By Paolo Favaro
In the parts of photograph processing and machine imaginative and prescient, there's a specific desire for software program which may, given an unfocused or motion-blurred photograph, infer the 3-dimensional form of a scene. This booklet describes the analytical methods that cross into designing such software program, delineates the choices open to programmers, and offers 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 available to complicated scholars or people with a level that incorporates simple linear algebra and calculus courses.
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Additional info for 3-D shape estimation and image restoration : exploiting defocus and motion blur
Y, v, s)]. So, there is an entire equivalence class of pairs (s, r) that generate the same image I. Therefore, we need a method to select one particular object (s, r) from the equivalence class. One way to do so is to make use of additional structure of the problem. For instance, one could impose that the object be smooth or its depth and radiance positive. This can be done through a methodology called regularization, which we introduce in the next section and use throughout the rest of this book.
Therefore, again in principle, it is possible to reconstruct the shape of a scene uniquely. Consider two scenes with surfaces s and s , respectively. 40 3. Some analysis: When can 3-D shape be reconstructed from blurred images? 1. We say that a surface s is weakly indistinguishable from a surface s if, for all possible radiances r, there exists at least a radiance r such that Isr (y, v) = Isr (y, v) ∀y∈Ω ∀ v ∈ V. 6) Two surfaces are weakly distinguishable if they are not weakly indistinguishable.
Where σ is the standard deviation of the noise n. 28) so that sˆ, rˆ = arg max log(pn (J)) = arg min s,r s,r y∈Ω or, in the case of a continuous domain, sˆ, rˆ = arg min s,r Ω Isr (y) − J(y) 2 dy. 29) In the former case y∈Ω (Isr (y)−J(y))2 is the 2 norm of the difference between I and J, or 2 distance, whereas in the second case the integral is the L2 distance. In both cases we talk about a least-squares criterion, whose minimization yields the so-called least-squares solution. In the case of Poisson noise we write the probability pn as pn (J) = y∈Ω I(y)J(y) e−I(y) .