By Paolo Favaro

ISBN-10: 1846281768

ISBN-13: 9781846281761

ISBN-10: 1846286883

ISBN-13: 9781846286889

In the components of photograph processing and desktop 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 tactics that pass into designing such software program, delineates the choices open to programmers, and provides unique algorithms. Written for readers with pursuits in snapshot processing and laptop imaginative and prescient and with backgrounds in engineering, technology or arithmetic, this hugely sensible text/reference is out there to complex scholars or people with a level that incorporates simple linear algebra and calculus courses.

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Extra resources for 3-D shape estimation and image restoration : exploiting defocus and motion blur

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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 . 6), can be represented 20 2. Basic models of image formation by an operator Hs , Hs : L2 −→ RW ; r → I = Hs r. 6), one that is reminiscent of a linear system of equations, represented in matrix form. The following paragraph introduces operators that are useful in Chapter 4.

1. 1. 2 Band-limited radiances and degree of resolution In this section we analyze the observability of shape when the radiance is fixed once and for all. In order to make the analysis simple, we are forced to make somewhat unrealistic assumptions. 3. 1. Harmonic radiances are unaffected by focus setting. We show an image of a planar scene with two patches that have harmonic radiance (I(y1 , y2 ) = y22 − y12 on the top row, and I(y1 , y2 ) = y2 on the second row), and two patches that have a nonharmonic radiance in the third and fourth rows.

When there are no positivity constraints, Csisz´ar argues that the only consistent choice of discrepancy criterion is the least-squares distance. We always measure images on a discrete domain, so in both cases we measure the discrepancy on Ω ⊂ Z 2 , which is reflected in the algorithms described in Chapters 4 and 5. However, in certain cases it is easier to neglect the discretization of the domain and assume that the images are defined in the continuum Ω ⊂ R2 . This is the approach we follow in Chapters 6 through 8.

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


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