Priority pixel queue algorithm for geodesic distance transforms

Ikonen, Leena

doi:10.1016/j.imavis.2006.06.016

Cited by 11 publications

(5 citation statements)

References 17 publications

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“…Alternative digital distance transforms approximating spatial-tonal Euclidean distance or L 1 distance and efficient algorithms are discussed in [15,16].…”

Section: The Discrete Amoeba Constructionmentioning

confidence: 99%

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Morphological Amoebas Are Self-snakes

2010

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This paper is concerned with amoeba median filtering, a structureadaptive morphological image filter. It has been introduced by Lerallut et al. in a discrete formulation. Experimental evidence shows that iterated amoeba median filtering leads to segmentation-like results that are similar to those obtained by self-snakes, an image filter based on a partial differential equation. We establish this correspondence by analysing a space-continuous formulation of iterated median filtering. We prove that in the limit of vanishing radius of the structuring elements, iterated amoeba median filtering indeed approximates the partial differential equation of self-snakes. This result holds true under very general assumptions on the metric used to construct the amoebas. We present experiments with discrete iterated amoeba median filtering that confirm qualitative and quantitative predictions of our analysis.

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“…Alternative digital distance transforms approximating spatial-tonal Euclidean distance or L 1 distance and efficient algorithms are discussed in [15,16].…”

Section: The Discrete Amoeba Constructionmentioning

confidence: 99%

“…With regard to future improvements in the algorithmic realisation of amoeba filters, we mention also digital distance transforms, in particular the work by Borgefors [3,4] and Ikonen et al [15,16].…”

Section: Introductionmentioning

confidence: 99%

Morphological Amoebas Are Self-snakes

2010

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“…α controls the relative influences of tone and space in the calculation of the similarity measure of neighbour pixels. Algorithms based on priority queue data structures (Soille, 1994b), implementing Dijkstra algorithm, enable an efficient implementation of the local geodesic time with a computational complexity of O(ω 2 log ω 2 ) (Ikonen, 2007). They take advantage of the fact that the analysing windows Ω are finite and totally ordered, and they guarantee that pixels that effectively contribute to the output are processed only once.…”

Section: Smoothing Filter Derived From Local Geodesic Time On Gradienmentioning

confidence: 99%

“…Note that in fact the geodesic mask associated to the time τ g (P ) of Eq. (5) is constantly updated through the propagation of the geodesic time (Ikonen and Toivanen, 2007;Ikonen, 2007). For multichannel images f , the norm in Eq.…”

Section: Denoising Filter Derived From Local Geodesic Time On Image Vmentioning

confidence: 99%

Edge-Preserving Smoothing of Natural Images Based on Geodesic Time Functions

2008

Proceedings of the Third International Conference on Computer Vision Theory and Applications

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In this paper, we address the problem of edge-preserving smoothing of natural images. We introduce a novel adaptive approach derived from mathematical morphology as a preprocessing stage in feature extraction and/or image segmentation. Like other filtering methods, it assumes that the local neighbourhood of a pixel contains the essential information required for the estimation of local image properties. It performs a weighted averaging by combining both spatial and tonal information in a single similarity measure based on the local calculation of geodesic time functions from the estimated pixel. By designing relevant geodesic masks, it can deal with specific situation and type of images. We describe in the following two possible strategies and we show their capabilities at smoothing heterogeneous areas while preserving relevant structures in naturalgreyscale or multispectral-images displaying different features.

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“…Many algorithms for image analysis, especially those that can be described with the "recursive propagation" paradigm, can be implemented efficiently using priority queues. Examples are the distance transform in non-convex domains [1], the greyweighted distance transform [2,3], fast marching level sets [4], morphological reconstruction [5], area and attribute openings, closings and thinnings [6,7], the watershed transform [8], region growing [9] and skeletonisation [10]. All these algorithms are implemented using only insert and delete-min.…”

Section: Introductionmentioning

confidence: 99%

Revisiting priority queues for image analysis

Hendriks

2010

Pattern Recognition

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Many algorithms in image analysis require a priority queue, a data structure that holds pointers to pixels in the image, and which allows efficiently finding the pixel in the queue with the highest priority. However, very few articles describing such image analysis algorithms specify which implementation of the priority queue was used. Many assessments of priority queues can be found in the literature, but mostly in the context of numerical simulation rather than image analysis. Furthermore, due to the ever-changing characteristics of computing hardware, performance evaluated empirically 10 years ago is no longer relevant. In this paper I revisit priority queues as used in image analysis routines, evaluate their performance in a very general setting, and come to a very different conclusion than other authors: implicit heaps are the most efficient priority queues. At the same time, I propose a simple modification of the hierarchical queue (or bucket queue) that is more efficient than the implicit heap for extremely large queues.

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Priority pixel queue algorithm for geodesic distance transforms

Cited by 11 publications

References 17 publications

Morphological Amoebas Are Self-snakes

Morphological Amoebas Are Self-snakes

Edge-Preserving Smoothing of Natural Images Based on Geodesic Time Functions

Revisiting priority queues for image analysis

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