Shape basis interpretation for monocular deformable 3D reconstruction

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, we propose a novel interpretable shape model to encode object non-rigidity. We first use the initial frames of a monocular video to recover a rest shape, used later to compute a dissimilarity measure based on a distance matrix measurement. Spectral analysis is then applied to this matrix to obtain a reduced shape basis, that in contrast to existing approaches, can be physically interpreted. In turn, these pre-computed shape bases are used to linearly span the deformation of a wide variety of objects. We introduce the low-rank basis into a sequential approach to recover both camera motion and non-rigid shape from the monocular video, by simply optimizing the weights of the linear combination using bundle adjustment. Since the number of parameters to optimize per frame is relatively small, specially when physical priors are considered, our approach is fast and can potentially run in real time. Validation is done in a wide variety of real-world objects, undergoing both inextensible and extensible deformations. Our approach achieves remarkable robustness to artifacts such as noisy and missing measurements and shows an improved performance to competing methods.Peer ReviewedPostprint (author's final draft

A Fast Modal Space Transform for Robust Nonrigid Shape Retrieval

Nonrigid or deformable 3D objects are common in many application domains. Retrieval of such objects in large databases based on shape similarity is still a challenging problem. In this paper, we take advantages of functional operators as characterizations of shape deformation, and further propose a framework to design novel shape signatures for encoding nonrigid geometries. Our approach constructs a context-aware integral kernel operator on a manifold, then applies modal analysis to map this operator into a low-frequency functional representation, called fast functional transform, and finally computes its spectrum as the shape signature. In a nutshell, our method is fast, isometry-invariant, discriminative, smooth and numerically stable with respect to multiple types of perturbations. Experimental results demonstrate that our new shape signature for nonrigid objects can outperform all methods participating in the nonrigid track of the SHREC’11 contest. It is also the second best performing method in the real human model track of SHREC’14.postprin

3-D Shape Matching for Face Analysis and Recognition

The aims of this paper are to introduce a 3-D shape matching scheme for automatic face recognition and to demonstrate its invariance to pose and facial expressions. The core of this scheme lies on the combination of non-rigid deformation registration and statistical shape modelling. While the former matches 3-D faces regardless of facial expression variations, the latter provides a low-dimensional feature vector that describes the deformation after the shape matching process, thereby enabling robust identification of 3-D faces. In order to assist establishment of accurate dense point correspondences, an isometric embedding shape representation is introduced, which is able to transform 3-D faces to a canonical form that retains the intrinsic geometric structure and achieve shape alignment of 3-D faces independent from individual’s facial expression. The feasibility and effectiveness of the proposed method was investigated using standard publicly available Gavab and BU-3DFE databases, which contain faces expressions and pose variations. The performance of the system was compared with the existing benchmark approaches and it demonstrates that the proposed scheme provides a competitive solution for the face recognition task with real-world practicality

Machine Intelligence for Advanced Medical Data Analysis: Manifold Learning Approach

In the current work, linear and non-linear manifold learning techniques, specifically Principle Component Analysis (PCA) and Laplacian Eigenmaps, are studied in detail. Their applications in medical image and shape analysis are investigated. In the first contribution, a manifold learning-based multi-modal image registration technique is developed, which results in a unified intensity system through intensity transformation between the reference and sensed images. The transformation eliminates intensity variations in multi-modal medical scans and hence facilitates employing well-studied mono-modal registration techniques. The method can be used for registering multi-modal images with full and partial data. Next, a manifold learning-based scale invariant global shape descriptor is introduced. The proposed descriptor benefits from the capability of Laplacian Eigenmap in dealing with high dimensional data by introducing an exponential weighting scheme. It eliminates the limitations tied to the well-known cotangent weighting scheme, namely dependency on triangular mesh representation and high intra-class quality of 3D models. In the end, a novel descriptive model for diagnostic classification of pulmonary nodules is presented. The descriptive model benefits from structural differences between benign and malignant nodules for automatic and accurate prediction of a candidate nodule. It extracts concise and discriminative features automatically from the 3D surface structure of a nodule using spectral features studied in the previous work combined with a point cloud-based deep learning network. Extensive experiments have been conducted and have shown that the proposed algorithms based on manifold learning outperform several state-of-the-art methods. Advanced computational techniques with a combination of manifold learning and deep networks can play a vital role in effective healthcare delivery by providing a framework for several fundamental tasks in image and shape processing, namely, registration, classification, and detection of features of interest

Spectral methods for multimodal data analysis

Spectral methods have proven themselves as an important and versatile tool in a wide range of problems in the fields of computer graphics, machine learning, pattern recognition, and computer vision, where many important problems boil down to constructing a Laplacian operator and finding a few of its eigenvalues and eigenfunctions. Classical examples include the computation of diffusion distances on manifolds in computer graphics, Laplacian eigenmaps, and spectral clustering in machine learning. In many cases, one has to deal with multiple data spaces simultaneously. For example, clustering multimedia data in machine learning applications involves various modalities or ``views'' (e.g., text and images), and finding correspondence between shapes in computer graphics problems is an operation performed between two or more modalities. In this thesis, we develop a generalization of spectral methods to deal with multiple data spaces and apply them to problems from the domains of computer graphics, machine learning, and image processing. Our main construction is based on simultaneous diagonalization of Laplacian operators. We present an efficient numerical technique for computing joint approximate eigenvectors of two or more Laplacians in challenging noisy scenarios, which also appears to be the first general non-smooth manifold optimization method. Finally, we use the relation between joint approximate diagonalizability and approximate commutativity of operators to define a structural similarity measure for images. We use this measure to perform structure-preserving color manipulations of a given image

Geometry-Aware Network for Non-Rigid Shape Prediction from a Single View

We propose a method for predicting the 3D shape of a deformable surface from a single view. By contrast with previous approaches, we do not need a pre-registered template of the surface, and our method is robust to the lack of texture and partial occlusions. At the core of our approach is a {\it geometry-aware} deep architecture that tackles the problem as usually done in analytic solutions: first perform 2D detection of the mesh and then estimate a 3D shape that is geometrically consistent with the image. We train this architecture in an end-to-end manner using a large dataset of synthetic renderings of shapes under different levels of deformation, material properties, textures and lighting conditions. We evaluate our approach on a test split of this dataset and available real benchmarks, consistently improving state-of-the-art solutions with a significantly lower computational time.Comment: Accepted at CVPR 201