By Paolo Favaro
Within the parts of snapshot processing and machine imaginative and prescient, there's a specific desire for software program that could, given an unfocused or motion-blurred snapshot, infer the 3-dimensional form of a scene. This ebook describes the analytical approaches that pass into designing such software program, delineates the choices open to programmers, and offers unique algorithms. Written for readers with pursuits in photo processing and computing device imaginative and prescient and with backgrounds in engineering, technology or arithmetic, this hugely sensible text/reference is out there to complicated scholars or people with a level that comes with easy linear algebra and calculus classes.
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Extra resources for 3-D Shape Estimation and Image Restoration: Exploiting Defocus and Motion-Blur
F, f . Consider also the case where Ω is a discrete with the norm f = domain, that is, Ω ≡ RN ×M , where N is the number of columns of the CCD and M the number of rows. Because we collect K images by changing focus settings, the multifocal vector image I ∈ RK×N ×M . Let W = KM N . Then, we introduce the 2 space RW ∼ RK×N ×M , with the inner product ·, · : RW × RW −→ R deﬁned by . 13) A, A . If we interpret points in RW as W -dimensional and norm |A| = . vectors, then the inner product is the usual a, b = aT b with a, b ∈ RW .
1998]. The solution u can also be represented via Green’s function. 30) is deﬁned . 30) with initial conditions u(y, 0) = δ(x − y), and δ(·) is Dirac’s delta. The function G satisﬁes the equation u(x, ˙ t) = c u(x, t) u(x, 0) = r(x) u(y, t) = G(y, x, t)u(x, 0)dx = G(y, x, t)r(x)dx. 30). This explains why we so cherish Gaussians as point-spread functions, beyond the discussion leading to this section. Gaussians establish the equivalence between 5 Notational mea culpa: we use u for the solution of the isotropic heat equation as is customary in the PDE literature.
Unfortunately we cannot just ignore them. The reader who tries to test the 3-D reconstruction algorithms described in the next chapters to images obtained simply by changing the focus setting in a commercial camera will be disappointed to see that they fail to work because the image formation model above is not accurate. Fortunately, such artifacts are easy to eliminate by simple preprocessing or calibration procedures. 1, we discuss a simple calibration procedure that the reader can easily implement.
3-D Shape Estimation and Image Restoration: Exploiting Defocus and Motion-Blur by Paolo Favaro