The empirical moment matrix and its application in computer vision

Abstract

(GOG). The images on the first row are from the "probe" view and the second row are from the "gallery" view. In these examples, with the help of higher order moments, moM has better invariance property when the person has a fine-detailed non-Gaussian appearance, e.g., the dot-pattern in column 1, white strip on the backpack in column 2, black strip on a white shirt in column 3 and the stripe-pattern in column 4. . The best result for each metric learning is marked in red and the second best is in blue. The best combination across the whole dataset is mark in bold red. I would also like to thank Professor Mario Sznaier for his guidance and help on all kinds of different fundamental theoretical problems. His endless support makes me feel worried less to pursue the highest goal. I also want to thank Professor Richard Radke for showing me how to collaborate with other team players and the careful counsel on my manuscripts.I would like to thank Professor Jennifer Dy for serving as my committee member and for her insightful comments on my work.I would like to thank Dr. Milind Rajadhyaksha and Dr. Kivanc Kose for their help and wise advice on medical image processing. I'm thrilled to see my knowledge can help cancer patients.I also want to thank Professor Dana Brooks, Professor Mark Niedre and Professor Ningfang Mi for their patience and thoughtful guidance on the organization of NEPSSS seminars. I enjoyed the time with NEPSSS! I would like to thank the supportive faculties and staff in ALERT, especially Professor Michael Silevitch for his insightful advice and the "so what who cares" and Deanna Beirne for her help to maintain the machines and equipment of the project.I want to thank my collaborators from RPI, Dr. Ziyan Wu, Dr. Yang Li and Dr. Srikrishna Karanam for their thoughtful discussions and help on the CLE Airport project.I spent my six year Ph.D. life in one of the best labs, and I would thank all my lab mates, collaborators, mentors and best friends in the Robust System Lab. I would like to thank Binlong, Fei, Walter, Xuefeng, Xiao, Burak, Tom, Oliver, Yongfang, Yin, Ichiro, Zulqarnain, Jing, Weijia, Caglayan, Rasmus, Jose, Sadjad, Tianyu, Wenqian, Bengisu, Angels, Qian, Begum, Xikang, Dong and Yuexi for their sharing and support.Last but the most important, I would like to thank three unique women in my life, my wife Dr. Wenjuan Qin and my daughters Shuhan and Shuxin. They are my source of happiness and power to help and support me through the tough but exciting six years.x Notations R, N set of real number, set of nonnegative integers x, x, X scalar, a vector in R n , a matrix in R m×n x(i) the i-th entry of x X(i, j) the (i, j)-th entry of X X F Frobenius norm of the matrix X ∈ R m×n Embedding local properties of an image, for instance its color intensities or the magnitude and orientation of its gradients, to create a representative feature is a critical component in many computer vision tasks, such as detection, classification, segmentation and tracking. A feature that is representative yet invariant t...