3-D Shape Estimation and Image Restoration: Exploiting by Paolo Favaro

By Paolo Favaro

Within the parts of picture processing and laptop imaginative and prescient, there's a specific desire for software program which can, given an unfocused or motion-blurred photograph, infer the 3-dimensional form of a scene. This booklet describes the analytical techniques that cross into designing such software program, delineates the choices open to programmers, and provides unique algorithms. Written for readers with pursuits in photograph processing and machine imaginative and prescient and with backgrounds in engineering, technology or arithmetic, this hugely sensible text/reference is on the market to complex scholars or people with a level that comes with simple linear algebra and calculus classes.

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Typically, for convenience, one assumes either a Gaussian or a Poisson model. In the rest of this book we explore both models, and derive inference algorithms that guarantee optimality with respect to the noise model above. 10) allows us to treat Gaussian and Poisson noise in a unified manner. 9) may seem complex at first, especially for the reader not comfortable with integrals. 9) as a matrix equation, using properties of Hilbert spaces. This analogy is useful per se, and it is exploited in Chapter 4 to design reconstruction algorithms.

By assuming that the surface s is smooth, we can relate again the diffusion coefficient c to the space-varying blurring coefficient σ via σ 2 (x) 2tc(x). 37) Therefore, we can represent the image of a nonequifocal scene as the solution of a partial differential equation, where the diffusion coefficient c is related to the focus setting. This interpretation comes in handy in Chapters 6 and 8, where we tap efficient numerical schemes to solve partial differential equations in order to implement shape reconstruction algorithms.

48) 34 2. 3 (On capturing motion-blurred images). How can we capture motion-blurred images? Some consumer cameras come equipped with so-called auto-bracketing, that is, the capability of automatically capturing multiple images of the same scene with different exposures during the same session. However, even a cheaper automatic camera can be used, by following a simple procedure. First collect a sequence of images. Time averaging the sequence simulates a long shutter interval. For example, one could collect three images [J¯1 , J¯2 , J¯3 ], and then 3 consider J1 = J¯2 as one motion-blurred image and J2 = 1/3 i=1 J¯i as the second motion-blurred image.

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