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By Yi-Tong Zhou

This monograph is an outgrowth of the authors' fresh study at the de­ velopment of algorithms for a number of low-level imaginative and prescient difficulties utilizing man made neural networks. particular difficulties thought of are static and movement stereo, computation of optical stream, and deblurring a picture. From a mathematical standpoint, those inverse difficulties are ill-posed in keeping with Hadamard. Researchers in computing device imaginative and prescient have taken the "regularization" method of those difficulties, the place one comes up with a suitable power or fee functionality and unearths a minimal. extra constraints equivalent to smoothness, integrability of surfaces, and renovation of discontinuities are extra to the price functionality explicitly or implicitly. reckoning on the character of the inver­ sion to be played and the limitations, the associated fee functionality may show numerous minima. Optimization of such nonconvex features may be very concerned. even if growth has been made in making ideas equivalent to simulated annealing computationally extra moderate, it's our view that you will frequently locate passable ideas utilizing deterministic optimization algorithms.

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EO i U for i = 0, 1, ... ,4. 12) which shows that the denominator of each term is a monotonically increasing function of the window size. Hence the variance of the output becomes smaller and smaller as the window size increases. Considering the effects of spatial quantization (as discussed in Chapter 3) and noise, a window with the size of three to seven pixels is recommended for natural images. 2 ESTIMATION OF CHAMFER DISTANCE VALUES The Chamfer distance value is defined as the distance from the non-edge pixel to the nearest edge pixel [BTBW77].

Since the first derivatives of the intensity function in homogeneous regions are small, the inputs are small and the neurons tend to take the same state as their neighbors because of the smoothness constraint. No doubt, the neurons near the boundary will be first affected by the neighbors corresponding to inhomogeneous regions. As the neurons corresponding to homogeneous regions are-sequentially updated, they will all be affected by the boundary conditions, thus surfaces in homogeneous regions can be interpolated.

20 . 00 , -20. - 40 . ~~~~--~--~--~--~------~--~--~~--~ O. 5. 10 . 15 . 20 . 25. )0 . 35 . 40 . 45 . 50 . 55 . 60 . 3. A section of a real image with amplitude bias 20 and 30 dB noise. (a) Intensity values of original and noisy images. (b) First order derivatives of intensity values of original and 'n oisy images. 3. Estimation of Intensity Derivatives Example 2: An amplitude bias of size 20 and white Gaussian noise corresponding to 20 dB SNR were added to the original image. 4 shows a section of the image taken from the same location as in Example 1.

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