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Mohammad Rouhani, & Angel Sappa. (2013). The Richer Representation the Better Registration. TIP - IEEE Transactions on Image Processing, 22(12), 5036–5049.
Abstract: 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.
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Mohammad Rouhani, & Angel Sappa. (2012). Non-Rigid Shape Registration: A Single Linear Least Squares Framework. In 12th European Conference on Computer Vision (Vol. 7578, pp. 264–277). LNCS. Springer Berlin Heidelberg.
Abstract: This paper proposes a non-rigid registration formulation capturing both global and local deformations in a single framework. This formulation is based on a quadratic estimation of the registration distance together with a quadratic regularization term. Hence, the optimal transformation parameters are easily obtained by solving a liner system of equations, which guarantee a fast convergence. Experimental results with challenging 2D and 3D shapes are presented to show the validity of the proposed framework. Furthermore, comparisons with the most relevant approaches are provided.
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Mohammad Rouhani, & Angel Sappa. (2012). Implicit Polynomial Representation through a Fast Fitting Error Estimation. TIP - IEEE Transactions on Image Processing, 21(4), 2089–2098.
Abstract: Impact Factor
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.
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Mohammad Rouhani, & Angel Sappa. (2011). Correspondence Free Registration through a Point-to-Model Distance Minimization. In 13th IEEE International Conference on Computer Vision (pp. 2150–2157).
Abstract: 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.
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Mohammad Rouhani, & Angel Sappa. (2011). Implicit B-Spline Fitting Using the 3L Algorithm. In 18th IEEE International Conference on Image Processing (pp. 893–896).
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Mohammad Rouhani, & Angel Sappa. (2010). A Fast accurate Implicit Polynomial Fitting Approach. In 17th IEEE International Conference on Image Processing (1429–1432).
Abstract: 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.
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Mohammad Rouhani, & Angel Sappa. (2010). Relaxing the 3L Algorithm for an Accurate Implicit Polynomial Fitting. In 23rd IEEE Conference on Computer Vision and Pattern Recognition (pp. 3066–3072).
Abstract: 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.
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Mohammad Rouhani, & Angel Sappa. (2009). A Novel Approach to Geometric Fitting of Implicit Quadrics. In 8th International Conference on Advanced Concepts for Intelligent Vision Systems (Vol. 5807, 121–132). LNCS. Springer Berlin Heidelberg.
Abstract: This paper presents a novel approach for estimating the geometric distance from a given point to the corresponding implicit quadric curve/surface. The proposed estimation is based on the height of a tetrahedron, which is used as a coarse but reliable estimation of the real distance. The estimated distance is then used for finding the best set of quadric parameters, by means of the Levenberg-Marquardt algorithm, which is a common framework in other geometric fitting approaches. Comparisons of the proposed approach with previous ones are provided to show both improvements in CPU time as well as in the accuracy of the obtained results.
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