Analysis of Shapes to Measure Surfaces: An Approach for Detection of Deformations

This paper presents a method to analyse 3D planar surfaces and to measure variations on it. The method is oriented to the detection of deformations on the elastic object surfaces formed by flat faces. These deformations are usually caused when two bodies, a solid and another elastic object, come in contact and there are contact pressures among their faces. Our method describes a strategy to model the shape of deformation using a mathematical approach based on two concepts: Histogram and Map of curvature. In particular, we describe the algorithm for deformations in order to use it in visual control and inspection tasks for manipulation processes with robot hands. Several experiments and their results are shown to evaluate the validity and robustness of the method to detect and measure deformations in grasping tasks. To do it, some virtual scenarios were created to simulate contacts with fingers of a hand robot.The research leading to these results has received funding from the Spanish Government and European FEDER funds (DPI2012-32390) and the Valencia Regional Government (PROMETEO/2013/085)

3D time series analysis of cell shape using Laplacian approaches

Background: Fundamental cellular processes such as cell movement, division or food uptake critically depend on cells being able to change shape. Fast acquisition of three-dimensional image time series has now become possible, but we lack efficient tools for analysing shape deformations in order to understand the real three-dimensional nature of shape changes. Results: We present a framework for 3D+time cell shape analysis. The main contribution is three-fold: First, we develop a fast, automatic random walker method for cell segmentation. Second, a novel topology fixing method is proposed to fix segmented binary volumes without spherical topology. Third, we show that algorithms used for each individual step of the analysis pipeline (cell segmentation, topology fixing, spherical parameterization, and shape representation) are closely related to the Laplacian operator. The framework is applied to the shape analysis of neutrophil cells. Conclusions: The method we propose for cell segmentation is faster than the traditional random walker method or the level set method, and performs better on 3D time-series of neutrophil cells, which are comparatively noisy as stacks have to be acquired fast enough to account for cell motion. Our method for topology fixing outperforms the tools provided by SPHARM-MAT and SPHARM-PDM in terms of their successful fixing rates. The different tasks in the presented pipeline for 3D+time shape analysis of cells can be solved using Laplacian approaches, opening the possibility of eventually combining individual steps in order to speed up computations

On Nonrigid Shape Similarity and Correspondence

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape comparison. Here, we explore the applicability of related shape similarity measures to the problem of shape correspondence, adopting spectral type distances. We propose to evaluate the spectral kernel distance, the spectral embedding distance and the novel spectral quasi-conformal distance, comparing the manifolds from different viewpoints. By matching the shapes in the spectral domain, important attributes of surface structure are being aligned. For the purpose of testing our ideas, we introduce a fully automatic framework for finding intrinsic correspondence between two shapes. The proposed method achieves state-of-the-art results on the Princeton isometric shape matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks

As-Built 3D Heritage City Modelling to Support Numerical Structural Analysis: Application to the Assessment of an Archaeological Remain

Terrestrial laser scanning is a widely used technology to digitise archaeological, architectural and cultural heritage. This allows for modelling the assets’ real condition in comparison with traditional data acquisition methods. This paper, based on the case study of the basilica in the Baelo Claudia archaeological ensemble (Tarifa, Spain), justifies the need of accurate heritage modelling against excessively simplified approaches in order to support structural safety analysis. To do this, after validating the 3Dmeshing process frompoint cloud data, the semi-automatic digital reconstitution of the basilica columns is performed. Next, a geometric analysis is conducted to calculate the structural alterations of the columns. In order to determine the structural performance, focusing both on the accuracy and suitability of the geometric models, static and modal analyses are carried out by means of the finite element method (FEM) on three different models for the most unfavourable column in terms of structural damage: (1) as-built (2) simplified and (3) ideal model without deformations. Finally, the outcomes show that the as-built modelling enhances the conservation status analysis of the 3D heritage city (in terms of realistic compliance factor values), although further automation still needs to be implemented in the modelling process

Towards multiple 3D bone surface identification and reconstruction using few 2D X-ray images for intraoperative applications

This article discusses a possible method to use a small number, e.g. 5, of conventional 2D X-ray images to reconstruct multiple 3D bone surfaces intraoperatively. Each bone’s edge contours in X-ray images are automatically identified. Sparse 3D landmark points of each bone are automatically reconstructed by pairing the 2D X-ray images. The reconstructed landmark point distribution on a surface is approximately optimal covering main characteristics of the surface. A statistical shape model, dense point distribution model (DPDM), is then used to fit the reconstructed optimal landmarks vertices to reconstruct a full surface of each bone separately. The reconstructed surfaces can then be visualised and manipulated by surgeons or used by surgical robotic systems

Multiple Shape Registration using Constrained Optimal Control

Lagrangian particle formulations of the large deformation diffeomorphic metric mapping algorithm (LDDMM) only allow for the study of a single shape. In this paper, we introduce and discuss both a theoretical and practical setting for the simultaneous study of multiple shapes that are either stitched to one another or slide along a submanifold. The method is described within the optimal control formalism, and optimality conditions are given, together with the equations that are needed to implement augmented Lagrangian methods. Experimental results are provided for stitched and sliding surfaces