Hongchuan Yu

1D-PCA, 2D-PCA to nD-PCA

In this paper, we first briefly reintroduce the 1D and 2D forms of the classical principal component analysis (PCA). Then, the PCA technique is further developed and extended to an arbitrary n-dimensional space. Analogous to 1D- and 2D-PCA, the new nD-PCA is applied directly to n-order tensors (n ges 3) rather than 1-order tensors (1D vectors) and 2-order tensors (2D matrices). In order to avoid the difficulties faced by tensors computations (such as the multiplication, general transpose and Hermitian symmetry of tensors), our proposed nD-PCA algorithm has to exploit a newly proposed higher-order singular value decomposition (HO-SVD). To evaluate the validity and performance of nD-PCA, a series of experiments are performed on the FRGC 3D scan facial database

GVF-based anisotropic diffusion models

In this paper, the gradient vector flow fields are introduced in image restoration. Within the context of flow fields, the shock filter, mean curvature flow, and Perona-Malik equation are reformulated. Many advantages over the original models can be obtained; these include numerical stability, large capture range, and high-order derivative estimation. In addition, a fairing process is introduced in the anisotropic diffusion, which contains a fourth-order derivative and is reformulated as the intrinsic Laplacian of curvature under the level set framework. By applying this fairing process, the shape boundaries will become more apparent. In order to overcome numerical errors, the intrinsic Laplacian of curvature is computed from the gradient vector flow fields instead of the observed images.

Complete invariants for robust face recognition

In this paper, we propose two complete sets of similarity invariant descriptors under the Fourier-Mellin transform and the analytical Fourier-Mellin transform (AFMT) frameworks, respectively. The magnitude and phase spectra are jointly processed in our case, and the presented invariants are complete and can be used to reconstruct the image. Their numerical properties are also revealed through image reconstruction. In order to simplify the invariant feature data for recognition and discrimination, a 2D-PCA approach is incorporated into the presented complete invariant descriptor. The obtained compact representation through the 2D-PCA preserves the essential structure of the objects in an image. We tested this compact form on the ORL, Yale and BioID face databases for experimental verification, and achieved a face verification under similarity transforms with a much inferior equal error rate (EER) compared to when the 2D-PCA-based compact form is used without complete invariants.

Fast and exact discrete geodesic computation based on triangle-oriented wavefront propagation

Computing discrete geodesic distance over triangle meshes is one of the fundamental problems in computational geometry and computer graphics. In this problem, an effective window pruning strategy can significantly affect the actual running time. Due to its importance, we conduct an in-depth study of window pruning operations in this paper, and produce an exhaustive list of scenarios where one window can make another window partially or completely redundant. To identify a maximal number of redundant windows using such pairwise cross checking, we propose a set of procedures to synchronize local window propagation within the same triangle by simultaneously propagating a collection of windows from one triangle edge to its two opposite edges. On the basis of such synchronized window propagation, we design a new geodesic computation algorithm based on a triangle-oriented region growing scheme. Our geodesic algorithm can remove most of the redundant windows at the earliest possible stage, thus significantly reducing computational cost and memory usage at later stages. In addition, by adopting triangles instead of windows as the primitive in propagation management, our algorithm significantly cuts down the data management overhead. As a result, it runs 4--15 times faster than MMP and ICH algorithms, 2-4 times faster than FWP-MMP and FWP-CH algorithms, and also incurs the least memory usage.

An RBF-Based Reparameterization Method for Constrained Texture Mapping

Texture mapping has long been used in computer graphics to enhance the realism of virtual scenes. However, to match the 3D model feature points with the corresponding pixels in a texture image, surface parameterization must satisfy specific positional constraints. However, despite numerous research efforts, the construction of a mathematically robust, foldover-free parameterization that is subject to positional constraints continues to be a challenge. In the present paper, this foldover problem is addressed by developing radial basis function (RBF)-based reparameterization. Given initial 2D embedding of a 3D surface, the proposed method can reparameterize 2D embedding into a foldover-free 2D mesh, satisfying a set of user-specified constraint points. In addition, this approach is mesh free. Therefore, generating smooth texture mapping results is possible without extra smoothing optimization.

Level set methods and image segmentation

We discuss some questions for applying level set methods to image segmentation. During image segmentation, it has been found that the level sets function could be changed into a non-distance function with the initial level set function defined as a distance function. This causes some applications to fail, such as coupled surfaces propagation. In addition, the solution existence and uniqueness of the evolving equation in the level set method has not been discussed in detail. We firstly prove that the signed distance function could be presented to the level set function during the evolution of the level set function through the methods presented in (Sethian, 1999; Gomes and Faugeras, 2000). Furthermore, the solution existence and uniqueness of the level set function evolution equations are analyzed in detail under the distance function restriction. It has been proved that the solutions exist, but are not unique. Finally, this conclusion can be validated in the results of implementation on image segmentation.

Mean value coordinates–based caricature and expression synthesis

We present a novel method for caricature synthesis based on mean value coordinates (MVC). Our method can be applied to any single frontal face image to learn a specified caricature face pair for frontal and 3D caricature synthesis. This technique only requires one or a small number of exemplar pairs and a natural frontal face image training set, while the system can transfer the style of the exemplar pair across individuals. Further exaggeration can be fulfilled in a controllable way. Our method is further applied to facial expression transfer, interpolation, and exaggeration, which are applications of expression editing. Additionally, we have extended our approach to 3D caricature synthesis based on the 3D version of MVC. With experiments we demonstrate that the transferred expressions are credible and the resulting caricatures can be characterized and recognized.

Geodesics on Point Clouds

We present a novel framework to compute geodesics on implicit surfaces and point clouds. Our framework consists of three parts, particle based approximate geodesics on implicit surfaces, Cartesian grid based approximate geodesics on point clouds, and geodesic correction. The first two parts can effectively generate approximate geodesics on implicit surfaces and point clouds, respectively. By introducing the geodesic curvature flow, the third part produces smooth and accurate geodesic solutions. Differing from most of the existing methods, our algorithms can converge to a given tolerance. The presented computational framework is suitable for arbitrary implicit hypersurfaces or point clouds with high genus or high curvature.

Adaptive Multi-view Semi-supervised Nonnegative Matrix Factorization

Multi-view clustering, which explores complementary information between multiple distinct feature sets, has received considerable attention. For accurate clustering, all data with the same label should be clustered together regardless of their multiple views. However, this is not guaranteed in existing approaches. To address this issue, we propose Adaptive Multi-View Semi-Supervised Nonnegative Matrix Factorization AMVNMF, which uses label information as hard constraints to ensure data with same label are clustered together, so that the discriminating power of new representations are enhanced. Besides, AMVNMF provides a viable solution to learn the weight of each view adaptively with only a single parameter. Using