Shape registration using characteristic functions

This paper presents a fast algorithm for the registration of shapes implicitly represented by their characteristic functions. The proposed algorithm aims to recover the transformation parameters (scaling, rotation, and translation) by minimizing a dissimilarity term between two shapes. The algorithm is based on phase correlation and statistical shape moments to compute the registration parameters individually. The algorithm proposed here is applied to various registration problems, to address issues such as the registration of shapes with various topologies, and registration of complex shapes containing various numbers of sub-shapes. Our method proposed here is characterized with a better performance for registration over large databases of shapes, a better accuracy, a higher convergence speed and robustness at the presence of excessive noise in comparison with other state-of-the-art shape registration algorithms in the literatur

Robust On-Manifold Optimization for Uncooperative Space Relative Navigation with a Single Camera

Optical cameras are gaining popularity as the suitable sensor for relative navigation in space due to their attractive sizing, power, and cost properties when compared with conventional flight hardware or costly laser-based systems. However, a camera cannot infer depth information on its own, which is often solved by introducing complementary sensors or a second camera. In this paper, an innovative model-based approach is demonstrated to estimate the six-dimensional pose of a target relative to the chaser spacecraft using solely a monocular setup. The observed facet of the target is tackled as a classification problem, where the three-dimensional shape is learned offline using Gaussian mixture modeling. The estimate is refined by minimizing two different robust loss functions based on local feature correspondences. The resulting pseudomeasurements are processed and fused with an extended Kalman filter. The entire optimization framework is designed to operate directly on the SE(3) manifold, uncoupling the process and measurement models from the global attitude state representation. It is validated on realistic synthetic and laboratory datasets of a rendezvous trajectory with the complex spacecraft Envisat, demonstrating estimation of the relative pose with high accuracy over full tumbling motion. Further evaluation is performed on the open-source SPEED dataset

Least squares contour alignment

The contour alignment problem, considered in this paper, is to compute the minimal distance in a least squares sense, between two explicitly represented contours, specified by corresponding points, after arbitrary rotation, scaling, and translation of one of the contours. This is a constrained nonlinear optimization problem with respect to the translation, rotation and scaling parameters, however, it is transformed into an equivalent linear least squares problem by a nonlinear change of variables. Therefore, a global solution of the contour alignment problem can be computed efficiently. It is shown that a normalization of the cost function minimum value is invariant to ordering and affine transformation of the contours and can be used as a measure for the distance between the contours. A solution is also proposed to the problem of finding a point correspondence between the contours

The method of signature recognition based on least squares contour alignment and windows technique

This paper presents a new method of recognizing handwritten signatures. Signature was treated as a collection of features of specific values. As features the values of x, y coordinates of signature points have been used. The method discussed in the paper is a modification of the method based on least squares contour alignment. This modification consists of dividing signatures into windows of the preset size and measuring the value of similarity between the windows according to their position in the signature. The effectiveness of the method was verified in practice. During the study, the influence of the parameters of the method on the obtained results was determined