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SIAM J. Appl. Math. 68, pp. 599-618 (20 pages)
A Phase Field Method for Joint Denoising, Edge Detection, and Motion Estimation in Image Sequence Processing
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Add to FacebookThe estimation of optical flow fields from image sequences is incorporated in a Mumford–Shah approach for image denoising and edge detection. Possibly noisy image sequences are considered as input and a piecewise smooth image intensity, a piecewise smooth motion field, and a joint discontinuity set are obtained as minimizers of the functional. The method simultaneously detects image edges and motion field discontinuities in a rigorous and robust way. It is able to handle information on motion that is concentrated on edges. Inherent to it is a natural multiscale approximation that is closely related to the phase field approximation for edge detection by Ambrosio and Tortorelli. We present an implementation for two-dimensional image sequences with finite elements in space and time. This leads to three linear systems of equations, which have to be solved in a suitable iterative minimization procedure. Numerical results and different applications underline the robustness of the approach presented.
© 2007 Society for Industrial and Applied Mathematics
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Received December 11, 2006
Accepted August 24, 2007
Published online December 07, 2007
Accepted August 24, 2007
Published online December 07, 2007
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