A statistical approach to multi-scale edge detection

Abstract We propose a statistical approach to combining edge cues at multiple scales using data driven probability distributions. These distributions are learnt on the Sowerby and South Florida datasets which include the ground truth positions of edges. We evaluate our results using Chernoff information and conditional entropy. Our results demonstrate the effectiveness of multi-scale processing and validate previous heuristics such as coarse-to-fine edge tracking.

[1]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Sean Dougherty,et al.  Edge Detector Evaluation Using Empirical ROC Curves , 2001, Comput. Vis. Image Underst..

[3]  P. J. Burt,et al.  Fast Filter Transforms for Image Processing , 1981 .

[4]  Alan L. Yuille,et al.  Statistical Edge Detection: Learning and Evaluating Edge Cues , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Alan L. Yuille,et al.  Order Parameters for Detecting Target Curves in Images: When Does High Level Knowledge Help? , 2004, International Journal of Computer Vision.

[6]  Yoshua Bengio,et al.  Pattern Recognition and Neural Networks , 1995 .

[7]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[8]  Alan L. Yuille,et al.  Fundamental bounds on edge detection: an information theoretic evaluation of different edge cues , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[9]  Daniel Snow,et al.  Efficient optimization of a deformable template using dynamic programming , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[10]  David Mumford,et al.  Filtering, Segmentation and Depth , 1993, Lecture Notes in Computer Science.

[11]  Alan L. Yuille,et al.  Scaling Theorems for Zero Crossings , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Alan L. Yuille,et al.  Order parameters for minimax entropy distributions: when does high level knowledge help? , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[13]  J. Koenderink The structure of images , 2004, Biological Cybernetics.

[14]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[15]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[16]  Alan L. Yuille,et al.  Fundamental Limits of Bayesian Inference: Order Parameters and Phase Transitions for Road Tracking , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Donald Geman,et al.  An Active Testing Model for Tracking Roads in Satellite Images , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[19]  Andrew P. Witkin,et al.  Uniqueness of the Gaussian Kernel for Scale-Space Filtering , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  P. Burt Fast filter transform for image processing , 1981 .

[21]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .