3-D shape estimation and image restoration : exploiting by Paolo Favaro

By Paolo Favaro

In the components of snapshot processing and desktop imaginative and prescient, there's a specific want for software program that may, given an unfocused or motion-blurred snapshot, infer the third-dimensional form of a scene. This booklet describes the analytical techniques that move into designing such software program, delineates the choices open to programmers, and provides unique algorithms. Written for readers with pursuits in photograph processing and desktop imaginative and prescient and with backgrounds in engineering, technological know-how or arithmetic, this hugely useful text/reference is offered to complicated scholars or people with a level that comes with uncomplicated linear algebra and calculus courses.

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47) j where V1,2 is the spatial velocity of the jth object; occasionally we omit the argument 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 .

5) We now turn our attention to whether the problem of shape from defocus can be solved. In order to do so, we need to understand what “solving” means, as there are many facets to the problem. We start by assuming that the radiance can be chosen arbitrarily (as in an active illumination scenario) and ask whether shape can be recovered unambiguously, regardless of the algorithm used. 2 Observability of shape Suppose we have a white Lambertian (Appendix A) scene that we can illuminate as we wish, or, even simpler, that we can directly choose its radiance.

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, B) → A, B = Trace{AB T } 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 .

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