Mesh texturing is an essential part of 3D scene reconstruction that enables a more realistic perception than the geometry alone and even compensates for inaccurate geometry. In this work we present a flexible formulation for color correction of textured scenes based on color augmentation per face. It can be employed as a post-processing step after selecting the best keyframe per face to compensate for color differences between pairs of neighboring faces. We present a Markov Random Field (MRF) formulation to find the best keyframes as well as the optimal color augmentations. We use a simple model to avoid reflection and camera vignetting during the view selection. Our model for color correction finds the piecewise-linear augmentation to be added to the texture patches of faces. It encourages smoothness inside every fragment while compensating color differences along view transitions. Moreover, we speed up the optimization by breaking down the formulation into multiple binary MRFs that estimate the best augmentations from coarse to fine resolutions. The experimental results prove our method outperforming the state of the art methods.

This paper presents a fast and flexible curve, and surface reconstruction technique based on implicit B-spline. This representation does not require any parameterization and it is locally supported. This fact has been exploited in this paper to propose a reconstruction technique through solving a sparse system of equations. This method is further accelerated to reduce the dimension to the active control lattice. Moreover, the surface smoothness and user interaction are allowed for controlling the surface. Finally, a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions. The whole framework is very fast and efficient and can handle large cloud of points with very low computational cost. The experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies. Comparisons with other fitting methods highlight the superiority of the proposed approach in the presence of noise and missing data.

Non rigid registration is an important task in computer vision with many applications in shape and motion modeling. A fundamental step of the registration is the data association between the source and the target sets. Such association proves difficult in practice, due to the discrete nature of the information and its corruption by various types of noise, e.g. Outliers and missing data. In this paper we investigate the benefit of the implicit representations for the non-rigid registration of 3D point clouds. First, the target points are described with small quadratic patches that are blended through partition of unity weighting. Then, the discrete association between the source and the target can be replaced by a continuous distance field induced by the interface. By combining this distance field with a proper deformation term, the registration energy can be expressed in a linear least square form that is easy and fast to solve. This significantly eases the registration by avoiding direct association between points. Moreover, a hierarchical approach can be easily implemented by employing coarse-to-fine representations. Experimental results are provided for point clouds from multi-view data sets. The qualitative and quantitative comparisons show the out performance and robustness of our framework.

In this paper, the registration problem is formulated as a point to model distance minimization. Unlike most of the existing works, which are based on minimizing a point-wise correspondence term, this formulation avoids the correspondence search that is time-consuming. In the first stage, the target set is described through an implicit function by employing a linear least squares fitting. This function can be either an implicit polynomial or an implicit B-spline from a coarse to fine representation. In the second stage, we show how the obtained implicit representation is used as an interface to convert point-to-point registration into point-to-implicit problem. Furthermore, we show that this registration distance is smooth and can be minimized through the Levengberg–Marquardt algorithm. All the formulations presented for both stages are compact and easy to implement. In addition, we show that our registration method can be handled using any implicit representation though some are coarse and others provide finer representations; hence, a tradeoff between speed and accuracy can be set by employing the right implicit function. Experimental results and comparisons in 2D and 3D show the robustness and the speed of convergence of the proposed approach.

This paper presents a simple distance estimation for implicit polynomial fitting. It is computed as the height of a simplex built between the point and the surface (i.e., a triangle in 2-D or a tetrahedron in 3-D), which is used as a coarse but reliable estimation of the orthogonal distance. The proposed distance can be described as a function of the coefficients of the implicit polynomial. Moreover, it is differentiable and has a smooth behavior . Hence, it can be used in any gradient-based optimization. In this paper, its use in a Levenberg-Marquardt framework is shown, which is particularly devoted for nonlinear least squares problems. The proposed estimation is a generalization of the gradient-based distance estimation, which is widely used in the literature. Experimental results, both in 2-D and 3-D data sets, are provided. Comparisons with state-of-the-art techniques are presented, showing the advantages of the proposed approach.

This paper presents a novel formulation, which derives in a smooth minimization problem, to tackle the rigid registration between a given point set and a model set. Unlike most of the existing works, which are based on minimizing a point-wise correspondence term, we propose to describe the model set by means of an implicit representation. It allows a new definition of the registration error, which works beyond the point level representation. Moreover, it could be used in a gradient-based optimization framework. The proposed approach consists of two stages. Firstly, a novel formulation is proposed that relates the registration parameters with the distance between the model and data set. Secondly, the registration parameters are obtained by means of the Levengberg-Marquardt algorithm. Experimental results and comparisons with state of the art show the validity of the proposed framework.

This paper proposes a novel extension of the 3L algorithm to the B-Splines solution space. The 3L algorithm is a fast algebraic method for fitting a set of points through implicit curves or surfaces. It was originally proposed for Implicit Polynomials, which although simple and attractive are not flexible representations. In this paper Implicit B-Splines (IBSs) are used to define the solution space of the 3L algorithm. IBSs offer flexible representations, which can be locally controlled. These properties are exploited for regularizing the solution space. The experimental results illustrate that the proposed framework outperforms previous formulation.

This paper presents a novel method to increase the accuracy of linear fitting of implicit polynomials. The proposed method is based on the 3L algorithm philosophy. The novelty lies on the relaxation of the additional constraints, already imposed by the 3L algorithm. Hence, the accuracy of the final solution is increased due to the proper adjustment of the expected values in the aforementioned additional constraints. Although iterative, the proposed approach solves the fitting problem within a linear framework, which is independent of the threshold tuning. Experimental results, both in 2D and 3D, showing improvements in the accuracy of the fitting are presented. Comparisons with both state of the art algorithms and a geometric based one (non-linear fitting), which is used as a ground truth, are provided.

This paper presents a novel hybrid approach that combines state of the art fitting algorithms: algebraic-based and geometric-based. It consists of two steps; first, the 3L algorithm is used as an initialization and then, the obtained result, is improved through a geometric approach. The adopted geometric approach is based on a distance estimation that avoids costly search for the real orthogonal distance. Experimental results are presented as well as quantitative comparisons.

This paper presents a novel approach for estimating the shortest Euclidean distance from a given point to the corresponding implicit quadric fitting surface. It first estimates the orthogonal orientation to the surface from the given point; then the shortest distance is directly estimated by intersecting the implicit surface with a line passing through the given point according to the estimated orthogonal orientation. The proposed orthogonal distance estimation is easily obtained without increasing computational complexity; hence it can be used in error minimization surface fitting frameworks. Comparisons of the proposed metric with previous approaches are provided to show both improvements in CPU time as well as in the accuracy of the obtained results. Surfaces fitted by using the proposed geometric distance estimation and state of the art metrics are presented to show the viability of the proposed approach.