By A. Ardeshir Goshtasby
A definitive and finished evaluation of present literature and the main leading edge applied sciences within the box of snapshot registration. rather well equipped and written. a must have for laptop experts.
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Additional info for 2-D and 3-D Image Registration: for Medical, Remote Sensing, and Industrial Applications
However, we see that if illuminations at (x1 , y) and (x2 , y) are different, gradients at (x1 , y) and (x2 , y) will be different too. If, instead of intensity 24 PREPROCESSING differences, intensity ratios are used as the metric to characterize scene changes, we will have f (x1 + 1, y) f (x1 , y) i(x1 + 1, y)p(x1 + 1, y) = . 29) by Rx [f (x1 , y)] = p(x1 + 1, y) . 30) Similarly, the property ratio at point (x2 , y) is determined from Rx [f (x2 , y)] = p(x2 + 1, y) . 31) As can be observed, if surface property at (x1 , y) is the same as that at (x2 , y) and the surface property at (x1 + 1, y) is the same as that at (x2 + 1, y), we will ﬁnd Rx [f (x1 , y)] = Rx [f (x2 , y)].
A Gaussian, however, approaches zero exponentially and in practice the inﬁnity may be replaced by a small number. Assuming the accuracy of a computer is and the standard deviations of all Gaussians are equal to σ, we ﬁnd √ − σ −2 ln √ ≤ j ≤ σ −2 ln . 41) In digital images, it has been shown  that it is sufﬁcient to vary j in the range [-5,5]. Using larger values of j will not change the curve ﬁtting result. A nice property of this curve is that it does not require the solution of a system of equations to obtain it.
Smoothing or convolving an image with a Gaussian and then determining its Laplacian is the same as convolving the image with the Laplacian of Gaussian (LoG). 19) where denotes convolution. 19), G(x, y) can be replaced with G(x)G(y); therefore, the LoG of an image can be computed from LoG[f (x, y)] = ∂ 2 G(x) ∂x2 G(y) f (x, y) + G(x) ∂ 2 G(y) ∂y 2 f (x, y). 20) IMAGE SEGMENTATION 19 Edge detection by the LoG operator was proposed by Marr and Hildreth  in a pioneering paper on edge detection.
2-D and 3-D Image Registration: for Medical, Remote Sensing, and Industrial Applications by A. Ardeshir Goshtasby