By Paolo Favaro
In the parts of picture processing and computing device imaginative and prescient, there's a specific want for software program that may, given an unfocused or motion-blurred picture, infer the three-d form of a scene. This ebook describes the analytical approaches 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 machine imaginative and prescient and with backgrounds in engineering, technology or arithmetic, this hugely sensible text/reference is obtainable to complicated scholars or people with a level that incorporates uncomplicated linear algebra and calculus courses.
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Extra resources for 3-D shape estimation and image restoration : exploiting defocus and motion blur
6. On the choice of objective function in shape from defocus 47 conditions discussed in previous sections are satisﬁed, we need to impose further constraints. For instance, of all possible solutions, we may wish to ﬁnd the smoothest, or the one with minimum energy, or one that satisﬁes additional constraints. Such constraints can be imposed in a minimization scheme, as we do in the next chapters. Regularization is a broad topic that is well beyond the scope of this book. In Appendix F we only summarize the elements that are crucial to the design of shape from defocus algorithms, and refer the reader to [Kirsch, 1996] for more details.
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.
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. The shutter interval for the second image J2 is approximately three times the shutter interval of the ﬁrst image J1 . In this case, the data collection is rather simple, because no alignment and no synchronization are required, but it is based on the assumption that motion does not change among the three frames.
3-D shape estimation and image restoration : exploiting defocus and motion blur by Paolo Favaro