We propose a systematic approach for registering cross-source point clouds that come from different kinds of sensors. This task is especially challenging due to the presence of significant missing data, large variations in point density, scale difference, large proportion of noise, and outliers. The robustness of the method is attributed to the extraction of macro and micro structures. Macro structure is the overall structure that maintains similar geometric layout in cross-source point clouds. Micro structure is the element (e.g., local segment) being used to build the macro structure. We use graph to organize these structures and convert the registration into graph matching. With a novel proposed descriptor, we conduct the graph matching in a discriminative feature space. The graph matching problem is solved by an improved graph matching solution, which considers global geometrical constraints. Robust cross source registration results are obtained by incorporating graph matching outcome with RANSAC and ICP refinements. Compared with eight state-of-the-art registration algorithms, the proposed method invariably outperforms on Pisa Cathedral and other challenging cases. In order to compare quantitatively, we propose two challenging cross-source data sets and conduct comparative experiments on more than 27 cases, and the results show we obtain much better performance than other methods. The proposed method also shows high accuracy in same-source data sets.
Torki and Elgammal @cite_42 use local features in images to learn manifold symbol. The authors first learn a feature embedding representation that contains the spatial structure of the features as well as the local appearance similarity. The out-of-sample method is then used to embed the features from new images. Similarly, Yuan @cite_31 transforms every point in a point clouds into a shape representation, in order to cast the problem of point sets matching as a shape registration problem, which is the Schrodinger distance transform (SDT) representation. The problem is then transformed into solving a static Schrodinger equation in place of the consistent static Hamilton-Jacobi equation in the setting. The SDT representation is an analytic expression which can be normalized to have unit L2 norm in accordance with theoretical physics literature. The outline of this method is "points set" @math "SDTs" @math "minimize the geodesic distance".
@cite_31 @cite_42
2012048508 2026164926 2909750748 2810912957
In this paper, we cast the problem of point cloud matching as a shape matching problem by transforming each of the given point clouds into a shape representation called the Schrodinger distance transform (SDT) representation. This is achieved by solving a static Schrodinger equation instead of the corresponding static Hamilton-Jacobi equation in this setting. The SDT representation is an analytic expression and following the theoretical physics literature, can be normalized to have unit 2 norm -- making it a square-root density, which is identified with a point on a unit Hilbert sphere, whose intrinsic geometry is fully known. The Fisher-Rao metric, a natural metric for the space of densities leads to analytic expressions for the geodesic distance between points on this sphere. In this paper, we use the well known Riemannian framework never before used for point cloud matching, and present a novel matching algorithm. We pose point set matching under rigid and non-rigid transformations in this framework and solve for the transformations using standard nonlinear optimization techniques. Finally, to evaluate the performance of our algorithm -- dubbed SDTM -- we present several synthetic and real data examples along with extensive comparisons to state-of-the-art techniques. The experiments show that our algorithm outperforms state-of the-art point set registration algorithms on many quantitative metrics. Local features have proven very useful for recognition. Manifold learning has proven to be a very powerful tool in data analysis. However, manifold learning application for images are mainly based on holistic vectorized representations of images. The challenging question that we address in this paper is how can we learn image manifolds from a punch of local features in a smooth way that captures the feature similarity and spatial arrangement variability between images. We introduce a novel framework for learning a manifold representation from collections of local features in images. We first show how we can learn a feature embedding representation that preserves both the local appearance similarity as well as the spatial structure of the features. We also show how we can embed features from a new image by introducing a solution for the out-of-sample that is suitable for this context. By solving these two problems and defining a proper distance measure in the feature embedding space, we can reach an image manifold embedding space. Computer graphics, 3D computer vision and robotics communities have produced multiple approaches to representing 3D geometry for rendering and reconstruction. These provide trade-offs across fidelity, efficiency and compression capabilities. In this work, we introduce DeepSDF, a learned continuous Signed Distance Function (SDF) representation of a class of shapes that enables high quality shape representation, interpolation and completion from partial and noisy 3D input data. DeepSDF, like its classical counterpart, represents a shape's surface by a continuous volumetric field: the magnitude of a point in the field represents the distance to the surface boundary and the sign indicates whether the region is inside (-) or outside (+) of the shape, hence our representation implicitly encodes a shape's boundary as the zero-level-set of the learned function while explicitly representing the classification of space as being part of the shapes interior or not. While classical SDF's both in analytical or discretized voxel form typically represent the surface of a single shape, DeepSDF can represent an entire class of shapes. Furthermore, we show state-of-the-art performance for learned 3D shape representation and completion while reducing the model size by an order of magnitude compared with previous work. In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the benefit to bring naturally a second desirable quantity when comparing shapes — the spatial covariance — in addition to the conventional affine-shape representation. We derived then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the underlying manifold. Specifically, our approach involves three steps: (1) landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of fixed-rank to build time-parameterized trajectories; (2) a temporal warping is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; (3) finally, a pairwise proximity function SVM is used to classify them, incorporating the (dis-)similarity measure into the kernel function. We show that such representation and metric achieve competitive results in applications as action recognition and emotion recognition from 3D skelet al data, and facial expression recognition from videos. Experiments have been conducted on several publicly available up-to-date benchmarks.