By Marco Alexander Treiber
This useful and authoritative text/reference offers a wide creation to the optimization tools used in particular in laptop imaginative and prescient. that allows you to facilitate figuring out, the presentation of the equipment is supplemented through uncomplicated movement charts, through pseudocode implementations that demonstrate deeper insights into their mode of operation. those discussions are additional supported through examples taken from very important purposes in machine imaginative and prescient. themes and contours: presents a entire assessment of laptop vision-related optimization; covers a variety of concepts from classical iterative multidimensional optimization to state of the art themes of graph cuts and GPU-suited overall variation-based optimization; describes intimately the optimization equipment hired in computing device imaginative and prescient purposes; illuminates key innovations with truly written and step by step motives; provides distinctive details on implementation, together with pseudocode for many methods.
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Additional resources for Optimization for Computer Vision: An Introduction to Core Concepts and Methods
10 Illustrating the aligning performance for some traffic signs. Top row: template shapes. Bottom row: matched templates in some query images visible as yellow overlays (© 2012 IEEE. Reprinted, with permission, from Domokos et al. , because f ðxÞ is not continuously differentiable or because it is difficult to derive HðxÞ analytically and/or very costly to estimate it numerically. In those cases, zero-order methods like the method proposed by Powell can be applied. In the following, the method itself is presented in detail first before an example application is provided.
26 2 Continuous Optimization Fig. 5 Illustrating the refinement of the bounds of the solution. The blue points indicate current lower and upper bounds, whereas the red color of a point indicates that the point becomes a new bound. Left: as x1 (red) takes a higher function value than x2 (green), x1 is a new lower bound. Right: as x2 (red) takes a higher function value than x1 (green), x2 is a new upper bound 3. Refine the solution by applying a polynomial interpolation to the data found in step 2, where the refined bounds xiu and xil as well as two intermediate points were found (see below).
This condition corresponds to the fact that for one-dimensional functions, their second derivative has to be positive at a local minimum. Now let’s see how the two steps of Newton’s method can be implemented in practice. , ). 20), which involves explicitly calcuÀ ÁÀ1 lating the inverse H xk , is not applied. 18) is solved instead. Note also that no separate one-dimensional optimization is performed in this method. 20). The whole process is summarized in Fig. 7. , the initial solution x0 has to be sufficiently close to the true minimum of f ðxÃ Þ, because T ðδxÞ is a sufficiently good approximation of f ðxÞ in just a limited local neighborhood around the optimum.