Skeleton-based canonical forms for non-rigid 3D shape retrieval

The retrieval of non-rigid 3D shapes is an important task. A common technique is to simplify this problem to a rigid shape retrieval task by producing a bending invariant canonical form for each shape in the dataset to be searched. It is common for these techniques to attempt to ``unbend'' a shape by applying multidimensional scaling to the distances between points on the mesh, but this leads to unwanted local shape distortions. We instead perform the unbending on the skeleton of the mesh, and use this to drive the deformation of the mesh itself. This leads to a computational speed-up and less distortions of the local details of the shape. We compare our method against other canonical forms and our experiments show that our method achieves state-of-the-art retrieval accuracy in a recent canonical forms benchmark, and only a small drop in retrieval accuracy over state-of-the-art in a second recent benchmark, while being significantly faster

An evaluation of canonical forms for non-rigid 3D shape retrieval

Canonical forms attempt to factor out a non-rigid shape’s pose, giving a pose-neutral shape. This opens up the possibility of using methods originally designed for rigid shape retrieval for the task of non-rigid shape retrieval. We extend our recent benchmark for testing canonical form algorithms. Our new benchmark is used to evaluate a greater number of state-of-the-art canonical forms, on five recent non-rigid retrieval datasets, within two different retrieval frameworks. A total of fifteen different canonical form methods are compared. We find that the difference in retrieval accuracy between different canonical form methods is small, but varies significantly across different datasets. We also find that efficiency is the main difference between the methods

DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.Comment: 10 pages, 11 Figure

Learning shape correspondence with anisotropic convolutional neural networks

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the presence of topological noise and missing parts, mainly due to the limited capability to model such deformations axiomatically. Several recent works showed that invariance to complex shape transformations can be learned from examples. In this paper, we introduce an intrinsic convolutional neural network architecture based on anisotropic diffusion kernels, which we term Anisotropic Convolutional Neural Network (ACNN). In our construction, we generalize convolutions to non-Euclidean domains by constructing a set of oriented anisotropic diffusion kernels, creating in this way a local intrinsic polar representation of the data (`patch'), which is then correlated with a filter. Several cascades of such filters, linear, and non-linear operators are stacked to form a deep neural network whose parameters are learned by minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks

Statistical Modelling of Craniofacial Shape

With prior knowledge and experience, people can easily observe rich shape and texture variation for a certain type of objects, such as human faces, cats or chairs, in both 2D and 3D images. This ability helps us recognise the same person, distinguish different kinds of creatures and sketch unseen samples of the same object class. The process of capturing this prior knowledge is mathematically interpreted as statistical modelling. The outcome is a morphable model, a vector space representation of objects, that captures the variation of shape and texture. This thesis presents research aimed at constructing 3DMMs of craniofacial shape and texture using new algorithms and processing pipelines to offer enhanced modelling abilities over existing techniques. In particular, we present several fully automatic modelling approaches and apply them to a large dataset of 3D images of the human head, the Headspace dataset, thus generating the first public shape-and- texture 3D Morphable Model (3DMM) of the full human head. We call this the Liverpool-York Head Model, reflecting the data collection and statistical modelling respectively. We also explore the craniofacial symmetry and asymmetry in template morphing and statistical modelling. We propose a Symmetry-aware Coherent Point Drift (SA-CPD) algorithm, which mitigates the tangential sliding problem seen in competing morphing algorithms. Based on the symmetry-constrained correspondence output of SA-CPD, we present a symmetry-factored statistical modelling method for craniofacial shape. Also, we propose an iterative process of refinement for a 3DMM of the human ear that employs data augmentation. Then we merge the proposed 3DMMs of the ear with the full head model. As craniofacial clinicians like to look at head profiles, we propose a new pipeline to build a 2D morphable model of the craniofacial sagittal profile and augment it with profile models from frontal and top-down views. Our models and data are made publicly available online for research purposes

Spatial Displays and Spatial Instruments

The conference proceedings topics are divided into two main areas: (1) issues of spatial and picture perception raised by graphical electronic displays of spatial information; and (2) design questions raised by the practical experience of designers actually defining new spatial instruments for use in new aircraft and spacecraft. Each topic is considered from both a theoretical and an applied direction. Emphasis is placed on discussion of phenomena and determination of design principles

Model-Based Multiple 3D Object Recognition in Range Data

Vision guided systems are relevant for many industrial application areas, including manufacturing, medicine, service robots etc. A task common to these applications consists of detecting and localizing known objects in cluttered scenes. This amounts to solve the "chicken and egg" problem consisting of data assignment and parameter estimation, that is to localize an object and to determine its pose. In this work, we consider computer vision techniques for the special scenario of industrial bin-picking applications where the goal is to accurately estimate the positions of multiple instances of arbitrary, known objects that are randomly assembled in a bin. Although a-priori knowledge of the objects simplifies the problem, model symmetries, mutual occlusion as well as noise, unstructured measurements and run-time constraints render the problem far from being trivial. A common strategy to cope with this problem is to apply a two-step approach that consists of rough initialization estimation for each objects' position followed by subsequent refinement steps. Established initialization procedures only take into account single objects, however. Hence, they cannot resolve contextual constraints caused by multiple object instances and thus yield poor estimates of the objects' pose in many settings. Inaccurate initial configurations, on the other hand, cause state-of-the-art refinement algorithms to be unable to identify the objects' pose, such that the entire two-step approach is likely to fail. In this thesis, we propose a novel approach for obtaining initial estimates of all object positions jointly. Additionally, we investigate a new local, individual refinement procedure that copes with the shortcomings of state-of-the-art approaches while yielding fast and accurate registration results as well as a large region of attraction. Both stages are designed using advanced numerical techniques such as large-scale convex programming and geometric optimization on the curved space of Euclidean transformations, respectively. They complement each other in that conflicting interpretations are resolved through non-local convex processing, followed by accurate non-convex local optimization based on sufficiently good initializations. Exhaustive numerical evaluation on artificial and real-world measurements experimentally confirms the proposed two-step approach and demonstrates the robustness to noise, unstructured measurements and occlusions as well as showing the potential to meet run-time constraints of real-world industrial applications