Yaxin Peng

Manifold Preserving: An Intrinsic Approach for Semisupervised Distance Metric Learning

In this paper, we address the semisupervised distance metric learning problem and its applications in classification and image retrieval. First, we formulate a semisupervised distance metric learning model by considering the metric information of inner classes and interclasses. In this model, an adaptive parameter is designed to balance the inner metrics and intermetrics by using data structure. Second, we convert the model to a minimization problem whose variable is symmetric positive-definite matrix. Third, in implementation, we deduce an intrinsic steepest descent method, which assures that the metric matrix is strictly symmetric positive-definite at each iteration, with the manifold structure of the symmetric positive-definite matrix manifold. Finally, we test the proposed algorithm on conventional data sets, and compare it with other four representative methods. The numerical results validate that the proposed method significantly improves the classification with the same computational efficiency.

LieTrICP: An improvement of trimmed iterative closest point algorithm

Abstract We propose a robust registration method for two point sets using Lie group parametrization. Our algorithm is termed as LieTrICP, as it combines the advantages of the Trimmed Iterative Closest Point (TrICP) algorithm and Lie group representation. Given two low overlapped point sets, we first find the correspondence for every point, then select the overlapped point pairs, and use Lie group representation to estimate the geometric transformation from the selected point pairs. These three steps are conducted iteratively to obtain the optimal transformation. The novelties of this algorithm are twofold: (1) it generalizes the TrICP to the anisotropic case; and (2) it gives a unified Lie group framework for point set registration, which can be extended to more complicated transformations and high dimensional problems. We conduct extensive experiments to demonstrate that our algorithm is more accurate and robust than several other algorithms in a variety of situations, including missing points, perturbations and outliers.

Iwasawa decomposition: a new approach to 2D affine registration problem

In this paper, 2D affine registration problem was studied. First, combining with the procedure of traditional iterative closest point method, the registration problem was modeled as an optimization problem on Lie group

Affine registration for multidimensional point sets under the framework of Lie group

GL(2,{\mathfrak{R}})

Soft shape registration under lie group frame

. To assure the registration non-degenerate, some reasonable constraints were introduced into the model by Iwasawa decomposition. Then, a series of quadratic programming were used to approximate the registration problem and a novel affine registration algorithm was proposed. At last, several illustration and comparison experiments were presented to demonstrate the performance and efficiency of the proposed algorithm. Particularly, a way of selecting a good initial registration based on ICA method to achieve the global minimum was suggested.

A semi-automatic method for burn scar delineation using a modified Chan-Vese model

In this paper, we propose an object(s)-of-interest (OOI) segmentation method for images with inhomogeneous intensities. First, we define a discrimination function for each pixel, labelling whether the pixel belongs to OOI based on the characteristics of OOI. This function is then integrated with image gradient to construct a stopping function in an energy functional. Finally, this energy functional is minimized by means of level set evolution, which guides the motion of the zero level set toward object boundaries. The results demonstrate that our model is effective.

Virus image classification using multi-scale completed local binary pattern features extracted from filtered images by multi-scale principal component analysis

Abstract. An affine registration algorithm for multidimensional point sets under the framework of Lie group is proposed. This algorithm studies the affine registration between two data sets, and puts the expectation maximization-iterative closest point (EM-ICP) algorithm into the framework of Lie group, since all affine transformations form a Lie transformation group. The registration is carried out via minimizing an energy functional depending on elements of the affine transformation Lie group. The key point for applying the idea of Lie group is that, during the minimization via iteration, we must guarantee the next iteration step of the transformation is still an element in the same group, starting from an element in a Lie group. Our solution is utilizing the element of Lie algebra to represent that of Lie group near the identity via the exponential map, i.e., we use the first canonical coordinate representation of Lie group. Several comparative experiments between the proposed Lie-EM-ICP algorithm and the Lie-ICP algorithm are performed, showing that the proposed algorithm is more accurate and robust, especially in the presence of outliers. This algorithm can also be generalized to other registration problems in general, provided that desired transformations are within certain Lie group.

Lie-EM-ICP algorithm: a novel frame for 2D shape registration

Abstract We propose a trimmed strategy for affine registration of point sets using the Lie group parameterization. All affine transformations form an affine Lie group, thus finding an optimal transformation in registration is reduced to finding an optimal element in the affine group. Given two point sets (with outliers) and an initial element in the transformation group, we seek the optimal group element iteratively by minimizing an energy functional. This is conducted by sequentially finding the closest correspondence of two point sets, estimating the overlap rate of two sets, and finding the optimal affine transformation via the exponential map of the affine group. This method improves the trimmed iterative closest point algorithm (TrICP) in two aspects: (1) We use the Lie group parameterization to implement TrICP. (2) We also extend TrICP to the case of affine transformations. The performance of the proposed algorithm is demonstrated by using the LiDAR data acquired in the Mount St. Helens area. Both visual inspections and evaluation index (root mean trimmed squared distance) indicate that our algorithm performs consistently better than TrICP and other related algorithms, especially in the presence of outliers and missing points.