Simultaneous compaction and factorization of sparse image motion matrices
Matrices that collect the image coordinates of point features tracked through video - one column per feature - have often low rank, either exactly or approximately. This observation has led to many matrix factorization methods for 3D reconstruction, motion segmentation, or regularization of feature trajectories. However, temporary occlusions, image noise, and variations in lighting, pose, or object geometry often confound trackers. A feature that reappears after a temporary tracking failure - whatever the cause - is regarded as a new feature by typical tracking systems, resulting in very sparse matrices with many columns and rendering factorization problematic. We propose a method to simultaneously factor and compact such a matrix by merging groups of columns that correspond to the same feature into single columns. This combination of compaction and factorization makes trackers more resilient to changes in appearance and short occlusions. Preliminary experiments show that imputation of missing matrix entries - and therefore matrix factorization - becomes significantly more reliable as a result. Clean column merging also required us to develop a history-sensitive feature reinitialization method we call feature snapping that aligns merged feature trajectory segments precisely to each other. © 2012 Springer-Verlag.
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