Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
The robust estimation of multiple motions: parametric and piecewise-smooth flow fields
Computer Vision and Image Understanding
Signal differentiation through a Green's function approach
Pattern Recognition Letters
From Photometric-Motion to Shape from Shading
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Data-Based Motion Simulation Through a Green's Function Approach
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Efficient, recursively implemented differential operator, with application to edge detection
Pattern Recognition Letters
Disparity estimation through Green’s functions of matching equations
Biological Cybernetics
Motion synthesis through 1D affine matching
Pattern Analysis & Applications
An iterative image registration technique with an application to stereo vision
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 2
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When filtering an input image, the Green's functions of matching equations are capable of inducing a broad class of motions, a property that has led to their use in several computer graphics and computer vision applications. In all such applications, the Green's functions of second-order differential equations have been considered, even though no justification has been given for their preference over simpler, first-order equations. Here we present a study of first-order one-dimensional matching equations, both in the uniform and in the affine motion models. Comparing their Green's functions with those of the corresponding second-order cases, we find evidence for the latter's superiority in motion synthesis. We also propose and discuss a general discretization scheme for Green's functions of one-dimensional matching equations, showing that the affine motion model is particularly sensitive to the sampling frequency. In this case, we advocate the use of area sampling, for allowing realistic motion simulations.