We present an approach to simultaneously solve the two problems of face alignment and 3D face reconstruction from an input 2D face image of arbitrary poses and expressions. The proposed method iteratively and alternately applies two sets of cascaded regressors, one for updating 2D landmarks and the other for updating reconstructed poseexpression-normalized (PEN) 3D face shape. The 3D face shape...

We extend the classical Domino problem to any tiling of rhombus-shaped tiles. For subshift X edge-to-edge rhombus tilings, such as Penrose subshift, we prove that associated X-Domino is $$\varPi _1^0$$ -hard and therefore undecidable. It -complete when given by a computable sequence forbidden patterns.

Parallelograms are one of the basic building blocks in two-dimensional tiling. They have important applications in a wide variety of science and engineering fields, such as wireless communication networks, urban transportation, operations research, etc. Different from rectangles and squares, the coordinates of a random point in parallelograms are no longer independent. As a case study of parall...

3D face reconstruction is a very challenging problem in computer vision, and is used as a prerequisite for many important vision tasks, e.g., face recognition and face frontalization. The importance of 3D face reconstruction is that we can estimate illumination and pose information by using the 3D shape of the face. Since the human face is a non-rigid 3D object, estimating the 2D shape of the f...

In several disciplines as diverse as shape analysis, location theory, quality control, archaeology, and psychometrics, it can be of interest to fit a circle through a set of points. We use the result that it suffices to locate a center for which the variance of the distances from the center to a set of given points is minimal. In this paper, we propose a new algorithm based on iterative majoriz...

This paper focuses on the problem of 3D shape categorization. For a given set of training 3D shapes, a 3D shape recognition system must be able to predict the class label for a test 3D shape. We introduce a novel discriminative approach for recognizing 3D shape categories which is based on a 3D Spatial Pyramid (3DSP) decomposition. 3D local descriptors computed on the 3D shapes have to be extra...

The need for quantification of cell growth patterns in a multilayer, multi-cellular tissue necessitates the development of a 3D reconstruction technique that can estimate 3D shapes and sizes of individual cells from Confocal Microscopy (CLSM) image slices. However, the current methods of 3D reconstruction using CLSM imaging require large number of image slices per cell. But, in case of Live Cel...

We propose a new approach to easily creating 3D geometric models. A technique called interactive evolutionary computation (IEC) is introduced to accelerate user s invention and inspiration of new shapes. The proposed IEC-based design system generates aesthetically pleasing shapes through the simulation of natural evolutionary processes. The user only is required to specify his/her subjective pr...

In this paper, 24 three-dimensional (3D) vocal-tract (VT) shapes extracted from MRI data are used to derive a parametric model for the vocal-tract. The method is as follows: rst, each 3D VT shape is sampled using a semi-cylindrical grid whose position is determined by reference points based on VT anatomy. After that, the VT projections onto each plane of the grid are represented by their two ma...