Sergei Voronin

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.

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.

A point-to-plane registration algorithm for orthogonal transformations

The key point of the ICP algorithm is the search of either an orthogonal or affine transformations, which is the best in sense of the quadratic metric to combine two point clouds with a given correspondence between points. The point-toplane metric performs better than the point-point metric in terms of the accuracy and convergence rate. A closed-form solution to the point-to-plane case for orthogonal transformations is an open problem. In this presentation, we propose an approximation of the closed-form solution to the point-to-plane problem for orthogonal transformations.

An efficient algorithm of 3D total variation regularization

One of the most known techniques for signal and image denoising is based on total variation regularization (TV regularization). There are two known types of the discrete TV norms: isotropic and anisotropic. One of the key difficulties in the TV-based image denoising problem is the nonsmoothness of the TV norms. Many properties of the TV regularization for 1D and 2D cases are well known. On the contrary, the multidimensional TV regularization, basically, an open problem. In this work, we deal with TV regularization in the 3D case for the anisotropic norm. The key feature of the proposed method is to decompose the large problem into a set of smaller and independent problems, which can be solved efficiently and exactly. These small problems are can be solved in parallel. Computer simulation results are provided to illustrate the performance of the proposed algorithm for restoration of degraded data.

Image dehazing using total variation regularization

Images of outdoor scenes are often degraded by particles and water droplets in the atmosphere. Haze, fog, and smoke are such phenomena due to atmospheric absorption and scattering. Numerous image dehazing (haze removal) methods have been proposed in the last two decades, and the majority of them employ an image enhancing or restoration approach. Different variants of local adaptive algorithms for single image dehazing are also known. A haze-free image must have higher contrast compared with the input hazy image. It is possible to remove haze by maximizing the local contrast of the restored image. Some haze removal approaches estimate a dehazed image from an observed hazed scene by solving an objective function, whose parameters are adapted to local statistics of the hazed image inside a moving window. In the signal and image processing a common way to solve the denoising problem utilizes the total variation regularization. In this presentation we propose a new algorithm combining local estimates of depth maps toward a global map by regularization the total variation for piecewise-constant functions. Computer simulation results are provided to illustrate the performance of the proposed algorithm for restoration of hazed images.

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’s method with the taut string approach leads to a clear geometric description of the extremal function.

An efficient direct method for image registration of flat objects

Image alignment of rigid surfaces is a rapidly developing area of research and has many practical applications. Alignment methods can be roughly divided into two types: feature-based methods and direct methods. Known SURF and SIFT algorithms are examples of the feature-based methods. Direct methods refer to those that exploit the pixel intensities without resorting to image features and image-based deformations are general direct method to align images of deformable objects in 3D space. Nevertheless, it is not good for the registration of images of 3D rigid objects since the underlying structure cannot be directly evaluated. In the article, we propose a model that is suitable for image alignment of rigid flat objects under various illumination models. The brightness consistency assumptions used for reconstruction of optimal geometrical transformation. Computer simulation results are provided to illustrate the performance of the proposed algorithm for computing of an accordance between pixels of two images.