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Various fundamental applications in computer vision and machine learning require finding the basis of a certain subspace. Examples of such applications include face detection, motion estimation, and activity recognition. An increasing interest has been recently placed on this area as a result of significant advances in the mathematics of matrix rank optimization. Interestingly, robust subspace estimation can be posed as a low-rank optimization problem, which can be solved efficiently using techniques such as the method of Augmented Lagrange Multiplier. In this book, the authors discuss fundamental formulations and extensions for low-rank optimization-based subspace estimation and representation. By minimizing the rank of the matrix containing observations drawn from images, the authors demonstrate  how to solve four fundamental computer vision problems, including video denosing, background subtraction, motion estimation, and activity recognition.

Computer vision. --- Trajectory optimization. --- Optimization, Trajectory --- Aerodynamics --- Space trajectories --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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This thesis presents fundamental work that explains two mysteries concerning the trajectory of interplanetary spacecraft. For the first problem, the so-called Pioneer anomaly, a wholly new and innovative method was developed for computing all contributions to the acceleration due to onboard thermal sources. Through a careful analysis of all parts of the spacecraft Pioneer 10 and 11, the application of this methodology has yielded the observed anomalous acceleration. This marks a major achievement, given that this problem remained unsolved for more than a decade. For the second anomaly, the flyby anomaly, a tiny glitch in the velocity of spacecraft that perform gravity assisting maneuvers on Earth, no definitive answer is put forward; however a quite promising strategy for examining the problem is provided and a new mission is proposed. The proposal largely consists in using the Galileo Navigational Satellite System to track approaching spacecraft, and in considering a small test body that approaches Earth from a highly elliptic trajectory.

Physics. --- Extraterrestrial Physics, Space Sciences. --- Theoretical, Mathematical and Computational Physics. --- Aerospace Technology and Astronautics. --- Astrophysics. --- Astronautics. --- Physique --- Astrophysique --- Astronautique --- Space trajectories. --- Space vehicles -- Propulsion systems. --- Trajectory optimization -- Mathematical models. --- Astronomy & Astrophysics --- Physical Sciences & Mathematics --- Astrophysics --- Trajectory optimization --- Linear programming. --- Mathematical models. --- Optimization, Trajectory --- Space vehicles --- Trajectories --- Space sciences. --- Aerospace engineering. --- Aerodynamics --- Space trajectories --- Astrodynamics --- Space flight --- Trajectories (Mechanics) --- Production scheduling --- Programming (Mathematics) --- Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). --- Space sciences --- Aeronautics --- Astronomical physics --- Astronomy --- Cosmic physics --- Physics --- Mathematical physics. --- Aeronautical engineering --- Astronautics --- Engineering --- Physical mathematics --- Science and space --- Space research --- Cosmology --- Science --- Mathematics