TR2006-043

Fast Construction of Covariance Matrices for Arbitrary Size Image Windows


    •  Porikli, F., Tuzel, O., "Fast Construction of Covariance Matrices for Arbitrary Size Image Windows", IEEE International Conference on Image Processing (ICIP), October 2006, pp. 1581-1584.
      BibTeX TR2006-043 PDF
      • @inproceedings{Porikli2006oct1,
      • author = {Porikli, F. and Tuzel, O.},
      • title = {Fast Construction of Covariance Matrices for Arbitrary Size Image Windows},
      • booktitle = {IEEE International Conference on Image Processing (ICIP)},
      • year = 2006,
      • pages = {1581--1584},
      • month = oct,
      • issn = {1522-4880},
      • url = {https://www.merl.com/publications/TR2006-043}
      • }
  • Research Areas:

    Artificial Intelligence, Computer Vision, Machine Learning

Abstract:

We present a novel, integral image based algorithm to compute feature covariance matrices within all arbitrary size rectangular regions in an image. This technique significantly improves the computational load of covariance matrix extraction process by taking advantage of the spatial arrangement of points. Covariance is an essential measure of how much the deviation of two or more variables or processes match. In our case, these variables correspond to point features such as coordinate, color, gradient, orientation, and filter responses. Integral images are intermediate image representations used for calculation of region sums. Each point of the integral image is a summation of all the points inside the rectangle bounded by the upper left corner of the image and the point of interest. Using this representation, any rectangular region sum can be computed in constant time. We follow a similar idea for fast calculation of region covariance. We construct integral images for all separate features as well as integral images of the multiplication of any two feature combinations. Using these set of integral images and region corner point coordinates, we directly extract the covariance matrix coefficients. We show that the proposed integral image based method decreases the computational load to quadratic time.

 

  • Related News & Events

    •  NEWS    ICIP 2006: 3 publications by Oncel Tuzel, Anthony Vetro, Huifang Sun and others
      Date: October 8, 2006
      Where: IEEE International Conference on Image Processing (ICIP)
      MERL Contacts: Anthony Vetro; Huifang Sun
      Brief
      • The papers "Extensions of H.264/AVC for Multiview Video Compression" by Martinian, E., Behrens, A., Xin, J., Vetro, A. and Sun, H., "Fast Construction of Covariance Matrices for Arbitrary Size Image Windows" by Porikli, F. and Tuzel, O. and "A Cascading Framework of Contour Motion and Deformation Estimation for Non-Rigid Object Tracking" by Shao, J., Porikli, F. and Chellappa, R. were presented at the IEEE International Conference on Image Processing (ICIP).
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