PT Journal
AU Carme Julia
   Angel Sappa
   Felipe Lumbreras
   Joan Serrat
   Antonio Lopez
TI Rank Estimation in Missing Data Matrix Problems
SO Journal of Mathematical Imaging and Vision
JI JMIV
PY 2011
BP 140
EP 160
VL 39
IS 2
DI 10.1007/s10851-010-0229-z
AB A novel technique for missing data matrix rank estimation is presented. It is focused on matrices of trajectories, where every element of the matrix corresponds to an image coordinate from a feature point of a rigid moving object at a given frame; missing data are represented as empty entries. The objective of the proposed approach is to estimate the rank of a missing data matrix in order to fill in empty entries with some matrix completion method, without using or assuming neither the number of objects contained in the scene nor the kind of their motion. The key point of the proposed technique consists in studying the frequency behaviour of the individual trajectories, which are seen as 1D signals. The main assumption is that due to the rigidity of the moving objects, the frequency content of the trajectories will be similar after filling in their missing entries. The proposed rank estimation approach can be used in different computer vision problems, where the rank of a missing data matrix needs to be estimated. Experimental results with synthetic and real data are provided in order to empirically show the good performance of the proposed approach.
ER