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Approximating large convolutions in digital images.

D M Mount1, T Kanungo, N S Netanyahu

  • 1Dept. of Comput. Sci., Maryland Univ., College Park, MD 20740, USA. mount@cs.umd.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 8, 2008
PubMed
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We developed a new algorithm for computing binary convolutions in image processing. This method efficiently calculates convolutions using convex polygonal kernels, achieving O(kmn) time complexity for k-sided kernels.

Area of Science:

  • Computer Vision
  • Image Processing
  • Computational Geometry

Background:

  • Binary convolutions are crucial in image processing and mathematical morphology.
  • Computing these convolutions can be computationally expensive, particularly with large kernels.

Purpose of the Study:

  • To present an efficient algorithm for computing binary convolutions with convex polygonal kernels.
  • To demonstrate that valid binary convolutions can be computed more efficiently than standard methods for large kernels.

Main Methods:

  • The algorithm utilizes a convex polygonal kernel, allowing flexibility in digitization.
  • It employs Bresenham's line-drawing algorithm and prefix-sums for incremental updates.
  • The convolution is computed in O(kmn) time for an m x n image and a k-sided kernel.

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Main Results:

  • A novel algorithm for valid binary convolutions with convex polygonal kernels is presented.
  • The algorithm achieves a running time of O(kmn), independent of kernel area or perimeter.
  • The method avoids the need for Fast Fourier Transforms.

Conclusions:

  • The proposed algorithm offers a significant efficiency improvement for computing binary convolutions with convex polygonal kernels.
  • This approach provides a practical solution for image processing tasks involving large kernels.
  • The technique combines geometric properties of kernels with efficient computational methods.