ON THE SELECTION OF SHAPE FUNCTION SPACES OF TRIANGULAR PLATE ELEMENTS

Using the method of undetermined coefficients, we construct a set of shape function spaces of nine-node triangular plate elements converging for any meshes, which generalize Spect's element and Veubeke's element.

Analysis on a Set of 12-parameter Rectangular Plate Element with High Accuracy

It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini＇s element＇s, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.

Geometric Morphometrics Applied to Cartography

The morphological differences between two geographical maps can be highlighted by a polycentric distance cartogram resulting from a bidimensional regression.Beyond the communicational interest of the transformations thus produced,the method makes it possible to reveal the differences in structure and therefore constitutes a real research tool.However,bidimensional regression can only compare the shape of two maps.Since the 1990s,geometric morphometrics has revolutionized the morphological analysis of natural structures(and others).It has since been applied in many fields of research but not in cartography.This article describes the theoretical and methodological bases of a method combining bidimensional regression with a geometric morphometrics approach to compare the shape of several geographical maps.Geometric morphometrics and bidimensional regression indeed share common approaches of the statistical shape analysis like homologous landmarks and interpolation grids.However,there is no software in geometric morphometrics capable of directly reading geographical data,which would facilitate the work of cartographers accustomed to GIS software.That is why we present MapMorphy,a tool specifically developed for this task.An example on ancient maps illustrates the method.

On 3D face reconstruction via cascaded regression in shape space

Cascaded regression has been recently applied to reconstruct 3D faces from single 2D images directly in shape space, and has achieved state-of-the-art performance. We investigate thoroughly such cascaded regression based 3D face reconstruction approaches from four perspectives that are not well been studied： （1） the impact of the number of 2D landmarks; （2） the impact of the number of 3D vertices; （3） the way of using standalone automated landmark detection methods; （4） the convergence property. To answer these questions, a simplified cascaded regression based 3D face reconstruction method is devised. This can be integrated with standalone automated landmark detection methods and reconstruct 3D face shapes that have the same pose and expression as the input face images, rather than normalized pose and expression. An effective training method is also proposed by disturbing the automatically detected landmarks. Comprehensive evaluation experiments have been carried out to compare to other 3D face reconstruction methods. The results not only deepen the understanding of cascaded regression based 3D face reconstruction approaches, but also prove the effectiveness of the proposed method.

Shape correspondence for cel animation based on a shape association graph and spectral matching

We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes.We formulate the correspondence problem as an adapted quadratic assignment problem,which comprehensively considers both the intrinsic geometric and topology of regions to find the globally optimal correspondence.To simultaneously represent the geometric and topological similarities between regions,we propose a shape association graph(SAG),whose node attributes indicate the geometric distance between regions,and whose edge attributes indicate the topological distance between combined region pairs.We convert topological distance to geometric distance between geometric objects with topological features of the pairs,and introduce Kendall shape space to calculate the intrinsic geometric distance.By utilizing the spectral properties of the affinity matrix induced by the SAG,our approach can efficiently extract globally optimal region correspondences,even if shapes have inconsistent topology and severe deformation.It is also robust to shapes undergoing similarity transformations,and compatible with parallel computing techniques.