Correspondence search using Delaunay triangulation Rishu Gupta

Table of Contents  Introduction  Feature Point Extraction  Delaunay Triangulation  Edge extraction and Length Calculation  Edge length comparison  Nearest neighbor calculation  Correlation  Result

Feature Point  The feature points for the image can be the point with some characteristics like corner, high intensity point etc..  It can be calculated with the help of many techniques.  Harris Corner Detector  SIFT (Shift Invariant Feature Transform)  SURF(Speeded Up Robust Features)

Harris Corner Detection-Feature Point Change of intensity for the shift [u,v]: Intensity Shifted intensity Window function or Window function w(x,y) = Gaussian1 in window, 0 outside

Delaunay Triangulation  The historical technique of computational geometry used for explaining the topology of the scattered feature points. The topological structure for the feature points is explained with the help of the Delaunay Triangulation

Edge Extraction and Length Calculation  One edge from the first image is selected and the length is calculated and stored.  The edges from the second image are extracted and length is calculated and comparison is performed on the basis of edge length.

Nearest Neighbor Calculation  The first neighborhood points of the edges are calculated using the simplex method. First neighborhood points are the points which are directly linked to the edges.

Correlation of the Competent Matches  After the computation of the nearest neighborhood matches the correlation is performed with the gray intensity values of the images.  Before computing the correlation the gray values of the images are normalized.  The general formula for normalized correlation is:

 The competent edge with the maximum value for the correlation is taken as the appropriate edge and the neighborhood points are the exact correspondence points.

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