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We introduced a corner detection framework based on condition theory, that allows us to establish deep connections between the most commonly used detectors and to investigate their properties in a principled manner.

 

with Dr. C. Kenney and Prof. B. S. Manjunath

(2003-now) In this project we developed a unified framework to analyze different corner detectors that are based on the spectral properties of the image autocorrelation matrix. The main mathematical tool used to carry out our analysis is based on the condition theory. Using this approach we were able to show that some of the most commonly used corner detectors can be unified by choosing an appropriate matrix norm. The mathematical framework we developed allowed us to easily extend some of the commonly used detectors to images with pixel dimension greater than 2 (i.e. tomographic images) and intensity dimension greater than one (like RGB or multispectral images). We are now using these tools to identify which relevant properties are shared by some of the commonly used corner detectors and which ones make them unique. Moreover we are interested in applying the condition theory framework to detect the intrinsic structure of a neighborhood of an image point. This is leading us to develop a multiscale condition theory based point detector framework.

 

Related Publications

  1. M. Zuliani, C. Kenney and B. S. Manjunath,
    "A Mathematical Comparison of Point Detectors"
    Second IEEE Image and Video Registration Workshop (IVR), Washington, DC, Jun. 2004.
    VRL ID 130: [abstract] [PDF] [BibTex]

    Abstract preview: "Selecting salient points from two or more images for computing correspondences is a fundamental problem in image analysis. Three methods originally proposed by Harris et al., by Noble et al. and by Sh..." [more]

  2. C. S. Kenney, B. S. Manjunath, M. Zuliani, M. G. A. Hewer and A. Van Nevel,
    "A condition number for point matching with application to registration and postregistration error estimation"
    IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 11, pp. 1437 - 1454, Nov. 2003.
    VRL ID 126: [abstract] [PDF] [BibTex]

    Abstract preview: "Selecting salient points from two or more images for computing correspondence is a well studied problem in image analysis. This paper describes a new and effective technique for selecting these tiepoi..." [more]

  3. C. S. Kenney, M. Zuliani and B. S. Manjunath,
    "An Axiomatic Approach to Corner Detection"
    Proc. International Conference on Computer Vision and Pattern Recognition (CVPR), San Diego, CA, USA, Jun. 2005.
    double-blind review
    VRL ID 144: [abstract] [PDF] [BibTex]

    Abstract preview: "This paper presents an axiomatic approach to corner detection. In the first part of the paper we review five currently used corner detection methods (Harris-Stephens, Forstner, Shi-Tomasi, Rohr, and K..." [more]

  4. Marco Zuliani,
    "Computational Methods for Automatic Image Registration"
    Ph.D. Thesis, University of California, Santa Barbara, Dec. 2006.
    [abstract] [PDF] [BibTex]

    Abstract preview: "Image registration is the process of establishing correspondences between two or more images taken at different times, from different viewpoints, under different lighting conditions, and/or by differe..." [more]

Click here for the IVR 2004 presentation (hosted at CVPR 204), or here to see the CVPR 2005 poster.