unit  125  receives digital image data from image input unit  25 . Digital image data can be medical images, which may be obtained through medical imaging. Digital image data may be, for example, mammography images, brain scan images, chest X-ray images, etc. 
         [0042]    Operation of image processing unit  35  will be next described in the context of mammography images, for using a probabilistic atlas and/or a shape model for cancer detection in mammography images. However, the principles of the current invention apply equally to other areas of medical image processing, and to cancer detection using a probabilistic atlas and/or a shape model for other types of anatomical objects besides breasts. 
         [0043]    Image operations unit  125  receives a set of breast images from image input unit  25  and may perform preprocessing and preparation operations on the breast images. Preprocessing and preparation operations performed by image operations unit  125  may include resizing, cropping, compression, color correction, etc., that change size and/or appearance of breast images. Image operations unit  125  may also extract breast shape information from breast images, and may store or extract information about breast images, such as views of mammograms. 
         [0044]    Image operations unit  125  sends the preprocessed breast images to shape registration unit  135 , which performs shape registration for breasts in the breast images. For shape registration, shape registration unit  135  represents breast shapes using a shape model, to obtain registered breast shapes. Shape registration unit  135  retrieves information about the shape model from probabilistic atlas reference unit  155 , which stores parameters that define the shape model. Probabilistic atlas reference unit  155  also stores one or more probabilistic cancer atlases that include information about probability of cancer at locations inside breasts, for various views of breasts recorded in mammograms. 
         [0045]    Cancer detection unit  145  receives registered breast shapes from shape registration unit  135 . Cancer detection unit  145  also retrieves probabilistic cancer atlas data from probabilistic atlas reference unit  155 . Using probabilistic cancer atlas data, cancer detection unit  145  detects presence or probability of cancer in registered breast shapes. The outputs of cancer detection unit  145  are locations and probability estimates for cancer structures in breasts. Cancer detection unit  145  outputs breast images, together with locations and probability estimates for cancer structures in breasts. Such breast images with locations and probability estimates for cancer structures may be output to image output unit  55 , printing unit  45 , and/or display  65 . 
         [0046]    Operation of the components included in image processing unit  35  illustrated in  FIG. 2  will be next described with reference to  FIG. 3 . Inage operations unit  125 , shape registration unit  135 , cancer detection unit  145 , and probabilistic atlas reference unit  155  are software systems/applications. Image operations unit  125 , shape registration unit  135 , cancer detection unit  145 , and probabilistic atlas reference unit  155  may also be purpose built hardware such as FPGA, ASIC, etc. 
         [0047]      FIG. 3  is a flow diagram illustrating operations performed by an image processing unit  35  for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 2 . 
         [0048]    Image operations unit  125  receives a breast image from image input unit  25  (S 201 ). Image operations unit  125  performs preprocessing and preparation operations on the breast image (S 203 ). Preprocessing and preparation operations performed by image operations unit  125  may include resizing, cropping, compression, color correction, etc., that change size and/or appearance of breast images. Image operations unit  125  also extracts breast shape information from the breast image (S 205 ), and stores or extracts information about the view of the breast image (S 207 ). 
         [0049]    Image operations unit  125  sends the preprocessed breast image to shape registration unit  135 , which performs shape registration for the breast in the image to obtain a registered breast shape (S 209 ). For shape registration, shape registration unit  135  uses a shape model for breast shapes (S 211 ). The shape model describes how shape varies from breast to breast. The shape model is retrieved from probabilistic atlas reference unit  155  (S 211 ). 
         [0050]    Cancer detection unit  145  receives the registered breast shape from shape registration unit  135 . Cancer detection unit  145  retrieves data for a probabilistic cancer atlas from probabilistic atlas reference unit  155  (S 215 ). The probabilistic cancer atlas includes information about probability of cancer at various locations inside breasts. Using probabilistic cancer atlas data, cancer detection unit  145  detects presence or probability of cancer in the registered breast shape (S 217 ). Cancer detection unit  145  outputs locations and probability estimates for cancer formations in the breast from the breast image (S 219 ). Such output results may be output to image output unit  55 , printing unit  45 , and/or display  65 . 
         [0051]      FIG. 4  is a block diagram of an image processing unit  35 A for cancer detection using a probabilistic atlas to obtain a cancer probability image according to an embodiment of the present invention illustrated in  FIG. 2 . As shown in  FIG. 4 , the image processing unit  35 A according to this embodiment includes: an image operations unit  125 A; a shape registration unit  135 A; an atlas warping unit  301 ; a probability image extraction unit  303 ; and a probabilistic atlas reference unit  155 . The atlas warping unit  301  and the probability image extraction unit  303  are included in a cancer detection unit  145 A. 
         [0052]    Image operations unit  125 A receives a set of breast images from image input unit  25 , and may perform preprocessing and preparation operations on the breast images. Preprocessing and preparation operations performed by image operations unit  125 A may include resizing, cropping, compression, color correction, etc., that change size and/or appearance of breast images. Image operations unit  125 A creates breast mask images that identify pixels belonging to breasts in the breast images. Breast mask images are also called breast shape silhouettes in the current application. Breast mask images may be created, for example, by detecting breast borders or breast clusters, for the breasts shown in the breast images. Image operations unit  125 A may also store/extract information about breast images, such as views of mammograms. 
         [0053]    Image operations unit  125 A sends the breast mask images to shape registration unit  135 A, which performs shape registration for breast mask images. For shape registration, shape registration unit  135 A describes breast mask images using a shape model, to obtain registered breast shapes. Shape registration unit  135 A retrieves information about the shape model from probabilistic atlas reference unit  155 , which stores parameters that define the shape model. 
         [0054]    Each mammogram view is associated with a shape model. A shape model may consist of a baseline breast atlas shape and a set of deformation modes. In one embodiment, the baseline breast atlas shape is a mean breast shape representing the average shape of a breast for a given mammogram view, but other baseline breast atlas shapes may also be used. The deformation modes define directions of deformation for contour points of breasts in breast images onto corresponding contour points of the breast in the baseline breast atlas shape. The shape model is obtained by training off-line, using large sets of training breast images. A baseline breast atlas shape can be obtained from sets of training breast images. Deformation modes, describing variation of shapes of training breast images from the baseline breast atlas shape, are also obtained by training. Details on generation of a breast shape model using sets of training breast images can be found in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0055]    A breast mask shape may then be represented using the shape model from probabilistic atlas reference unit  155 . A breast mask shape may be expressed as a function of the baseline breast atlas shape, which may be a mean breast shape (B a ), and of shape model deformation modes, as: 
         [0000]    
       
         
           
             
               
                 
                   
                     Breast 
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                     Shape 
                   
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         [0000]    where p is an offset (such as a 2D offset) to the mean breast shape B a  to account for a rigid translation of the entire shape, L i , i=1 . . . k is the set of deformation modes of the shape model, and α i , i=1 . . . k are a set of parameters that define the deviations of Breast Shape from the mean breast shape along the axes associated with the principal deformation modes. The parameters α i , i=1 . . . k are specific to each breast mask. Hence, an arbitrary breast mask may be expressed as a sum of the fixed mean breast shape (B a ), a linear combination of fixed deformation modes L i  multiplied by coefficients α i , and a 2D offset p. Details on how a mean breast shape/baseline breast atlas shape B a  and deformation modes L i , i=1 . . . k are obtained during training, using training breast images can be found in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0056]    Each mammogram view v i  is associated with one mean breast shape (B a     —     vi ) specific to that view, and with a set of deformation modes L i     —     vi , i=1 . . . k vi  specific to that view. 
         [0057]    For each breast mask image B mask     —     new  received from image operations unit  125 A, shape registration unit  135 A retrieves the mean breast shape (B a     —     vi ) and the set of deformation modes L i     —     vi , i=1 . . . k vi  associated with the view v i  of the breast mask image B mask     —     new . Shape registration unit  135 A next identifies the parameters α i , i=1 . . . k vi  and a 2D offset p for the breast mask image B mask     —     new , to fit the breast mask image B mask     —     new  with its correct shape representation in the form: 
         [0000]    
       
         
           
             
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         [0058]    Atlas warping unit  301  receives the registration results for the breast mask image B mask     —     new  from shape registration unit  135 A. Registration results for the breast mask image B mask     —     new  include the parameters α i , i=1 . . . k vi  for the breast mask image B mask     —     new , the 2D offset p, and the functional representation 
         [0000]    
       
         
           
             
               Breast 
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         [0000]    for the breast mask image B mask     —     new . Atlas warping unit  301  then warps the breast mask image B mask     —     new  to a probabilistic cancer atlas A vi  specific to the view v i  of the breast mask image B mask     —     new . The probabilistic cancer atlas data is stored in probabilistic atlas reference unit  155 . 
         [0059]    The probabilistic cancer atlas A vi  includes an image of the mean breast shape B a     —     vi  for view v i , together with probabilities for cancer associated with each pixel in the mean breast shape B a     —     vi . Hence, the probabilistic cancer atlas A vi  is a weighted pixel image, in which each pixel in the mean breast shape B a     —     vi  is weighted by a cancer probability for that pixel. Pixels in the mean breast shape B a     —     vi  may be weighted by cancer probabilities in a number of different ways. For example, the intensities of pixels in the mean breast shape B a     —     vi  may be set based on associated cancer probability; color of pixels in the mean breast shape B a     —     vi  may be set based on associated cancer probability; a separate data structure containing cancer probabilities may be associated with pixels in the mean breast shape B a     —     vi ; etc. 
         [0060]    The probabilistic cancer atlas is obtained by training off-line, using large sets of training breast images with previously identified cancer structures. The shapes of the training breast images are represented as linear combinations of deformation modes obtained during training. Using shape representations for the training breast images, previously identified cancer structures in the training breast images are mapped to the baseline breast atlas shape. By overlapping cancer positions from the training images onto the baseline breast atlas shape, a probabilistic atlas with the probability for cancer in the baseline breast atlas shape is obtained. Additional details on generation of a probabilistic atlas using sets of training breast images with previously identified cancer structures can be found in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0061]    After atlas warping unit  301  warps the breast mask image B mask     —     new  to probabilistic cancer atlas A vi , a warped breast mask image B mask     —     new     —     warped  is obtained. Cancer probability weights from the probabilistic cancer atlas A vi  are associated with pixels in the warped image B mask     —     new     —     warped . Probability image extraction unit  303  receives the warped breast mask image B mask     —     new     —     warped , as well as shape registration information of the form 
         [0000]    
       
         
           
             
               
                 Breast 
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                 Shape 
               
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         [0000]    establishing a correspondence between pixels of B mask     —     new     —     warped  and pixels of B mask     —     new . Hence, B a     —     vi  is the mean atlas silhouette for the view vi, while B mask     —     new     —     warped  is the silhouette of B mask     —     new  warped into the mean atlas space. 
         [0062]    Probability image extraction unit  303  warps the B mask     —     new     —     warped  image back to the original B mask     —     new . A probability image P mask     —     new , is obtained, which includes an image of the breast mask image B mask     —     new , together with probabilities for cancer associated with each pixel in the breast mask image B mask     —     new . Hence, the probability image P mask     —     new  is a weighted pixel image, in which each pixel of the breast mask image B mask     —     new  is weighted by the cancer probability for that pixel. Probability image extraction unit  303  outputs the probability image P mask     —     new . The probability image P mask     —     new  may be output to image output unit  55 , printing unit  45 , and/or display  65 . 
         [0063]    Image operations unit  125 A, shape registration unit  135 A, atlas warping unit  301 , probability image extraction unit  303 , and probabilistic atlas reference unit  155  are software systems/applications. Image operations unit  125 A, shape registration unit  135 A, atlas warping unit  301 , probability image extraction unit  303 , and probabilistic atlas reference unit  155  may also be purpose built hardware such as FPGA, ASIC, etc. 
         [0064]      FIG. 5  is a flow diagram illustrating operations performed by an image operations unit  125 A included in an image processing unit  35 A for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 4 . 
         [0065]    Image operations unit  125 A receives a raw or preprocessed breast image from image input unit  25  (S 401 ). The breast image may be retrieved by image operations unit  125 A from, for example, a breast imaging hospital apparatus, a database of breast images, etc. Image operations unit  125 A may perform preprocessing operations on the breast image (S 403 ). Preprocessing operations may include resizing, cropping, compression, color correction, etc. 
         [0066]    Image operations unit  125 A creates a breast mask image for the breast image (S 405 ). The breast mask image may be created by detecting breast borders for the breast in the breast image. Image operations unit  125 A may create a breast mask image by detecting breast borders using methods described in the US patent application titled “Method and Apparatus for Breast Border Detection”, application Ser. No. 11/366,495, by Daniel Russakoff and Akira Hasegawa, filed on Mar. 3, 2006, the entire contents of which are hereby incorporated by reference. With the techniques described in the “Method and Apparatus for Breast Border Detection” application, pixels in the breast image are represented in a multi-dimensional space, such as a 4-dimensional space with x-locations of pixels, y-locations of pixels, intensity value of pixels, and distance of pixels to a reference point. K-means clustering of pixels is run in the multi-dimensional space, to obtain clusters for the breast image. Cluster merging and connected components analysis is then run using relative intensity measures, brightness pixel values, and cluster size, to identify a cluster corresponding to the breast in the breast image. A set of pixels, or a mask, containing breast pixels is obtained. The set of pixels for a breast in a breast image, forms a breast mask B mask  for that breast image. 
         [0067]    Image operations unit  125 A may also segment the breast area from the background in a mammogram, to create shape silhouettes, using methods described in the publication “Automated Segmentation of Digitized Mammograms” by Wirth, A. and Stapinski, M., Academic Radiology 2 (1995), p. 1-9, the entire contents of which are hereby incorporated by reference. 
         [0068]    Other breast border detection techniques may also be used by image operations unit  125 A to obtain a breast mask image. 
         [0069]    Image operations unit  125 A also stores information about the breast image, such as information about the view of the mammogram (S 407 ). Examples of mammogram views are MLL (medio-lateral left), MLR (medio-lateral right), CCL (cranio-caudal left), CCR (cranio-caudal right), RCC, LRR, LMLO (left medio-lateral oblique), and RMLO (right medio-lateral oblique). Image operations unit  125 A outputs the breast mask image, and view information about the breast image (S 409 ), to shape registration unit  135 A. 
         [0070]      FIG. 6  is a flow diagram illustrating operations performed by a shape registration unit  135 A included in an image processing unit  35 A for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 4 . 
         [0071]    Shape registration unit  135 A receives from image operations unit  125 A a preprocessed breast image, represented as a breast mask image B mask     —     new  (S 470 ). Information about the mammogram view v i  of the breast image is also received (S 470 ). Shape registration unit  135 A retrieves from probabilistic atlas reference unit  155  data that defines the shape model for that view. Such data includes a mean breast shape (B a     —     vi ), shape model deformation modes L i , i=1 . . . k vi  for the view v i  of the breast mask image B mask     —     new , and a 2D offset p to account for a rigid translation of the entire shape (S 472 ). 
         [0072]    Shape registration unit  135 A fits the breast mask image B mask     —     new  with its correct shape representation as a linear combination of the deformation modes, 
         [0000]    
       
         
           
             
               Shape 
               = 
               
                 
                   B 
                   a_vi 
                 
                 + 
                 p 
                 + 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     
                       k 
                       vi 
                     
                   
                    
                   
                     
                       α 
                       i 
                     
                      
                     
                       L 
                       i 
                     
                   
                 
               
             
             , 
           
         
       
     
         [0000]    by determining parameters α i , i=1 . . . k vi  and 2D offset p. 
         [0073]    To fit the breast mask image B mask     —     new  with its correct shape representation, shape registration unit  135 A optimizes the α i  values, together with an x offset p x  and a y offset p y , for a total of k+2 parameters (p x , p y , α), where α=(α 1 , α 2 , . . . , α k ) and p=(p x , p y ) (S 478 ). For optimization, shape registration unit  135 A uses a cost function defined as the mean distance to edge. For a (p x , p y , α) parameter set, shape registration unit  135 A calculates the new shape resulting from this parameter set by formula 
         [0000]    
       
         
           
             Shape 
             = 
             
               
                 B 
                 a_vi 
               
               + 
               p 
               + 
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   
                     k 
                     vi 
                   
                 
                  
                 
                   
                     α 
                     i 
                   
                    
                   
                     L 
                     i 
                   
                    
                   
                       
                   
                    
                   
                     
                       ( 
                       
                         S 
                          
                         
                             
                         
                          
                         480 
                       
                       ) 
                     
                     . 
                   
                 
               
             
           
         
       
     
         [0000]    The center of mass (Shape.COM) of Shape is then calculated (S 480 ). For each shape point on the exterior (border) of Shape, shape registration unit  135 A generates a ray containing the Shape.COM and the shape point, finds the intersection point of the ray with the edge of B mask     —     new , and calculates how far the shape point is from the intersection point obtained in this manner. This technique is further illustrated in  FIG. 8D . In an alternative embodiment, the minimum distance from the shape point to the edge of B mask     —     new  is calculated. 
         [0074]    The mean of the distances between shape points and intersection points is then calculated (S 482 ). Optimized α i  and p values are selected for which the mean attains a minimum (S 484 ). 
         [0075]    Shape registration unit  135 A may use the downhill simplex method, also known as the Nelder-Mead or the amoeba algorithm (S 486 ), to fit the breast mask image B mask     —     new  with its correct shape representation, by minimizing distances of edge points of Shape to points on the edge of the breast mask image B mask     —     new . The downhill simplex method is a single-valued minimization algorithm that does not require derivatives. The downhill simplex algorithm is typically very robust. 
         [0076]    With the Nelder-Mead method, the k+2 parameters (p x , p y , α) form a simplex in a multi-dimensional space. The Nelder-Mead method minimizes the selected cost function, by moving points of the simplex to decrease the cost function. A point of the simplex may be moved by reflections against a plane generated by other simplex points, reflection and expansion of the simplex obtained after reflection, contraction of the simplex, etc. 
         [0077]    Once parameters of the shape model are optimized for the breast mask image B mask     —     new , shape registration unit  135 A outputs the shape registration results for the breast mask image B mask     —     new  to the atlas warping unit  301  (S 492 ). 
         [0078]      FIG. 7  is a flow diagram illustrating exemplary operations performed by a cancer detection unit  145 A included in an image processing unit  35 A for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 4 .  FIG. 7  illustrates exemplary operations that may be performed by an atlas warping unit  301  and a probability image extraction unit  303  included in a cancer detection unit  145 A. 
         [0079]    Atlas warping unit  301  warps the registered shape for breast mask image B mask     —     new  to a probabilistic cancer atlas A vi  for the view v i  of the breast mask image B mask     —     new . Warping to probabilistic cancer atlas A vi  may be performed by triangulating the breast mask B mask     —     new  using its center of mass and its edge points (S 501 ). After shape registration has been performed by shape registration unit  135 A, each triangle in the breast mask B mask     —     new  corresponds to a triangle in the probabilistic cancer atlas A vi  (S 503 ). Since the probabilistic cancer atlas A vi  has the shape of the baseline breast atlas shape B a     —     vi , each triangle in the breast mask B mask     —     new  also corresponds to a triangle in the baseline breast atlas shape B a     —     vi . The pixels inside corresponding triangles of the atlas A vi  (or B a     —     vi ) can be warped back and forth to triangles in breast mask B mask     —     new , using a bilinear interpolation (S 503 ). For a correspondence between two triangles, bilinear interpolation in 2D is performed by multiplying each of the vertices by appropriate relative weights, as further described in  FIG. 8J . 
         [0080]    Probability image extraction unit  303  warps back corresponding triangles of the atlas A vi  (or B a     —     vi ), to triangles in breast mask B mask     —     new  (S 505 ). Cancer probabilities associated with pixels in triangles of the atlas image A vi  (or B a     —     vi ) hence become associated with pixels in triangles of breast mask B mask     —     new  (S 507 ), and a cancer probability image for the breast mask B mask     —     new  is obtained (S 507 ). The cancer probability image for the breast mask B mask     —     new  illustrates likely and unlikely locations for cancer in the breast mask B mask     —     new  and hence in the original breast image associated with the breast mask B mask     —     new . 
         [0081]      FIG. 8A  illustrates an exemplary baseline breast atlas shape for the ML view for a shape model stored in the probabilistic atlas reference unit  155 . The baseline breast atlas shape in  FIG. 8A  represents the set of pixels that have a 95% or more chance of appearing in a breast mask image in the ML view. The baseline breast atlas shape shown in  FIG. 8A  may be obtained using techniques described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0082]      FIG. 8B  illustrates exemplary deformation modes for a shape model stored in the probabilistic atlas reference unit  155 . The breast shape in figure I 510  is an exemplary baseline breast atlas shape (mean shape) for the ML view. 
         [0083]    The first 3 modes (L 1 , L 2 , L 3 ) of deformation are shown. The first mode of deformation is L 1 . Contours D 2  and D 3  define the deformation mode L 1 . The deformation mode L 1  can be represented by directions and proportional length of movement for each contour point from the D 2  contour to a corresponding contour point from the D 3  contour. Contours D 4  and D 5  define the second deformation mode L 2 , and contours D 6  and D 7  define the third deformation mode L 3 . 
         [0084]    The deformation modes shown in  FIG. 8B  may be obtained by training, using techniques described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0085]      FIG. 8C  illustrates another set of exemplary deformation modes for a shape model stored in the probabilistic atlas reference unit  155 . The deformation modes shown in  FIG. 8C  were obtained by training a shape model using 4900 training breast images of ML view, using techniques described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 17 deformation modes, capturing 99% of the variance in the breast images data set, were obtained. The representations of the first 4 modes L 1 , L 2 , L 3  and L 4  are shown in  FIG. 8C . The representations of the first 4 modes L 1 , L 2 , L 3  and L 4  shown in  FIG. 8C  together capture 85% of the data&#39;s variance. For each mode shown in  FIG. 8C , the mean breast shape (baseline breast atlas shape) for the ML view is plotted with dots (points), while the arrows represent the distance traveled by one point for that mode from −2 standard deviations to +2 standard deviations of the mean breast shape. Mode L 1  captures 52% of the variance in the breast images data set, mode L 2  captures 18% of the variance in the breast images data set, mode L 3  captures 10% of the variance in the breast images data set, and mode L 4  captures 4% of the variance in the breast images data set. The rest of the deformation modes (L 5  to L 17 ) are not shown. 
         [0086]      FIG. 8D  illustrates exemplary aspects of the operation of calculating a cost function by a shape registration unit  135 A for a registered shape according to an embodiment of the present invention illustrated in  FIG. 6 . Shape registration is performed for the breast mask B mask     —     new  S 511  using an α i , i=1 . . . k parameter set and a 2D offset p. A shape bounded by contour C 512  is obtained from formula 
         [0000]    
       
         
           
             
               Shape 
               = 
               
                 
                   B 
                   a_vi 
                 
                 + 
                 p 
                 + 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     
                       k 
                       vi 
                     
                   
                    
                   
                     
                       α 
                       i 
                     
                      
                     
                       L 
                       i 
                     
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where B a     —     vi  is a mean breast shape for view v i  of the breast mask B mask     —     new , and L 1 , i=1 . . . k vi  are shape model deformation modes. The center of mass COM for the Shape bounded by contour C 512  is found. For a point S 1  on the contour (exterior) of Shape, a line is drawn through the COM point. The line intersects the contour (perimeter) of breast mask B mask     —     new  S 511  at point S 2 . The distance to edge is the distance d between points S 1  and S 2 . Distances d are obtained for all points on the contour (exterior) C 512  of Shape, and a cost function is obtained as the mean of all distances d. 
         [0087]      FIG. 8E  illustrates exemplary results of the operation of performing shape registration for breast masks by a shape registration unit  135 A according to an embodiment of the present invention illustrated in  FIG. 6 . As shown in  FIG. 8E , breast masks I 513  and I 514  are fit with shape representations. The shape registration results bounded by contours C 513  and C 514  are effectively describing the shapes of breast masks I 513  and I 514 . The downhill simplex algorithm was used by shape registration unit  135 A to obtain the shape registration results shown in  FIG. 8E . 
         [0088]      FIG. 8F  illustrates an exemplary ML view probabilistic atlas for probability of cancer in breasts stored in the probabilistic atlas reference unit  155 . For the ML view probabilistic atlas in  FIG. 8F , the contour C 515  is the contour of the mean breast shape (baseline breast atlas shape) B a     —     ML  for the ML view. The region R 515 A indicates the highest probability of cancer, followed by regions R 515 B, then R 515 C, and R 515 D. As shown in the probabilistic atlas, the probability for cancer is largest in the center of a breast, and decreases towards edges of the mean breast shape. 
         [0089]      FIG. 8G  illustrates an exemplary CC view probabilistic atlas for probability of cancer in breasts stored in the probabilistic atlas reference unit  155 . For the CC view probabilistic atlas in  FIG. 8G , the contour C 516  is the contour of the mean breast shape for the CC view. The region R 516 A indicates the highest probability of cancer, followed by regions R 516 B, then R 516 C, and R 516 D. As shown in the probabilistic atlas, the probability for cancer is largest in the center left region of a breast, and decreases towards edges of the mean breast shape. 
         [0090]      FIG. 8H  illustrates exemplary aspects of the operation of generating a cancer probability image for a breast image by an image processing unit  35 A for cancer detection using a probabilistic atlas according to an embodiment of the present invention illustrated in  FIG. 4 . As illustrated in  FIG. 8H , a breast image I 518  is input by image operations unit  125 A. Image operations unit  125 A extracts a breast mask image I 519  for the breast image I 518 . Shape registration unit  135 A performs shape registration for the breast mask image, by representing the shape of the breast mask using a shape model. The shape representation contour C 520  fits the shape of the breast mask from image I 519 . Atlas warping unit  301  warps the breast mask registered shape I 520  to a probabilistic cancer atlas I 522  by generating a correspondence between pixels of the breast mask registered shape I 520  and pixels of the probabilistic atlas I 522 . Using the correspondence, probability image extraction unit  303  warps the probabilistic cancer atlas I 522  onto the breast mask registered shape I 520 , hence obtaining a cancer probability image I 523  for the breast image I 518 . 
         [0091]      FIG. 8I  illustrates exemplary aspects of the operation of warping a breast mask to an atlas using triangulation by a cancer detection unit  145 A according to an embodiment of the present invention illustrated in  FIG. 7 . 
         [0092]    Atlas warping unit  301  warps a registered shape S 530  for a breast mask image B mask     —     new  I 530  to a probabilistic cancer atlas A vi  A 532  shown in image I 532 . Warping to probabilistic cancer atlas A vi  A 532  is performed by triangulating the breast mask shape S 530  based on its center of mass COM_ 530  and edge points. A test point P_ 530  is used to generate each triangle in the breast mask shape S 530 . For example, a triangle T_ 530  is generated using the center of mass COM_ 530  and the test point P_ 530  and touching the edges of mask shape S 530 . The triangle is warped to probabilistic cancer atlas A vi  A 532  onto a corresponding triangle T_ 532 , with the COM_ 530  and the test point P_ 530  mapped to corresponding points PC_ 532  and P_ 532 . The probabilistic cancer atlas A vi  A 532  is then warped onto registered shape S 530  by warping each triangle T_ 532  back onto the corresponding triangle T_ 530  of the breast mask B mask     —     new  I 530 . The cancer probability values associated with each pixel in the probabilistic cancer atlas A vi  A 532  are also warped onto registered shape S 530 , and a probability image I 534  is obtained. The probability image I 534  contains probability for cancer at pixels in breast mask image B mask     —     new  I 530 . 
         [0093]      FIG. 8J  illustrates exemplary aspects of the operation of bilinear interpolation according to an embodiment of the present invention illustrated in  FIG. 7 . The pixels inside corresponding triangles of the atlas A vi  (or B a     —     vi ) can be warped back and forth to triangles in breast mask B mask     —     new , using a bilinear interpolation, as described at  FIG. 7 . For a correspondence between two triangles, bilinear interpolation in 2D is performed by multiplying each of the vertices by appropriate relative weights as described in  FIG. 8J . Given a triangle with vertices A, B, and C, the pixel intensity at point D can be obtained as: 
         [0000]        D=A*wA/T   abc   +B*wB/T   abc   +C*wC/T   abc   (2) 
         [0000]    where A, B, and C are pixel intensities at triangle vertices, T abc  is the area of triangle ABC, wA is the area of triangle BCD, wB is the area of triangle ACD, and wC is the area of triangle ABD, so that T abc =wA+wB+wC. Hence, given pixels A, B, and C of a triangle inside atlas A vi  (or inside B a     —     vi ), and corresponding pixels A′, B′, and C′ of a corresponding triangle in breast mask B mask     —     new , a pixel D inside triangle ABC can be warped to a pixel D′ inside triangle A′B′C′, using equation (2) in triangle A′B′C′. 
         [0094]      FIG. 9  is a block diagram of an image processing unit  35 B for cancer detection using comparative breast analysis according to a second embodiment of the present invention illustrated in  FIG. 2 . As shown in  FIG. 9 , the image processing unit  35 B according to this embodiment includes: an image operations unit  125 B; a shape registration unit  135 B; an atlas warping unit  570 ; a comparative breast analysis unit  580 ; and a probabilistic atlas reference unit  155 . The atlas warping unit  570  and the comparative breast analysis unit  580  are included in a cancer detection unit  145 B. 
         [0095]    Image operations unit  125 B receives a set of breast images from image input unit  25 , and may perform preprocessing and preparation operations on the breast images. Preprocessing and preparation operations performed by image operations unit  125 B may include resizing, cropping, compression, color correction, etc., that change size and/or appearance of breast images. Image operations unit  125 B creates breast mask images. Breast mask images may be created, for example, by detecting breast borders or breast clusters for the breasts shown in the breast images. Image operations unit  125 B may also store/extract information about breast images, such as view of mammograms. 
         [0096]    Image operations unit  125 B may perform preprocessing and breast mask extraction operations in a similar manner to image operations unit  125 A described in  FIG. 5 . Image operations unit  125 B may create breast mask images by detecting breast borders using methods described in the US patent application titled “Method and Apparatus for Breast Border Detection”, application Ser. No. 11/366,495, by Daniel Russakoff and Akira Hasegawa, filed on Mar. 3, 2006, the entire contents of which are hereby incorporated by reference. 
         [0097]    Image operations unit  125 B sends the breast mask images to shape registration unit  135 B, which performs shape registration for breast mask images. For shape registration, shape registration unit  135 B describes breast mask images using a shape model, to obtain registered breast shapes. Shape registration unit  135 B retrieves information about the shape model from probabilistic atlas reference unit  155 , which stores parameters that define the shape model. 
         [0098]    The shape model, together with a probabilistic cancer atlas stored in the probabilistic atlas reference unit  155 , have been described at  FIG. 4 , and can be generated off-line, using training breast images. Details on generation of a breast shape model and a probabilistic cancer atlas using sets of training breast images can be found in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. Probabilistic atlas reference unit  155  stores information for shape models for breasts, for various views. 
         [0099]    Shape registration unit  135 B may perform shape registration in a manner similar to shape registration unit  135 A, as described at  FIG. 6 . As described at  FIG. 4 , a shape model for a given mammogram view includes a baseline breast atlas shape and a set of deformation modes. Atlas warping unit  570  receives the registration results for the breast mask images from shape registration unit  135 B, and warps the breast mask images to probabilistic cancer atlases associated with the views of the breast mask images. Atlas warping unit  570  may also warp breast mask images to baseline breast atlas shapes specific to the views of the breast mask images. Atlas warping unit  570  may perform warping of breast mask images to baseline breast atlas shapes or to probabilistic cancer atlases in a manner similar to atlas warping unit  301 , using techniques described at  FIG. 4  and at  FIG. 7 . 
         [0100]    Comparative breast analysis unit  580  receives warped breast mask images from atlas warping unit  570  and performs a comparative analysis between warped breast mask images. 
         [0101]    One technique by which cancer can be found in breasts is by searching for anomalies present in a left breast image from a person, that do not appear in the right breast image of that person, or vice versa. Suppose a left breast image I L  and a right breast image I R  obtained from a mammography machine are compared manually or by a computer. Because the left and the right breast shapes often do not coincide, it is unclear which pixels in the left breast image I L  and which pixels in the right breast image I R  should be compared and subtracted, in order to obtain a difference image that would expose breast anomalies. 
         [0102]    Using the image processing unit  35 B it is possible to establish a one-to-one correspondence between pixels in a left breast image and a right breast image. For a left breast image I L  and a right breast image I R  with the same mammogram view v and obtained from the same person, image operations unit  125 A obtains a left breast mask image B L     —     mask  and a right breast mask image B R     —     mask . Shape registration unit  135 B performs shape registration for left breast mask image B L     —     mask  and right breast mask image B R     —     mask  using the shape model for view v. 
         [0103]    Atlas warping unit  570  receives the registration results for the left breast mask image B L     —     mask  and the right breast mask image B R     —     mask . Atlas warping unit  570  uses the shape registration results and warps the left breast mask image B L     —     mask  and the right breast mask image B R     —     mask  into the atlas space. Atlas warping unit  570  warps the left breast mask image B L     —     mask  and the right breast mask image B R     —     mask  to the baseline breast atlas shape B a     —     v  associated with the view v, or to the probabilistic cancer atlas A v  associated with view v. Two warped images in the atlas space, B L     —     mask     —     warped  for the left breast and B R     —     mask     —     warped  for the right breast are obtained. The warped images B L     —     mask     —     warped  for the left breast and B R     —     mask     —     warped  for the right breast in the atlas space have the shape of baseline breast atlas shape B a     —     v , hence a one-to-one correspondence exists between pixels of warped images B L     —     mask     —     warped  and B R     —     mask     —     warped . 
         [0104]    A typical mass lesion/anomaly/cancer structure will appear as a cluster of high intensity pixels (appearing as a bright splotch) on a mammogram. 
         [0105]    Comparative breast analysis unit  580  receives the warped images B L     —     mask     —     warped  and B R     —     mask     —     warped  and subtracts them by, for example, subtracting corresponding pixel intensities. A subtraction image is obtained. Anomalies present in only one breast will appear in the subtraction image. Hence, cancer structures/mass lesions present in one breast, and which have no equivalent structures in the other breast, will be visible in the subtraction image. 
         [0106]    The left breast mask image B L     —     mask  and the right breast mask image B R     —     mask  may be warped either to the baseline breast atlas shape B a     —     v  (such as, for example, a mean breast shape) associated with the view v, or to the probabilistic cancer atlas A v  associated with view v. If the left breast mask image and the right breast mask image are warped to the probabilistic cancer atlas A v , the space searched for anomalies can be limited. In particular, the search space can be limited by performing image subtraction only for areas with a high prior likelihood of cancer, as indicated by the probabilistic cancer atlas. 
         [0107]    Comparative breast analysis unit  580  may also compare and subtract warped images of the same breast, taken at different times. For example, a warped image obtained from a mammogram taken a year ago, can be compared and subtracted from a warped image obtained from a mammogram taken 5 years ago, to observe structural changes that have occurred in the breast. 
         [0108]    Image processing unit  35 B hence provides a technique of warping different breast shapes into the same space and performing comparative analysis on the breast shapes in a common atlas space. 
         [0109]    Image operations unit  125 B, shape registration unit  135 B, atlas warping unit  570 , comparative breast analysis unit  580 , and probabilistic atlas reference unit  155  are software systems/applications. Image operations unit  125 B, shape registration unit  135 B, atlas warping unit  570 , comparative breast analysis unit  580 , and probabilistic atlas reference unit  155  may also be purpose built hardware such as FPGA, ASIC, etc. 
         [0110]      FIG. 10A  illustrates aspects of the operation of warping a cancer formation to an atlas for comparative breast analysis according to a second embodiment of the present invention illustrated in  FIG. 9 . A new breast image is warped onto a baseline breast atlas shape. A cancer formation located in the new breast image will also be warped onto the baseline breast atlas shape, indicating where on the baseline breast atlas shape the corresponding cancer formation is located. 
         [0111]      FIG. 10B  illustrates aspects of the operation of cancer detection using comparative breast analysis according to a second embodiment of the present invention illustrated in  FIG. 9 . As shown in  FIG. 10B , the right breast view of a person has a cancer formation, while the left breast view of the same person does not have cancer. The shapes of the right and left breast are different. The difference in breast shapes could be due to anatomical variability, and also to the presence of the cancer in the right breast, which increases the size of the right breast. 
         [0112]    Both right and left breasts are warped onto the baseline breast atlas shape, using transformations T 1  and T 2 . Even though the left and right breasts are different view mammograms, they are a pair of mirror images. For example, the MLL view is the mirror image of the MLR view about the vertical axis; hence one baseline breast atlas shape can be used for both MLL and MLR view mammograms. Similarly, the CCL view is the mirror image of the CCR view about the vertical axis; hence one baseline breast atlas shape can be used for both CCL and CCR view mammograms. In other words, the baseline breast atlas shapes for mirror images, such as MLL and MLR, are the same. By comparing the baseline breast atlas shapes W 1  and W 2  obtained by warping the right and left breasts, the cancer formation is detected, as it is present inside baseline breast atlas shape W 1  but not inside identical baseline breast atlas shape W 2 . When W 2  is subtracted from W 1  in the baseline breast atlas space, the cancer formation is obtained. 
         [0113]      FIG. 11  is a block diagram of an image processing unit  35 C for cancer detection using a probabilistic atlas to obtain a cancer probability image according to a third embodiment of the present invention illustrated in  FIG. 2 . As shown in  FIG. 11 , the image processing unit  35 C includes the following components: an image operations unit  620 A; a baseline shape unit  710 ; a shape parameterization unit  720 ; a deformation analysis unit  730 ; a training shape registration unit  740 ; an atlas output unit  750 ; an image operations unit  125 A; a shape registration unit  135 A; an atlas warping unit  301 ; a probability image extraction unit  303 ; and a probabilistic atlas reference unit  155 . Image operations unit  620 A, baseline shape unit  710 , shape parameterization unit  720 , deformation analysis unit  730 , training shape registration unit  740 , and atlas output unit  750  are included in a training system  772 . Image operations unit  125 A, shape registration unit  135 A, atlas warping unit  301 , probability image extraction unit  303 , and probabilistic atlas reference unit  155  are included in an operation system  778 . 
         [0114]    Operation of the image processing unit  35 C can generally be divided into two stages: (1) training; and (2) operation for breast cancer probability estimation. 
         [0115]    The principles involved in the training stage have been described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. In accordance with this third embodiment illustrated in  FIG. 11 , the image operations unit  620 A, baseline shape unit  710 , shape parameterization unit  720 , deformation analysis unit  730 , training shape registration unit  740 , and atlas output unit  750  train to generate a shape model and a probabilistic cancer atlas for breast shapes. The knowledge accumulated through training by training system  772  is sent to probabilistic atlas reference unit  155 . 
         [0116]    In accordance with this third embodiment of the present invention, the image operations unit  125 A, the shape registration unit  135 A, the atlas warping unit  301 , the probability image extraction unit  303 , and the probabilistic atlas reference unit  155  may function in like manner to the corresponding elements of the first embodiment illustrated in  FIG. 4 . During regular operation of image processing unit  35 C, probabilistic atlas reference unit  155  provides reference data training knowledge to shape registration unit  135 A, atlas warping unit  301  and probability image extraction unit  303 , for extracting an information about cancer probability in new breast images. The principles involved in the operation for breast cancer probability extraction for new breast images have been described in  FIGS. 4 ,  5 ,  6 ,  7 , and  8 . 
         [0117]    During the training stage, image operations unit  620 A receives a set of training breast images from image input unit  25 , performs preprocessing and preparation operations on the breast images, creates training breast mask images, and stores/extracts information about breast images, such as view of mammograms. Additional details regarding operation of image operations unit  620 A are described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. Image operations unit  620 A may create breast mask images by extracting breast borders using methods described in the US patent application titled “Method and Apparatus for Breast Border Detection”, application Ser. No. 11/366,495, by Daniel Russakoff and Akira Hasegawa, filed on Mar. 3, 2006, the entire contents of which are hereby incorporated by reference. Other breast border detection techniques can also be used by image operations unit  620 A to obtain shape mask images for breast images. 
         [0118]    Baseline shape unit  710  receives training breast mask images from image operations unit  620 A, and generates a baseline breast atlas shape such as, for example, a mean breast shape, from the training breast mask images. Baseline shape unit  710  may align the centers of mass of the training breast mask images. The alignment of centers of mass of training breast mask images results in a probabilistic map in which the brighter a pixel is, the more likely it is for the pixel to appear in a training breast mask image. A probability threshold may then be applied to the probabilistic map, to obtain a baseline breast atlas shape, such as, for example, a mean breast shape. Additional details regarding operation of baseline shape unit  710  are described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0119]    Shape parameterization unit  720  receives the training breast mask images and the baseline breast atlas shape, and warps the training breast mask images onto the baseline breast atlas shape, to define parameterization of breast shape. Shape parameterization unit  720  may use shape parameterization techniques adapted from “Automatic Generation of Shape Models Using Nonrigid Registration with a Single Segmented Template Mesh” by G. Heitz, T. Rohlfing and C. Maurer, Proceedings of Vision, Modeling and Visualization, 2004, the entire contents of which are hereby incorporated by reference. Control points may be placed along the edges of the baseline breast atlas shape. A deformation grid is generated using the control points. Using the deformation grid, the control points are warped onto training breast mask images. Shape information for training breast mask images is then given by the corresponding warped control points together with centers of mass of the shapes defined by the warped control points. Warping of control points from the baseline breast atlas shape onto training breast mask images may be performed by non-rigid registration, with B-splines transformations used to define warps from baseline breast atlas shape to training breast mask images. Shape parameterization unit  720  may perform non-rigid registration using techniques discussed in “Automatic Construction of 3-D Statistical Deformation Models of the Brain Using Nonrigid Registration”, by D. Rueckert, A. Frangi and J. Schnabel, IEEE Transactions on Medical Imaging, 22(8), p. 1014-1025, August 2003, the entire contents of which are hereby incorporated by reference. Shape parameterization unit  720  outputs shape representations for training breast mask images. Additional details regarding operation of shape parameterization unit  720  are described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0120]    Deformation analysis unit  730  uses breast shape parameterization results to learn a shape model that describes how shape varies from breast to breast. Using representations of shape for the training breast mask images, deformation analysis unit  730  finds the principal modes of deformation between the training breast mask images and the baseline breast atlas shape. Deformation analysis unit  730  may use Principal Components Analysis (PCA) techniques to find the principal modes of deformation. The principal components obtained from PCA represent modes of deformation between training breast mask images and the baseline breast atlas shape. Additional details regarding operation of deformation analysis unit  730  are described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0121]    The baseline breast atlas shape and the modes of deformation between training breast mask images and the baseline breast atlas shape, define a shape model. A shape model can be obtained for each mammogram view. Shape model information is sent to probabilistic atlas reference unit  155 , to be used during operation of image processing unit  35 C. 
         [0122]    Training shape registration unit  740  receives data that defines the shape model. Training shape registration unit  740  then fits training breast mask images with their correct shape representations, which are linear combinations of the principal modes of shape variation. Shape registration unit  740  may use the downhill simplex method, also known as the Nelder-Mead or the amoeba algorithm, to optimize parameters of the shape model for each training breast mask image in the training dataset, and optimally describe training breast mask images using the shape model. Additional details regarding operation of training shape registration unit  740  are described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0123]    Atlas output unit  750  receives from training shape registration unit  740  the results of shape registration for the set of training breast mask images analyzed. The set of training breast mask images have cancer formations that have been previously localized. Using shape registration results, the localized cancer formations in the training breast mask images are mapped from the training breast mask images onto the baseline breast atlas shape. An atlas is created with locations of the cancer formations in the baseline breast atlas shape. Since a large number of training breast mask images with previously localized cancer formations are used, the atlas is a probabilistic atlas that gives the probability of cancer formations for each pixel inside the baseline breast atlas shape. One probabilistic cancer atlas may be generated for each mammogram view. The probabilistic cancer atlases for various breast views are sent to probabilistic atlas reference unit  155 , to be used during operation of image processing unit  35 C. Additional details regarding operation of atlas output unit  750  are described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0124]    Image operations unit  620 A, baseline shape unit  710 , shape parameterization unit  720 , deformation analysis unit  730 , training shape registration unit  740 , atlas output unit  750 , image operations unit  125 A, shape registration unit  135 A, atlas warping unit  301 , probability image extraction unit  303 , and a probabilistic atlas reference unit  155  are software systems/applications. Image operations unit  620 A, baseline shape unit  710 , shape parameterization unit  720 , deformation analysis unit  730 , training shape registration unit  740 , atlas output unit  750 , image operations unit  125 A, shape registration unit  135 A, atlas warping unit  301 , probability image extraction unit  303 , and a probabilistic atlas reference unit  155  may also be purpose built hardware such as FPGA, ASIC, etc. 
         [0125]      FIG. 12  is a block diagram of an image processing unit  35 D for cancer detection using comparative breast analysis according to a fourth embodiment of the present invention illustrated in  FIG. 2 . As shown in  FIG. 12 , the image processing unit  35 D includes the following components: an image operations unit  620 A; a baseline shape unit  710 ; a shape parameterization unit  720 ; a deformation analysis unit  730 ; a training shape registration unit  740 ; an atlas output unit  750 ; an image operations unit  125 B; a shape registration unit  135 B; an atlas warping unit  570 ; a comparative breast analysis unit  580 ; and a probabilistic atlas reference unit  155 . Image operations unit  620 A, baseline shape unit  710 , shape parameterization unit  720 , deformation analysis unit  730 , training shape registration unit  740 , and atlas output unit  750  are included in a training system  772 . Image operations unit  125 B, shape registration unit  135 B, atlas warping unit  570 , comparative breast analysis unit  580 , and probabilistic atlas reference unit  155  are included in an operation system  878 . 
         [0126]    Operation of the image processing unit  35 D can generally be divided into two stages: (1) training; and (2) operation for breast cancer probability estimation. 
         [0127]    The principles involved in the training stage have been described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. In accordance with this fourth embodiment illustrated in  FIG. 12 , the image operations unit  620 A, baseline shape unit  710 , shape parameterization unit  720 , deformation analysis unit  730 , training shape registration unit  740 , and atlas output unit  750  train to generate a shape model and a probabilistic cancer atlas for breast shapes, as was also described at  FIG. 11 . The knowledge accumulated through training by training system  772  is sent to probabilistic atlas reference unit  155 . 
         [0128]    In accordance with this fourth embodiment of the present invention, the image operations unit  125 B, shape registration unit  135 B, atlas warping unit  570 , comparative breast analysis unit  580 , and probabilistic atlas reference unit  155  may function in like manner to the corresponding elements of the second embodiment illustrated in  FIG. 9 . During regular operation of image processing unit  35 D, probabilistic atlas reference unit  155  provides reference data training knowledge to shape registration unit  135 B, atlas warping unit  570  and comparative breast analysis unit  580  for cancer detection using comparative breast analysis of new breast images. The principles involved in the operation for comparative breast analysis for breast cancer detection have been described in  FIGS. 9 ,  5 ,  6 ,  8 ,  10 A and  10 B. 
         [0129]    Image operations unit  620 A, baseline shape unit  710 , shape parameterization unit  720 , deformation analysis unit  730 , training shape registration unit  740 , atlas output unit  750 , image operations unit  125 B, shape registration unit  135 B, atlas warping unit  570 , comparative breast analysis unit  580 , and probabilistic atlas reference unit  155  are software systems/applications. Image operations unit  620 A, baseline shape unit  710 , shape parameterization unit  720 , deformation analysis unit  730 , training shape registration unit  740 , atlas output unit  750 , image operations unit  125 B, shape registration unit  135 B, atlas warping unit  570 , comparative breast analysis unit  580 , and probabilistic atlas reference unit  155  may also be purpose built hardware such as FPGA, ASIC, etc. 
         [0130]    The methods and apparatuses described in the current application enable comparison of high-level shapes of two distinct breasts, for detection of cancer. The methods and apparatuses described in the current application obtain data for probability of cancer in breasts, using a probabilistic atlas with probabilities of cancer in a baseline breast atlas shape. The methods and apparatuses described in the current application are automatic and can be used in computer-aided detection of cancer in breasts. The methods and apparatuses described in the current application can use shape models for other anatomical parts besides breasts, and probabilistic atlases for other anomalous structures besides cancer structures. For example, the methods and apparatuses described in the current application can be used for detection of lung and colon cancer. The methods and apparatuses described in the current application can automatically detect other anomalous structures besides cancer structures, for other anatomical parts besides breasts. The methods and apparatuses described in the current application can use shape models for anatomical parts and probabilistic atlases for anomalous structures, generated using techniques described in the co-pending non-provisional application titled “Method and Apparatus for Probabilistic Atlas Based on Shape Modeling Technique”, the entire contents of which are hereby incorporated by reference. 
         [0131]    Although detailed embodiments and implementations of the present invention have been described above, it should be apparent that various modifications are possible without departing from the spirit and scope of the present invention.