By Matthieu Salzmann, Pascal Fua
Having the ability to get well the form of 3D deformable surfaces from a unmarried video circulation could give the opportunity to box reconstruction platforms that run on broadly to be had with out requiring really good units. even if, simply because many alternative 3D shapes could have almost a similar projection, such monocular form restoration is inherently ambiguous. during this survey, we are going to overview the 2 major periods of suggestions that experience proved ultimate thus far: The template-based equipment that depend on developing correspondences with a reference photograph during which the form is already recognized, and non-rigid structure-from-motion concepts that take advantage of issues tracked around the sequences to reconstruct a totally unknown form. In either circumstances, we'll formalize the strategy, speak about its inherent ambiguities, and current the sensible suggestions which were proposed to unravel them. To finish, we are going to recommend instructions for destiny learn. desk of Contents: advent / Early methods to Non-Rigid Reconstruction / Formalizing Template-Based Reconstruction / appearing Template-Based Reconstruction / Formalizing Non-Rigid constitution from movement / acting Non-Rigid constitution from movement / destiny instructions
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Additional info for Deformable Surface 3D Reconstruction from Monocular Images (Synthesis Lectures on Computer Vision)
U1 v1 ... bj P cj P dj P 0 ... 0 ... ... ... 0 cl P 0 el P ... 0 ... ... ... ... − 0 ... uj − vj ... − ... ... 0 ... ul vl ... ... 0 ⎥ ⎥ ... ⎥ ⎥ ⎥ ... ⎥ ⎥ . ⎥ ... ⎥ ⎥ ⎥ ... ⎦ ... The left half of Mm , which is of size 2Nc × 3Nv , Nc being the total number of correspondences, has at most rank 2Nv because P has rank 2. 3. LINEAR FORMULATION 23 as a linear combination of the others. 9) where vf,i,j is the j th coordinate of the i th vertex of facet f . This shows that the bottom two rows of the last column can be written as a linear function of the other columns.
4 are turned into equalities by introducing one slack variable for each correspondence. The sum of these slack variables can then be expressed as a quadratic function of the shape, and directly minimized in the objective function. The edge orientation constraints are either kept as constraints to yield a QP problem, or re-written as a quadratic regularizer, thus resulting in an unconstrained optimization problem. Fig. 5 depicts the reconstruction error of these two formulations, and compares them against the results of the SOCP approach.
2. 5: Comparison of the accuracies obtained with the SOCP formulation based on Salzmann et al. [2007a] with the QP and unconstrained (QO) formulations of Zhu et al. . Reconstructions were obtained with image noise variance 1 (left) and 2 (right). Note that the QP and QO approaches yield better results than the SOCP one. Courtesy of J. Zhu. 2 IMPOSING GEOMETRIC CONSTRAINTS The methods discussed in the previous section are very generic in that they make very few assumptions on the smoothness or physical properties of the surface.