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Properties of BV-G structures + textures decomposition models. Application to road detection in satellite images

Jerome Gilles, Yves Meyer

TL;DR

An algorithm for the detection of long and thin objects applied to a road networks detection application in aerial or satellite images is derived from a structures-textures image decomposition model proposed by the second author.

Abstract

In this paper we present some theoretical results about a structures-textures image decomposition model which was proposed by the second author. We prove a theorem which gives the behavior of this model in different cases. Finally, as a consequence of the theorem we derive an algorithm for the detection of long and thin objects applied to a road networks detection application in aerial or satellite images.

Properties of BV-G structures + textures decomposition models. Application to road detection in satellite images

TL;DR

An algorithm for the detection of long and thin objects applied to a road networks detection application in aerial or satellite images is derived from a structures-textures image decomposition model proposed by the second author.

Abstract

In this paper we present some theoretical results about a structures-textures image decomposition model which was proposed by the second author. We prove a theorem which gives the behavior of this model in different cases. Finally, as a consequence of the theorem we derive an algorithm for the detection of long and thin objects applied to a road networks detection application in aerial or satellite images.

Paper Structure

This paper contains 9 sections, 10 theorems, 59 equations, 5 figures.

Table of Contents

  1. Introduction
  2. $BV-L2$ model - The Rudin Osher Fatemi algorithm
  3. $BV-G$ decomposition model
  4. Decomposition model output
  5. General results
  6. Decomposition model properties
  7. Application
  8. Conclusion
  9. Practical algorithms

Key Result

Lemma 1

If $u\in L^2({\mathbb{R}}^2)$ and $v\in BV({\mathbb{R}}^2)$, then

Figures (5)

  • Figure 1: Example of image structures+textures decomposition.
  • Figure 2: Example of a portion of an aerial image: original image on top, $w$ component on bottom which lets appear enhanced roads.
  • Figure 3: Illustration of the constrast enhancement of thin and long structures.
  • Figure 4: Example of road network detection: original image on top, detected roads on bottom.
  • Figure 5: Segment to polygonal active contour conversion strategy.

Theorems & Definitions (10)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Theorem 1
  • Theorem 2
  • Lemma 5
  • Lemma 6
  • Lemma 7
  • Lemma 8