Comparison of Multiscale Morphology Approaches: PDE Implemented Via Curve Evolution Versus Chamfer Distance Transform

Butt, Muhammad Akmal; Maragos, Petros

doi:10.1007/978-1-4613-0469-2_5

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…In particular, finite difference methods such as the Osher-Sethian schemes [22,23,32] and the Rouy-Tourin method [25,38] are widely-used in this context. PDE-based algorithms for dilation/erosion offer two advantages over classical set-theoretic schemes [2,8,26]: first of all, they give excellent results for nondigitally scalable structuring elements whose shapes cannot be represented correctly on a discrete grid, for instance discs or ellipses. Secondly, the time t plays the role of a continuous scale parameter.…”

Section: Introductionmentioning

confidence: 99%

A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion

Breuß

Weickert

2006

J Math Imaging Vis

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Dilation and erosion are the fundamental operations in morphological image processing. Algorithms that exploit the formulation of these processes in terms of partial differential equations offer advantages for non-digitally scalable structuring elements and allow sub-pixel accuracy. However, the widely-used schemes from the literature suffer from significant blurring at discontinuities. We address this problem by developing a novel, flux corrected transport (FCT) type algorithm for morphological dilation / erosion with a flat disc. It uses the viscosity form of an upwind scheme in order to quantify the undesired diffusive effects. In a subsequent corrector step we compensate for these artifacts by means of a stabilised inverse diffusion process that requires a specific nonlinear multidimensional formulation. We prove a discrete maximum-minimum principle in this multidimensional framework. Our experiments show that the method gives a very sharp resolution of moving fronts, and it approximates rotation invariance very well.

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Section: Introductionmentioning

confidence: 99%

A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion

Breuß

Weickert

2006

J Math Imaging Vis

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“…Continuous multiscale morphology using the above curve evolution algorithm for numerically implementing the dilation PDE yields better approximations to disks and avoids the abrupt shape discretization inherent in modeling digital multiscale using discrete polygons [16,57]. Comparing it to discrete multiscale morphology using chamfer distance transforms, we note that for binary images: (1) the chamfer distance transform is easier to implement and yields similar errors for small scale dilations/erosions; (2) implementing the distance transform via curve evolution is more complex, but at medium and large scales gives a better and very close approximation to Euclidean geometry, i.e., to morphological operations with the disk structuring element.…”

Section: Differential Equations For Continuous-scale Morphologymentioning

confidence: 99%

Morphological Signal and Image Processing

Maragos¹

2009

Wireless, Networking, Radar, Sensor Array Processing, and Nonlinear Signal Processing

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“…Many other morphological processes such as openings, closings, top hats and morphological derivative operators can be derived from them. While dilation/erosion are frequently realised using a set-theoretical framework, an alternative formulation is available via partial differential equations (PDEs) (Alvarez et al 1993;Arehart et al 1993;Brockett and Maragos 1992;Butt and Maragos 1996;van den Boomgaard 1992). Compared to the set-theoretical approach, the latter offers the conceptual advantages of digital scalability and subpixel accuracy.…”

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confidence: 99%

Highly Accurate Schemes for PDE-Based Morphology with General Convex Structuring Elements

Breuβ

Weickert

2010

Int J Comput Vis

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The two fundamental operations in morphological image processing are dilation and erosion. These processes are defined via structuring elements. It is of practical interest to consider a variety of structuring element shapes. The realisation of dilation/erosion for convex structuring elements by use of partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high degree of rotational invariance. We validate the FCT-scheme theoretically by proving consistency and stability. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology.

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Comparison of Multiscale Morphology Approaches: PDE Implemented Via Curve Evolution Versus Chamfer Distance Transform

Cited by 5 publications

References 10 publications

A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion

A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion

Morphological Signal and Image Processing

Highly Accurate Schemes for PDE-Based Morphology with General Convex Structuring Elements

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