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.
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.