By Paolo Favaro
Within the components of snapshot processing and machine imaginative and prescient, there's a specific want for software program which may, given an unfocused or motion-blurred photograph, infer the three-d form of a scene. This booklet describes the analytical methods that move into designing such software program, delineates the choices open to programmers, and provides unique algorithms. Written for readers with pursuits in picture processing and computing device imaginative and prescient and with backgrounds in engineering, technological know-how or arithmetic, this hugely functional text/reference is available to complex scholars or people with a level that comes with easy linear algebra and calculus classes.
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Additional resources for 3-D Shape Estimation and Image Restoration: Exploiting Defocus and Motion-Blur
45) ω(t). 46) where V1,2 is the vector made of the ﬁrst two components of the velocity V . 47) j is the spatial velocity of the jth object; occasionally we omit the arguwhere V1,2 ment x in νj (x, t) for simplicity. When velocity V (t) is constant, we also omit the j argument t. Notice that there is a scale ambiguity in determining the velocity V1,2 and the depth map s given the image velocity ν. This ambiguity can be resolved by assigning, for instance, the mean depth to a prescribed value. Finally, we arrive at the following model for the intensity of a motion-blurred image at a ﬁxed pixel y ∈ Ωj .
52) becomes the following inhomogeneous anisotropic diffusion equation: u(x, ˙ t) = ∇ · (D(x)∇u(x, t)) u(x, 0) = r(x). 54) and by including the shutter time interval ΔT˜ in the velocity vector V , we have D(x) = σ 2 (x)Id + v 2 ΔT˜ 2 j j V1,2 V1,2 s2 (x) T . 56) Notice that the diffusion tensor just deﬁned is made of two terms: σ 2 (x)Id and j j T (V1,2 ) /s2 (x). The ﬁrst term corresponds to the isotropic component of the V1,2 tensor, and captures defocus. The second term corresponds to the anisotropic component of the tensor, and captures motion blur.
4. 7. Real point-spread functions. One can get an approximate measurement of a PSF by taking an image of a small distant light source. For large apertures (top) the PSF is approximated by a smoothed version of a pillbox, but when the aperture becomes smaller (bottom) the PSF is better approximated by a Gaussian. and [Pentland, 1987], [Subbarao, 1988], and [Chaudhuri and Rajagopalan, 1999]). One can even modify the optical system by placing suitable photographic masks in front of the lens to make the PSF Gaussian.
3-D Shape Estimation and Image Restoration: Exploiting Defocus and Motion-Blur by Paolo Favaro