Polygonal Modeling of Contours Using the Turning Angle Function

Several types of signatures have been defined to facilitate the analysis of contours of objects. The turning angle function of a given contour may be used as a signature to analyze the contour. We propose a method to use the turning angle function to derive a polygonal model of the given contour in such a manner as to preserve the important details in the contour. We demonstrate the usefulness of the resulting polygonal model in deriving efficient shape factors, and illustrate its application in the classification of breast masses. Most malignant breast tumors, as seen in mammograms, have rough and spiculated contours; on the contrary, benign masses usually have smooth, round, or oval contours. An index of spiculation derived from the proposed polygonal model was tested with a set of 111 contours of which 65 are related to benign masses and 46 are related to malignant tumors. A high classification accuracy of 0.92 was obtained, in terms of the area under the receiver operating characteristics curve, with a data compression of 0.025 on average.

[1]  Rangaraj M. Rangayyan,et al.  Detection of breast masses in mammograms by density slicing and texture flow-field analysis , 2001, IEEE Transactions on Medical Imaging.

[2]  Ian W. Ricketts,et al.  The Mammographic Image Analysis Society digital mammogram database , 1994 .

[3]  Moncef Gabbouj,et al.  Similarity retrieval of occluded shapes using wavelet-based shape features , 2000, SPIE Optics East.

[4]  Rajiv Mehrotra,et al.  Similar-Shape Retrieval in Shape Data Management , 1995, Computer.

[5]  Cyrus Shahabi,et al.  Image retrieval by shape: a comparative study , 2000, 2000 IEEE International Conference on Multimedia and Expo. ICME2000. Proceedings. Latest Advances in the Fast Changing World of Multimedia (Cat. No.00TH8532).

[6]  Longin Jan Latecki,et al.  Application of planar shape comparison to object retrieval in image databases , 2002, Pattern Recognit..

[7]  Rangaraj M. Rangayyan,et al.  Content-based retrieval and analysis of mammographic masses , 2005, J. Electronic Imaging.

[8]  Maryellen L. Giger,et al.  Computerized analysis of multiple-mammographic views: potential usefulness of special view mammograms in computer-aided diagnosis , 2001, IEEE Transactions on Medical Imaging.

[9]  Esther M. Arkin,et al.  An efficiently computable metric for comparing polygonal shapes , 1991, SODA '90.

[10]  Theodosios Pavlidis,et al.  Segmentation of Plane Curves , 1974, IEEE Transactions on Computers.

[11]  Stefan M. Rüger,et al.  Combining Features for Content-Based Sketch Retrieval - A Comparative Evaluation of Retrieval Performance , 2002, ECIR.

[12]  N. Petrick,et al.  Classification of mass and normal breast tissue on digital mammograms: multiresolution texture analysis. , 1995, Medical physics.

[13]  Theodosios Pavlidis,et al.  Computer Recognition of Handwritten Numerals by Polygonal Approximations , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  Rangaraj M. Rangayyan,et al.  Fractal Analysis of Contours of Breast Masses in Mammograms , 2007, Journal of Digital Imaging.

[15]  Rangaraj M. Rangayyan,et al.  Parabolic Modeling and Classification of Breast Tumors , 1997, Int. J. Shape Model..

[16]  R. Rangayyan,et al.  Boundary modelling and shape analysis methods for classification of mammographic masses , 2000, Medical and Biological Engineering and Computing.

[17]  Rangaraj M. Rangayyan,et al.  Measures of acutance and shape for classification of breast tumors , 1997, IEEE Transactions on Medical Imaging.

[18]  Sven Loncaric,et al.  A survey of shape analysis techniques , 1998, Pattern Recognit..

[19]  M L Giger,et al.  Computerized classification of benign and malignant masses on digitized mammograms: a study of robustness. , 2000, Academic radiology.

[20]  C. Metz.  Basic principles of ROC analysis. , 1978, Seminars in nuclear medicine.

[21]  Lubomir M. Hadjiiski,et al.  Improvement of mammographic mass characterization using spiculation meausures and morphological features. , 2001, Medical physics.

[22]  Ari Visa,et al.  Shape recognition of irregular objects , 1996, Other Conferences.

[23]  Jose A. Ventura,et al.  Segmentation of two-dimensional curve contours , 1992, Pattern Recognit..