Registration and Recognition in 3D

The simplest Computer Vision algorithm can tell you what color it sees when you point it at an object, but asking that computer what it is looking at is a much harder problem. Camera and LiDAR (Light Detection And Ranging) sensors generally provide streams pixel of values and sophisticated algorithms must be engineered to recognize objects or the environment. There has been significant effort expended by the computer vision community on recognizing objects in color images; however, LiDAR sensors, which sense depth values for pixels instead of color, have been studied less. Recently we have seen a renewed interest in depth data with the democratization provided by consumer depth cameras. Detecting objects in depth data is more challenging in some ways because of the lack of texture and increased complexity of processing unordered point sets. We present three systems that contribute to solving the object recognition problem from the LiDAR perspective. They are: calibration, registration, and object recognition systems. We propose a novel calibration system that works with both line and raster based LiDAR sensors, and calibrates them with respect to image cameras. Our system can be extended to calibrate LiDAR sensors that do not give intensity information. We demonstrate a novel system that produces registrations between different LiDAR scans by transforming the input point cloud into a Constellation Extended Gaussian Image (CEGI) and then uses this CEGI to estimate the rotational alignment of the scans independently. Finally we present a method for object recognition which uses local (Spin Images) and global (CEGI) information to recognize cars in a large urban dataset. We present real world results from these three systems. Compelling experiments show that object recognition systems can gain much information using only 3D geometry. There are many object recognition and navigation algorithms that work on images; the work we propose in this thesis is more complimentary to those image based methods than competitive. This is an important step along the way to more intelligent robots

Bayesian Methods and Confidence Intervals for Automatic Target Recognition of SAR Canonical Shapes

This research develops a new Bayesian technique for the detection of scattering primitives in synthetic aperture radar (SAR) phase history data received from a sensor platform. The primary goal of this research is the estimation of size, position, and orientation parameters defined by the “canonical” shape primitives of Jackson. Previous Bayesian methods for this problem have focused on the traditional maximum a posteriori (MAP) estimate based on the posterior density. A new concept, the probability mass interval, is developed. In this technique the posterior density is partitioned into intervals, which are then integrated to form a probability mass over that interval using the Gaussian quadrature numerical integration techniques. The posterior density is therefore discretized in such a way that the location of local peaks are preserved. A formal treatment is given to the effect of locally integrating the posterior density in the context of parameter estimation. It is shown that the operation of choosing the interval with the highest probability mass is equivalent to an optimum Bayesian estimator that places zero cost on a “range” of parameters. The range is user-controlled, and is akin to the idea of parameter resolution. Additionally the peak-preserving property allows the user to begin with coarse intervals and “zoom” in as they see fit. Associated with these estimates is a measure of quality called the credible interval (or credible set). The credible interval (set) is a region of parameter space where the “true” parameter is located with a user-defined probability. Narrow credible intervals are associated with high-quality estimates while wide credible intervals are associated with poor estimates. The techniques are implemented in state-of-the-art graphics processor unit (GPU) hardware, which allows the numerical integration to be performed in a reasonable time. A typical estimator requires several hundred million computations and the GPU implementation reduces the computation time from several hours to a few seconds. The mass interval estimation technique may be used on any Bayesian problem, but is demonstrated here using each of the canonical shape models of Jackson. The technique successfully estimates parameters in different scenarios including simple shapes, multiple shapes, incorrect shape (i.e. trying to estimate parameters using the wrong model). The results of this research are a new exploration of the posterior distributions of the canonical shape model, improved numerical integration strategies, and a new statistical technique for the Bayesian estimation of parameters

Instrumentation for Biological Research, Volume I, Sections 1 to 3 Final Report, Nov. 9, 1964 - Mar. 31, 1966

Bioinstrumentation for controlling and measuring parameters interacting with biological syste

Multimodal Three Dimensional Scene Reconstruction, The Gaussian Fields Framework

The focus of this research is on building 3D representations of real world scenes and objects using different imaging sensors. Primarily range acquisition devices (such as laser scanners and stereo systems) that allow the recovery of 3D geometry, and multi-spectral image sequences including visual and thermal IR images that provide additional scene characteristics. The crucial technical challenge that we addressed is the automatic point-sets registration task. In this context our main contribution is the development of an optimization-based method at the core of which lies a unified criterion that solves simultaneously for the dense point correspondence and transformation recovery problems. The new criterion has a straightforward expression in terms of the datasets and the alignment parameters and was used primarily for 3D rigid registration of point-sets. However it proved also useful for feature-based multimodal image alignment. We derived our method from simple Boolean matching principles by approximation and relaxation. One of the main advantages of the proposed approach, as compared to the widely used class of Iterative Closest Point (ICP) algorithms, is convexity in the neighborhood of the registration parameters and continuous differentiability, allowing for the use of standard gradient-based optimization techniques. Physically the criterion is interpreted in terms of a Gaussian Force Field exerted by one point-set on the other. Such formulation proved useful for controlling and increasing the region of convergence, and hence allowing for more autonomy in correspondence tasks. Furthermore, the criterion can be computed with linear complexity using recently developed Fast Gauss Transform numerical techniques. In addition, we also introduced a new local feature descriptor that was derived from visual saliency principles and which enhanced significantly the performance of the registration algorithm. The resulting technique was subjected to a thorough experimental analysis that highlighted its strength and showed its limitations. Our current applications are in the field of 3D modeling for inspection, surveillance, and biometrics. However, since this matching framework can be applied to any type of data, that can be represented as N-dimensional point-sets, the scope of the method is shown to reach many more pattern analysis applications

Optimal Control Applications in Space Situational Awareness

There are currently more than 19,000 trackable objects in Earth orbit, 1,300 of which are active. With so many objects populating the space object catalog and new objects being added at an ever increasing rate, ensuring continued access to space is quickly becoming a cornerstone of national security policies. Space Situational Awareness (SSA) supports space operations, space flight safety, implementing international treaties and agreements, protecting of space capabilities, and protecting of national interests. With respect to objects in orbit, this entails determining their location, orientation, size, shape, status, purpose, current tasking, and future tasking. For active spacecraft capable of propulsion, the problem of determining these characteristics becomes significantly more difficult. Optimal control techniques can be applied to object correlation, maneuver detection, maneuver/spacecraft characterization, fuel usage estimation, operator priority inference, intercept capability characterization, and fuel-constrained range set determination. A detailed mapping between optimal control applications and SSA object characterization support is reviewed and related literature visited. Each SSA application will be addressed starting from first principles using optimal control techniques. For each application, several examples of potential utility are given and discussed

Cartography

The terrestrial space is the place of interaction of natural and social systems. The cartography is an essential tool to understand the complexity of these systems, their interaction and evolution. This brings the cartography to an important place in the modern world. The book presents several contributions at different areas and activities showing the importance of the cartography to the perception and organization of the territory. Learning with the past or understanding the present the use of cartography is presented as a way of looking to almost all themes of the knowledge

Models for Human Navigation and Optimal Path Planning Using Level Set Methods and Hamilton-Jacobi Equations

We present several models for different physical scenarios which are centered around human movement or optimal path planning, and use partial differential equations and concepts from control theory. The first model is a game-theoretic model for environmental crime which tracks criminals' movement using the level set method, and improves upon previous continuous models by removing overly restrictive assumptions of symmetry. Next, we design a method for determining optimal hiking paths in mountainous regions using an anisotropic level set equation. After this, we present a model for optimal human navigation with uncertainty which is rooted in dynamic programming and stochastic optimal control theory. Lastly, we consider optimal path planning for simple, self-driving cars in the Hamilton-Jacobi formulation. We improve upon previous models which simplify the car to a point mass, and present a reasonably general upwind, sweeping scheme to solve the relevant Hamilton-Jacobi equation