An Algorithm for Associating the Features of Two Images / G. L. Scott, H. C. Longuet-Higgins A direct method for stereo correspondence based on singular value decomposition / M. Pilu. CSE 291 Seminar Presentation Andrew Cosand ECE CVRR. Outline. Correspondence Problem Examples Discrepancy
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CSE 291 Seminar Presentation
Which features in image A correspond to features in image B?
This task is trivial for humans, but difficult for computers.
Trinocular camera captures 3 images, horizontally and vertically offset.
Feature correspondence is used to extract depth information from stereo images
Corresponding features are tracked through sequential images to determine object or camera motion.
Object Motion Only
Small scale discrepancy constrains corresponding features to be close together.
Large scale discrepancy allows widely separated features.
Requires relationships between points
Define a distance metric between features
Create matrix of relationships for all possible feature pairs
SVD factors a matrix into the product of two orthogonal matrices and a diagonal matrix of singular values (eigenvalues).
G = TDU, G is m-by-n,
Use Singular Value Decomposition on matrix. G = TDU
Set diagonal elements of D to 1, ‘recover’ relationship matrix.
P = TIU = TU
Eliminating singular matrix rescales data in feature space, essentially sphereing it.
Largest feature in row and column indicates mutual best match (correspondence)
Gaussian Distance is essentially a kernel
Modify relationship metric to include gray-level correlation.
Gij = (e-(Cij – 1)2/22) e(-rij2/22)
Gij = ((Cij+1)/2) e(-rij2/22)
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