A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple-order derivatives for detecting local image characteristics
Computer Vision, Graphics, and Image Processing
Frequency Domain Analysis and Synthesis of Image Pyramid Generating Kernels
IEEE Transactions on Pattern Analysis and Machine Intelligence
Some advanced topics in filter design
Advanced topics in signal processing
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Local Visual Operator Which Recognizes Edges and Lines
Journal of the ACM (JACM)
Digital Step Edges from Zero Crossing of Second Directional Derivatives
IEEE Transactions on Pattern Analysis and Machine Intelligence
Static topographic modeling for facial expression recognition and analysis
Computer Vision and Image Understanding
The study of the auto color image segmentation
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part II
Full length article: Differentiation by integration using orthogonal polynomials, a survey
Journal of Approximation Theory
Hybrid method based on topography for robust detection of iris center and eye corners
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)
| Hi-index | 0.00 |
Computation of the derivatives of an image defined on a lattice structure is of paramount importance in computer vision. The solution implies least square fitting of a continuous function to a neighborhood centered on the site where the value of the derivative is sought. We present a systematic approach to the problem involving orthonormal bases spanning the vector space defined over the neighborhood. Derivatives of any order can be obtained by convolving the image with a priori known filters. We show that if orthonormal polynomial bases are employed the filters have closed form solutions. The same filter is obtained when the fitted polynomial functions have one consecutive degree. Moment preserving properties, sparse structure for some of the filters, and relationship to the Marr-Hildreth and Canny edge detectors are also proven. Expressions for the filters corresponding to fitting polynomials up to degree six and differentiation orders up to five, for the cases of unweighted data and data weighted by the discrete approximation of a Gaussian, are given in the appendices.