Generalized scale: Theory, algorithms, and application to image inhomogeneity correction

  • Authors:

  • Anant Madabhushi;Jayaram K. Udupa;Andre Souza

  • Affiliations:

  • Department of Biomedical Engineering, Rutgers The State University of New Jersey, Piscataway, NJ 08854, USA and Medical Image Processing Group, Department of Radiology, University of Pennsylvania, ...;Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104-6021, USA;Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104-6021, USA

  • Venue:
  • Computer Vision and Image Understanding
  • Year:
  • 2006

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Abstract

Scale is a fundamental concept useful in almost all image processing and analysis tasks including segmentation, filtering, interpolation, registration, visualization, and quantitative analysis. Broadly speaking, scale related work can be divided into three categories: (1) multi-scale or scale-space representation, (2) local scale, and (3) locally adaptive scale. The original formulation of scale in the form of scale-space theory came from the consideration of the presence of multiple scales in nature and the desire to represent measured signals at multiple scales. However, since this representation did not suggest how to select appropriate scales, the notion of local scale was proposed to pick the right scale for a particular application from the multi-scale representation of the image. Recently, there has been considerable interest in developing locally adaptive scales, the idea being to consider the local size of object in carrying out whatever local operations that are to be done on the image. However, existing locally adaptive models are limited by shape, size, and anisotropic constraints. In this work, we propose a generalized scale model which is spatially adaptive like other local morphometric models, and yet possesses the global spirit of multi-scale representations. We postulate that this semi-locally adaptive nature of generalized scale confers it certain distinct advantages over other global and local scale formulations. We also present a variant of the generalized scale notion that we refer to as the generalized ball scale, which, in addition to having the advantages of the generalized scale model, also has superior noise resistance properties. Both scale models are dependent only on two parameters for their estimation, and we demonstrate means by which optimal values for these parameters can be estimated. Both the generalized scales can be readily applied to solving a range of image processing problems. One such problem that we address in this paper is correcting for slowly varying background spatial intensity in Magnetic Resonance images. We demonstrate the superiority of the generalized scale based inhomogeneity correction methods over an existing scale-based correction technique.