Level lines shortening yields an image curvature microscope

Ciomaga, Adina; Monasse, Pascal; Morel, Jean‐Michel

doi:10.1109/icip.2010.5649850

Cited by 14 publications

(22 citation statements)

References 14 publications

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“…However, in natural images, the meaningful level lines are not all strictly separated, so in the future, we would like to relax this condition and tolerate a small superposition between the selected level lines. As a second future work, we aim at applying level lines shortening that yields an image curvature microscope [25] before extracting disjoint level lines. Another major perspective is to extend this method to 3D images and the tree of shapes for color images [26,27].…”

Section: Discussionmentioning

confidence: 99%

Meaningful disjoint level lines selection

Carlinet

Géraud

et al. 2014

2014 IEEE International Conference on Image Processing (ICIP)

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Many methods based on the morphological notion of shapes (i.e., connected components of level sets) have been proved to be very efficient in shape recognition and shape analysis. The inclusion relationship of the level lines (boundaries of level sets) forms the tree of shapes, a tree-based image representation with a high potential. Numerous applications using this tree representation have been proposed. In this article, we propose an efficient algorithm that extracts a set of disjoint level lines in the image. These selected level lines yield a simplified image with clean contours, which provides an intuitive idea about the main structure of the tree of shapes. Besides, we obtain a saliency map without transition problems around the contours by weighting level lines with their significance. Experimental results demonstrate the efficiency and usefulness of our method.

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Section: Discussionmentioning

confidence: 99%

Meaningful disjoint level lines selection

Carlinet

Géraud

et al. 2014

2014 IEEE International Conference on Image Processing (ICIP)

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“…The affine distance outside a non-convex shape uses the affine multiscale analysis associated with β − (s) defined in (8). We shall explore the properties of d A ((x, y), C 0 ) in that case.…”

Section: Affine Invariant Distance For Points Outside the Non-convex mentioning

confidence: 99%

“…We refer to [18] for detailed references on the subject and for a numerical analysis of the equation understood as a curve evolution. The particular case α = 1/3 was studied in detail in [5] and its numerical analysis is detailed in [8]. In the case α = 1 a proof was given in [7] that the curve evolution of the level lines of an image by curvature shortening is strictly equivalent to moving the image by curvature motion (1).…”

Section: Introductionmentioning

confidence: 99%

Affine Invariant Distance Using Multiscale Analysis

et al. 2015

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In this paper we introduce an affine invariant distance definition from a 2D point to the boundary of a bounded shape using morphological multiscale analysis. We study the mathematical behavior of this distance by examining separately the cases of convex and non-convex shapes. We prove that the proposed distance is bounded in the convex hull of the shape and infinite otherwise. A numerical scheme is given as well as experiments illustrating the behavior of the affine invariant distance.

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“…The result, which is displayed in Figure 2 (middle two images) has spurious oscillations along transversal lines. Based on the previously mentioned contributions, the authors introduced in [11] an algorithm that computes the image curvatures directly on the bilinear level lines, after their smoothing. The fact that one can compute, at any desired resolution, the bilinear level lines of the image yields a microscopic visualization of the curvature map, as displayed in Figure 2 (right).…”

Section: Introductionmentioning

confidence: 99%

“…We focus here on the thorough description and implementation of the accurate algorithm sketched in [11].…”

Section: Introductionmentioning

confidence: 99%

The Image Curvature Microscope: Accurate Curvature Computation at Subpixel Resolution

Ciomaga¹,

Monasse²,

Morel³

2017

Image Processing on Line

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We detail in this paper the numerical implementation of the so-called image curvature microscope, an algorithm that computes accurate image curvatures at subpixel resolution, and yields a curvature map conforming with our visual perception. In contrast to standard methods, which would compute the curvature by a finite difference scheme, the curvatures are evaluated directly on the level lines of the bilinearly interpolated image, after their independent smoothing, a step necessary to remove pixelization artifacts. The smoothing step consists in the affine erosion of the level lines through a geometric scheme, and can be applied in parallel to all level lines. The online algorithm allows the user to visualize the image of curvatures at different resolutions, as well as the set of level lines before and after smoothing. Source CodeThe ANSI C++ implementation reviewed by IPOL is given in the file curv.cpp. The complete source code, code documentation, and online demo are accessible at the IPOL web page of this article 1 . The level lines extraction (files levelLine.cpp, lltree.cpp) and level lines smoothing (file gass.cpp) are independent algorithms, out of the scope of this article, and details for their implementation are planned for separate IPOL publications.

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Level lines shortening yields an image curvature microscope

Cited by 14 publications

References 14 publications

Meaningful disjoint level lines selection

Meaningful disjoint level lines selection

Affine Invariant Distance Using Multiscale Analysis

The Image Curvature Microscope: Accurate Curvature Computation at Subpixel Resolution

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