Tensor Algebra: A Combinatorial Approach to the Projective Geometry of Figures

This paper explores the combinatorial aspects of symmetric and antisymmetric forms represented in tensor algebra. The development of geometric perspective gained from tensor algebra has resulted in the discovery of a novel projection operator for the Chow form of a curve in P3 with applications to computer vision

Probabilistic Search for Object Segmentation and Recognition

The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object probability, is introduced to infer an optimal sequence of object hypotheses to be evaluated for their match to the data. The truncated probability is partly determined by prior knowledge of the objects and partly learned from data. Some experiments on sequence quality and object segmentation and recognition from stereo data are presented. The article recovers classic concepts from object recognition (grouping, geometric hashing, alignment) from the probabilistic perspective and adds insight into the optimal ordering of object hypotheses for evaluation. Moreover, it introduces point-relation densities, a key component of the truncated probability, as statistical models of local surface shape.Comment: 18 pages, 5 figure

3DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registration

In this paper, we propose the 3DFeat-Net which learns both 3D feature detector and descriptor for point cloud matching using weak supervision. Unlike many existing works, we do not require manual annotation of matching point clusters. Instead, we leverage on alignment and attention mechanisms to learn feature correspondences from GPS/INS tagged 3D point clouds without explicitly specifying them. We create training and benchmark outdoor Lidar datasets, and experiments show that 3DFeat-Net obtains state-of-the-art performance on these gravity-aligned datasets.Comment: 17 pages, 6 figures. Accepted in ECCV 201

Automatic 3D facial model and texture reconstruction from range scans

This paper presents a fully automatic approach to fitting a generic facial model to detailed range scans of human faces to reconstruct 3D facial models and textures with no manual intervention (such as specifying landmarks). A Scaling Iterative Closest Points (SICP) algorithm is introduced to compute the optimal rigid registrations between the generic model and the range scans with different sizes. And then a new template-fitting method, formulated in an optmization framework of minimizing the physically based elastic energy derived from thin shells, faithfully reconstructs the surfaces and the textures from the range scans and yields dense point correspondences across the reconstructed facial models. Finally, we demonstrate a facial expression transfer method to clone facial expressions from the generic model onto the reconstructed facial models by using the deformation transfer technique

Learning and Matching Multi-View Descriptors for Registration of Point Clouds

Critical to the registration of point clouds is the establishment of a set of accurate correspondences between points in 3D space. The correspondence problem is generally addressed by the design of discriminative 3D local descriptors on the one hand, and the development of robust matching strategies on the other hand. In this work, we first propose a multi-view local descriptor, which is learned from the images of multiple views, for the description of 3D keypoints. Then, we develop a robust matching approach, aiming at rejecting outlier matches based on the efficient inference via belief propagation on the defined graphical model. We have demonstrated the boost of our approaches to registration on the public scanning and multi-view stereo datasets. The superior performance has been verified by the intensive comparisons against a variety of descriptors and matching methods

Asynchronous, Photometric Feature Tracking using Events and Frames

We present a method that leverages the complementarity of event cameras and standard cameras to track visual features with low-latency. Event cameras are novel sensors that output pixel-level brightness changes, called "events". They offer significant advantages over standard cameras, namely a very high dynamic range, no motion blur, and a latency in the order of microseconds. However, because the same scene pattern can produce different events depending on the motion direction, establishing event correspondences across time is challenging. By contrast, standard cameras provide intensity measurements (frames) that do not depend on motion direction. Our method extracts features on frames and subsequently tracks them asynchronously using events, thereby exploiting the best of both types of data: the frames provide a photometric representation that does not depend on motion direction and the events provide low-latency updates. In contrast to previous works, which are based on heuristics, this is the first principled method that uses raw intensity measurements directly, based on a generative event model within a maximum-likelihood framework. As a result, our method produces feature tracks that are both more accurate (subpixel accuracy) and longer than the state of the art, across a wide variety of scenes.Comment: 22 pages, 15 figures, Video: https://youtu.be/A7UfeUnG6c

Bayesian Point Set Registration

Point set registration involves identifying a smooth invertible transformation between corresponding points in two point sets, one of which may be smaller than the other and possibly corrupted by observation noise. This problem is traditionally decomposed into two separate optimization problems: (i) assignment or correspondence, and (ii) identification of the optimal transformation between the ordered point sets. In this work, we propose an approach solving both problems simultaneously. In particular, a coherent Bayesian formulation of the problem results in a marginal posterior distribution on the transformation, which is explored within a Markov chain Monte Carlo scheme. Motivated by Atomic Probe Tomography (APT), in the context of structure inference for high entropy alloys (HEA), we focus on the registration of noisy sparse observations of rigid transformations of a known reference configuration.Lastly, we test our method on synthetic data sets.Comment: 15 pages, 20 figure

LivePhantom: Retrieving Virtual World Light Data to Real Environments.

To achieve realistic Augmented Reality (AR), shadows play an important role in creating a 3D impression of a scene. Casting virtual shadows on real and virtual objects is one of the topics of research being conducted in this area. In this paper, we propose a new method for creating complex AR indoor scenes using real time depth detection to exert virtual shadows on virtual and real environments. A Kinect camera was used to produce a depth map for the physical scene mixing into a single real-time transparent tacit surface. Once this is created, the camera's position can be tracked from the reconstructed 3D scene. Real objects are represented by virtual object phantoms in the AR scene enabling users holding a webcam and a standard Kinect camera to capture and reconstruct environments simultaneously. The tracking capability of the algorithm is shown and the findings are assessed drawing upon qualitative and quantitative methods making comparisons with previous AR phantom generation applications. The results demonstrate the robustness of the technique for realistic indoor rendering in AR systems