111 research outputs found
N-Dimensional Principal Component Analysis
In this paper, we first briefly introduce the multidimensional Principal Component Analysis (PCA) techniques, and then amend our previous N-dimensional PCA (ND-PCA) scheme by introducing multidirectional decomposition into ND-PCA implementation. For the case of high dimensionality, PCA technique is usually extended to an arbitrary n-dimensional space by the Higher-Order Singular Value Decomposition (HO-SVD) technique. Due to the size of tensor, HO-SVD implementation usually leads to a huge matrix along some direction of tensor, which is always beyond the capacity of an ordinary PC. The novelty of this paper is to amend our previous ND-PCA scheme to deal with this challenge and further prove that the revised ND-PCA scheme can provide a near optimal linear solution under the given error bound. To evaluate the numerical property of the revised ND-PCA scheme, experiments are performed on a set of 3D volume datasets
A Compact and Complete AFMT Invariant with Application to Face Recognition
In this paper, we present a complete set of hybrid
similarity invariants under the Analytical Fourier-Mellin
Transform (AFMT) framework, and apply it to invariant face
recognition. Because the magnitude and phase spectra are not
processed separately, this invariant descriptor is complete. In order to simplify the invariant feature data for recognition and discrimination, a 2D-PCA approach is introduced into this complete invariant descriptor. The experimental results indicate that the presented invariant descriptor is complete and similarityinvariant. Its compact representation through the 2D-PCA preserves the essential structure of an object. Furthermore, we apply this compact form into ORL, Yale and BioID face databases for experimental verification, and achieve the desired results
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
Caricature Synthesis Based on Mean Value Coordinates
In this paper, a novel method for caricature synthesis is developed based on mean value coordinates (MVC). Our method can be applied to any single frontal face image to learn a specified caricature face exemplar pair for frontal and side view caricature synthesis. The technique only requires one or a small number of caricature face pairs and a natural frontal face 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 extended to facial expression transfer, interpolation and exaggeration, which are
applications of expression editing. Moreover, the deformation equation of MVC is modified to handle the case of polygon intersections and applied to lateral view caricature synthesis from a single frontal view image. Using experiments we demonstrate that the transferred expressions are credible and the resulting caricatures can be characterized and recognized
An extension of min/max flow framework
In this paper, the min/max flow scheme for image restoration is revised. The novelty consists of the fol-
24 lowing three parts. The first is to analyze the reason of the speckle generation and then to modify the
25 original scheme. The second is to point out that the continued application of this scheme cannot result
26 in an adaptive stopping of the curvature flow. This is followed by modifications of the original scheme
27 through the introduction of the Gradient Vector Flow (GVF) field and the zero-crossing detector, so as
28 to control the smoothing effect. Our experimental results with image restoration show that the proposed
29 schemes can reach a steady state solution while preserving the essential structures of objects. The third is
30 to extend the min/max flow scheme to deal with the boundary leaking problem, which is indeed an
31 intrinsic shortcoming of the familiar geodesic active contour model. The min/max flow framework pro-
32 vides us with an effective way to approximate the optimal solution. From an implementation point of
33 view, this extended scheme makes the speed function simpler and more flexible. The experimental
34 results of segmentation and region tracking show that the boundary leaking problem can be effectively
35 suppressed
Constrained Texture Mapping And Foldover-free Condition
Texture mapping has been widely used in image
processing and graphics to enhance the realism of CG scenes.
However to perfectly match the feature points of a 3D model
with the corresponding pixels in texture images, the
parameterisation which maps a 3D mesh to the texture space
must satisfy the positional constraints. Despite numerous
research efforts, the construction of a mathematically robust
foldover-free parameterisation subject to internal constraints
is still a remaining issue. In this paper, we address this
challenge by developing a two-step parameterisation method.
First, we produce an initial parameterisation with a method
traditionally used to solve structural engineering problems,
called the bar-network. We then derive a mathematical
foldover-free condition, which is incorporated into a Radial
Basis Function based scheme. This method is therefore able to
guarantee that the resulting parameterization meets the hard
constraints without foldovers
Constrained parameterization with applications to graphics and image processing.
Surface parameterization is to establish a transformation that maps the points on a surface to a specified parametric domain. It has been widely applied to computer graphics and image processing fields. The challenging issue is that the usual positional constraints always result in triangle flipping in parameterizations (also called foldovers). Additionally, distortion is inevitable in parameterizations. Thus the rigid constraint is always taken into account. In general, the constraints are application-dependent. This thesis thus focuses on the various constraints depended on applications and investigates the foldover-free constrained parameterization approaches individually. Such constraints usually include, simple positional constraints, tradeoff of positional constraints and rigid constraint, and rigid constraint. From the perspective of applications, we aim at the foldover-free parameterization methods with positional constraints, the as-rigid-as-possible parameterization with positional constraints, and the well-shaped well-spaced pre-processing procedure for low-distortion parameterizations in this thesis. The first contribution of this thesis is the development of a RBF-based re-parameterization algorithm for the application of the foldover-free constrained texture mapping. The basic idea is to split the usual parameterization procedure into two steps, 2D parameterization with the constraints of convex boundaries and 2D re-parameterization with the interior positional constraints. Moreover, we further extend the 2D re-parameterization approach with the interior positional constraints to high dimensional datasets, such as, volume data and polyhedrons. The second contribution is the development of a vector field based deformation algorithm for 2D mesh deformation and image warping. Many presented deformation approaches are used to employ the basis functions (including our proposed RBF-based re-parameterization algorithm here). The main problem is that such algorithms have infinite support, that is, any local deformation always leads to small changes over the whole domain. Our presented vector field based algorithm can effectively carry on the local deformation while reducing distortion as much as possible. The third contribution is the development of a pre-processing for surface parameterization. Except the developable surfaces, the current parameterization approaches inevitably incur large distortion. To reduce distortion, we proposed a pre-processing procedure in this thesis, including mesh partition and mesh smoothing. As a result, the resulting meshes are partitioned into a set of small patches with rectangle-like boundaries. Moreover, they are well-shaped and well-spaced. This pre-processing procedure can evidently improve the quality of meshes for low-distortion parameterizations
Geodesic computation on implicit surfaces
Geodesics have a wide range of applications in CAD, shape design and machine learning. Current research on geodesic computation focuses primarily on parametric surfaces and mesh representations. There is little work on implicit surfaces. In this paper, we present a novel algorithm able
to compute the exact geodesics on implicit surfaces. Although the existing Fast Marching Method can generate a geodesic path on a Cartesian grid that envelopes the implicit surface in question, this method, as well as
other existing methods, is unable to compute a geodesic on the original surface. The computed geodesic path is actually a polyline offsetting from the surface. Our approach provides a solution to two existing fundamental
problems, which are (1) to produce a Cartesian grid that can tightly embed the implicit surface concerned, which remains challenging; and (2) to formulate exact geodesics on the original implicit surface itself. Our algorithm consists of two steps, Cartesian grid based geodesic
computation and geodesic correction. The later corrects an approximate geodesic path so that it can be on the implicit surface. In addition, in comparison with other existing work, our methods can handle both low dimensional and high dimensional surfaces (hyper-surfaces)
- …