Artyom Makovetskii

A fusion algorithm for building three-dimensional maps

Recently various algorithms for building of three-dimensional maps of indoor environments have been proposed. In this work we use a Kinect camera that captures RGB images along with depth information for building three-dimensional dense maps of indoor environments. Commonly mapping systems consist of three components; that is, first, spatial alignment of consecutive data frames; second, detection of loop-closures, and finally, globally consistent alignment of the data sequence. It is known that three-dimensional point clouds are well suited for frame-to-frame alignment and for three-dimensional dense reconstruction without the use of valuable visual RGB information. A new fusion algorithm combining visual features and depth information for loop-closure detection followed by pose optimization to build global consistent maps is proposed. The performance of the proposed system in real indoor environments is presented and discussed.

Image restoration based on topological properties of functions of two variables

Image restoration refers to the problem of estimating an ideal image from its observed degraded one. Functions of two variables can be well described with two variations. One of them is a total variation for continuously differentiable functions. Another one is called a linear variation. The linear variation is a topological characteristic of a function of two variables whereas the total variation is a metrical characteristic of a function. A restoration algorithm based on both total variation-based regularization and variations is proposed. Computer simulation results illustrate the performance of the proposed algorithm for restoration of blurred images.

Modified gradient descent method for image restoration

function of two variables distorted by a known linear operator and additive noise is usually used in the problem of image restoration. It was shown that to solve the problem metrical as well as topological characteristics of the function of two variables should be used. In paper with the help of spectral analysis we derive conditions when the gradient decent method is able to restore images. Computer simulation results are provided to illustrate the performance of the gradient decent method for restoration of uniformly blurred signals.

Total variation regularization with bounded linear variations

One of the most known techniques for signal denoising is based on total variation regularization (TV regularization). A better understanding of TV regularization is necessary to provide a stronger mathematical justification for using TV minimization in signal processing. In this work, we deal with an intermediate case between one- and two-dimensional cases; that is, a discrete function to be processed is two-dimensional radially symmetric piecewise constant. For this case, the exact solution to the problem can be obtained as follows: first, calculate the average values over rings of the noisy function; second, calculate the shift values and their directions using closed formulae depending on a regularization parameter and structure of rings. Despite the TV regularization is effective for noise removal; it often destroys fine details and thin structures of images. In order to overcome this drawback, we use the TV regularization for signal denoising subject to linear signal variations are bounded.

An efficient point-to-plane registration algorithm for affine transformations

The problem of aligning of 3D point data is the known registration task. The most popular registration algorithm is the Iterative Closest Point (ICP) algorithm. The traditional ICP algorithm is a fast and accurate approach for rigid registration between two point clouds but it is unable to handle affine case. Recently, extension of the ICP algorithm for composition of scaling, rotation, and translation is proposed. A generalized ICP version for an arbitrary affine transformation is also suggested. In this paper, a new iterative algorithm for registration of point clouds based on the point-to-plane ICP algorithm with affine transformations is proposed. At each iteration, a closed-form solution to the affine transformation is derived. This approach allows us to get a precise solution for transformations such as rotation, translation, and scaling. With the help of computer simulation, the proposed algorithm is compared with common registration algorithms.

A modified iterative closest point algorithm for shape registration

The iterative closest point (ICP) algorithm is one of the most popular approaches to shape registration. The algorithm starts with two point clouds and an initial guess for a relative rigid-body transformation between them. Then it iteratively refines the transformation by generating pairs of corresponding points in the clouds and by minimizing a chosen error metric. In this work, we focus on accuracy of the ICP algorithm. An important stage of the ICP algorithm is the searching of nearest neighbors. We propose to utilize for this purpose geometrically similar groups of points. Groups of points of the first cloud, that have no similar groups in the second cloud, are not considered in further error minimization. To minimize errors, the class of affine transformations is used. The transformations are not rigid in contrast to the classical approach. This approach allows us to get a precise solution for transformations such as rotation, translation vector and scaling. With the help of computer simulation, the proposed method is compared with common nearest neighbor search algorithms for shape registration.

An Efficient Algorithm for Total Variation Denoising

One-dimensional total variation (TV) regularization can be used for signal denoising. We consider one-dimensional signals distorted by additive white Gaussian noise. TV regularization minimizes a functional consisting of the sum of fidelity and regularization terms. We derive exact solutions to one-dimensional TV regularization problem that help us to recover signals with the proposed algorithm. The proposed approach to finding exact solutions has a clear geometrical meaning. Computer simulation results are provided to illustrate the performance of the proposed algorithm for signal denoising.

Explicit solutions of one-dimensional total variation problem

This work deals with denosing of a one-dimensional signal corrupted by additive white Gaussian noise. A common way to solve the problem is to utilize the total variation (TV) method. Basically, the TV regularization minimizes a functional consisting of the sum of fidelity and regularization terms. We derive explicit solutions of the one-dimensional TV regularization problem that help us to restore noisy signals with a direct, non-iterative algorithm. Computer simulation results are provided to illustrate the performance of the proposed algorithm for restoration of noisy signals.

A regularization algorithm for registration of deformable surfaces

The registration of two surfaces is finding a geometrical transformation of a template surface to a target surface. The transformation combines the positions of the semantically corresponding points. The transformation can be considered as warping the template onto the target. To choose the most suitable transformation from all possible warps, a registration algorithm must satisfies some constraints on the deformation. This is called regularization of the deformation field. Often use regularization based on minimizing the difference between transformations for different vertices of a surface. The variational functional consists of the several terms. One of them is the functional of the ICP (Iterative Closest Point algorithm) variational subproblem for the point-to-point metric for affine transformations. Other elements of the functional are stiffness and landmark terms. In proposed presentation we use variational functional based on the point-toplane metric for affine transformations. In addition, the use of orthogonal transformations is considered. The proposed algorithm is robust relative to bad initialization and incomplete surfaces. For noiseless and complete data, the registration is one-to-one. With the help of computer simulation, the proposed method is compared with known algorithms for the searching of optimal geometrical transformation.

Development of a method for constructing a 3D accurate map of the surrounding environment

The problem at solving which the project is aimed consists in the development of methods of constructing a threedimensional combined dense map are of the accessible environment and determining a position of a robot in a relative coordinate system based on a history of camera positions and the robots motions, symbolic (semantic) tags.