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

By Paolo Favaro

In the components of photo processing and machine imaginative and prescient, there's a specific want for software program which could, given an unfocused or motion-blurred photo, infer the third-dimensional form of a scene. This e-book describes the analytical procedures that pass into designing such software program, delineates the choices open to programmers, and offers 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 functional text/reference is available to complicated scholars or people with a level that incorporates uncomplicated linear algebra and calculus courses.

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20) and ∇s(x) denotes the gradient of s with respect to x, as we derive in Ap. pendix A. For typical values of u0 = 1/F − 1/v and D, it is easy to see that the term ∇s(x)T (yu0 /v + x) can be neglected as long as the surface is sufficiently smooth. By doing this, we obtain h(y, x) = u20 1 π(D/2)2 |s(x)−u0 |2 0 ∀x∈Ψ ∀ x ∈ Ψ. 21) reduces to the pillbox kernel that we have discussed in the previous section. 1 Image formation nuisances and artifacts Commercial cameras allow changing the focus setting by moving the lens relative to the sensor.

Basic models of image formation We now resume our physical analogy and consider the case of a flat (equifocal) scene. 1 Equifocal imaging as isotropic diffusion Suppose our scene is a flat metal plate, with a heat distribution corresponding to its radiance; that is, the temperature at a point represents the radiant energy. Then blurring can be simulated by heat diffusing on the plate, which is governed, assuming the plate to be homogeneous, by the so-called isotropic heat equation. 30) ∀ x ∈ R2 .

30) is a function of space and time, whereas the optical setting u is a scalar value. 4. 32). Notice that the diffusion coefficient c and the time variable t are determined up to a common factor, which is easily resolved by fixing a nominal time, say t = 1/2. Now, what about scenes that are not equifocal? Does the analogy of a homogeneous metal plate still hold? 2 that, when the surface s is not an equifocal plane, the corresponding PSF is in general shift-varying, so the interpretation of the imaging process as the solution of the heat equation does not hold.

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