Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Parametric Curve Segment Extraction by Support Regions

Cem Ünsalan

TL;DR

The paper addresses the challenge of extracting curve segments directly in parametric form from images. It proposes form-ing curve support regions by thresholding the Laplacian of Gaussian (LoG) response and then fitting Fourier descriptors to their boundaries to recover parametric curve segments, partitioned into convex and concave parts via the Laplacian. Key contributions include the curve support region construction, Fourier-based boundary modeling, and curvature-based endpoint extraction, enabling robust segment recovery under rotation and affine transformations. The method offers a fast, integrated alternative to traditional edge-then-contour pipelines and demonstrates effectiveness on both black-and-white and grayscale images, with practical applicability to recognition tasks.

Abstract

We introduce a method to extract curve segments in parametric form from the image directly using the Laplacian of Gaussian (LoG) filter response. Our segmentation gives convex and concave curves. To do so, we form curve support regions by grouping pixels of the thresholded filter response. Then, we model each support region boundary by Fourier series and extract the corresponding parametric curve segment.

Parametric Curve Segment Extraction by Support Regions

TL;DR

The paper addresses the challenge of extracting curve segments directly in parametric form from images. It proposes form-ing curve support regions by thresholding the Laplacian of Gaussian (LoG) response and then fitting Fourier descriptors to their boundaries to recover parametric curve segments, partitioned into convex and concave parts via the Laplacian. Key contributions include the curve support region construction, Fourier-based boundary modeling, and curvature-based endpoint extraction, enabling robust segment recovery under rotation and affine transformations. The method offers a fast, integrated alternative to traditional edge-then-contour pipelines and demonstrates effectiveness on both black-and-white and grayscale images, with practical applicability to recognition tasks.

Abstract

We introduce a method to extract curve segments in parametric form from the image directly using the Laplacian of Gaussian (LoG) filter response. Our segmentation gives convex and concave curves. To do so, we form curve support regions by grouping pixels of the thresholded filter response. Then, we model each support region boundary by Fourier series and extract the corresponding parametric curve segment.
Paper Structure (9 sections, 18 equations, 5 figures)

This paper contains 9 sections, 18 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Curve Support Region (CSR) Extraction
  3. An Example in Continuous Domain
  4. An Example in Discrete Domain
  5. Parametric Curve Segment Extraction
  6. Experimental Results
  7. Experiments on Black and White Images
  8. Experiments on Grayscale Images
  9. Conclusions

Figures (5)

  • Figure 1: A curve segmentation example in continuous domain
  • Figure 2: Curve support regions and curve segments over the rectangle image
  • Figure 3: Parametric curve segments obtained from the 'S' shape in the original, rotated, affine transformed, affine transformed and rotated versions (from left to right respectively)
  • Figure 4: Parametric curve segments obtained from characters in the original, rotated, affine transformed, affine transformed and rotated versions (from left to right respectively)
  • Figure 5: Parametric curve segment extraction from grayscale images.