Partitioning Polygons via Graph Augmentation

Haunert, Jan‐Henrik; Meulemans, Wouter

doi:10.1007/978-3-319-45738-3_2

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…Because convex decomposition is still an HP-hard problem [26], there have many approximate solutions, such as dynamic programming, Steiner points, approximated decomposition, graph augmentation [14,17,25,8]. However, for our concerned non-convex problem, the difference from these approximators lies in two-fold: (1) our ROI is usually a simple polygon, e.g., hole-free, regionconnected and vertex-ordered.…”

Section: Convex Decomposition For a Non-convex Roimentioning

confidence: 99%

Non-rigid Interest Object Extraction Using Minimum Convex Coverage

Yang,

Zhang,

Zhang

et al. 2023

Preprint

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Interest object (IO) extraction, or called region of interest (ROI) selection, is a fundamental task in remote sensing (RS), computer vision, and machine learning. Due to the non-rigidity, e.g., shapelessness and color-uncertainty, of interest objects like fires, smokes, clouds, or top-view tree canopies in a RS image, an unideal results usually occurs in IO detection tasks because the model-training is carried on the pixels drawn from an inaccurate ROI, e.g., a bounding-box or convex region. Although it is simple, it fails to capture a complete interest object or sub-object, especially at the requirement of high-precision. In this work, we focus on the non-convex ROI and develop a method for the accurate pixel extraction. To speed pixel extraction, the given non-convex ROI is first decomposed into a minimum convex coverage, and then the ROI pixels can be quickly extracted out from the coverage by using convex operation. For the decomposition , we provide two strategies, named inner decomposition and outer decomposition. Computationally, batch-decision for pixel selection and logical operation for the decomposition are also presented to speed extraction. Theoretically , the existence of minimum coverage for both decompositions is proved. Finally, extensive experimental verifications are carried out on public and our collected RS images, and the results show the superiority of our method in terms of ease of use, rapidity and pixel-precision.

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Section: Convex Decomposition For a Non-convex Roimentioning

confidence: 99%

Non-rigid Interest Object Extraction Using Minimum Convex Coverage

Yang,

Zhang,

Zhang

et al. 2023

Preprint

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show abstract

“…Moreover, optimization is useful for evaluating heuristics. We need heuristics, because many optimization problems cannot be solved efficiently (e.g., References [25,28]). While heuristics can find some solutions in reasonable time, it is important to know the quality of these solutions.…”

Section: Optimization In Map Generalizationmentioning

confidence: 99%

“…As in Equation ( 6), we use denominator n − 2 to balance between the cost of type change and the cost of length. Integrating Equation (7) into Equation (25), we have…”

Section: A3 Constraintsmentioning

confidence: 99%

Finding Optimal Sequences for Area Aggregation—A ^⋆ vs. Integer Linear Programming

Peng

Wolff

Haunert

2020

ACM Trans. Spatial Algorithms Syst.

Self Cite

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To provide users with maps of different scales and to allow them to zoom in and out without losing context, automatic methods for map generalization are needed. We approach this problem for land-cover maps. Given two land-cover maps at two different scales, we want to find a sequence of small incremental changes that gradually transforms one map into the other. We assume that the two input maps consist of polygons, each of which belongs to a given land-cover type. Every polygon on the smaller-scale map is the union of a set of adjacent polygons on the larger-scale map. In each step of the computed sequence, the smallest area is merged with one of its neighbors. We do not select that neighbor according to a prescribed rule but compute the whole sequence of pairwise merges at once, based on global optimization. We have proved that this problem is NP-hard. We formalize this optimization problem as that of finding a shortest path in a (very large) graph. We present the A ⋆ algorithm and integer linear programming to solve this optimization problem. To avoid long computing times, we allow the two methods to return non-optimal results. In addition, we present a greedy algorithm as a benchmark. We tested the three methods with a dataset of the official German topographic database ATKIS. Our main result is that A ⋆ finds optimal aggregation sequences for more instances than the other two methods within a given time frame.

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“…Our approximation algorithm runs in O(n 3 log n) time and guarantees an O(k)-approximation factor. Although our algorithm may not be optimal, we hope that we provide some insight for further research, or for related graph augmentation problems [1,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Improving the dilation of a metric graph by adding edges

Gudmundsson¹,

Wong²

2020

Preprint

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Most of the literature on spanners focuses on building the graph from scratch. This paper instead focuses on adding edges to improve an existing graph. A major open problem in this field is: given a graph embedded in a metric space, and a budget of k edges, which k edges do we add to produce a minimum-dilation graph? The special case where k = 1 has been studied in the past, but no major breakthroughs have been made for k > 1. We provide the first positive result, an O(k)-approximation algorithm that runs in O(n 3 log n) time.

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Partitioning Polygons via Graph Augmentation

Cited by 7 publications

References 18 publications

Non-rigid Interest Object Extraction Using Minimum Convex Coverage

Non-rigid Interest Object Extraction Using Minimum Convex Coverage

Finding Optimal Sequences for Area Aggregation—A ^⋆ vs. Integer Linear Programming

Improving the dilation of a metric graph by adding edges

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Partitioning Polygons via Graph Augmentation

Cited by 7 publications

References 18 publications

Non-rigid Interest Object Extraction Using Minimum Convex Coverage

Non-rigid Interest Object Extraction Using Minimum Convex Coverage

Finding Optimal Sequences for Area Aggregation—A ⋆ vs. Integer Linear Programming

Improving the dilation of a metric graph by adding edges

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Product

Resources

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Finding Optimal Sequences for Area Aggregation—A ^⋆ vs. Integer Linear Programming