An efficient algorithm for non-rigid object registration

An efficient algorithm for registration of two non-rigid objects based on geometrical transformation of the template object to target object is proposed. The transformation is considered as warping of the template onto the target. To choose the most suitable transformation from all possible warps, a registration algorithm should satisfy deformation constraints referred to as regularization of non-rigid objects. In this work, we use variational functionals for affine transformations. With the help of computer simulation, the proposed method for searching the optimal geometrical transformation is compared with that of common algorithms

A fast total variation regularization algorithm for 2D piecewise constant radially symmetric functions

In this paper, total variation regularization (TV regularization) for 2D radially symmetric piecewise constant (RSPC) functions is considered. A system of equations solving the direct variational problem with the subgradient method is obtained. Using the system, we propose a Condat’s type algorithm for computation of an extremal function.The work was supported by the Ministry of Education and Science of Russian Federation (grant № 2.1743.2017)

Approximation of the exact solution of point clouds registration based on point-to-plane approach for orthogonal transformations

The most popular algorithm for aligning of 3D point data is the Iterative Closest Point (ICP). This paper proposes a new algorithm for orthogonal registration of point clouds based on the point-to-plane ICP algorithm for affine transformation. At each iterative step of the algorithm, an approximation of the closed-form solution for the orthogonal transformation is derived.The work was supported by the Ministry of Education and Science of Russian Federation (grant № 2.1743.2017)

A fast one dimensional total variation regularization algorithm

Denoising has numerous applications in communications, control, machine learning, and many other fields of engineering and science. A common way to solve the problem utilizes the total variation (TV) regularization. Many efficient numerical algorithms have been developed for solving the TV regularization problem. Condat described a fast direct algorithm to compute the processed 1D signal. In this paper, we propose a variant of the Condat’s algorithm based on the direct 1D TV regularization problem. The usage of the Condat algorithm with the taut string approach leads to a clear geometric description of the extremal function.The work was supported by Russian Science Foundation grant №15-19-10010

Affine registration of point clouds based on point-to-plane approach

The problem of aligning of 3D point data is the known registration task. The most popular registration algorithm is the Iterative Closest Point (ICP). This paper proposes a new algorithm for affine registration of point clouds by incorporating the affine transformation into the point-toplane ICP algorithm. At each iterative step of the algorithm, a closed-form solution for the affine transformation is derived.The work was supported by the Ministry of Education and Science of Russian Federation (grant № 2.1743.2017)

Affine registration of point clouds based on point-to-plane approach

The problem of aligning of 3D point data is the known registration task. The most popular registration algorithm is the Iterative Closest Point (ICP). This paper proposes a new algorithm for affine registration of point clouds by incorporating the affine transformation into the point-toplane ICP algorithm. At each iterative step of the algorithm, a closed-form solution for the affine transformation is derived.The work was supported by the Ministry of Education and Science of Russian Federation (grant № 2.1743.2017)