11,216 research outputs found

    Colour Text Segmentation in Web Images Based on Human Perception

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    There is a significant need to extract and analyse the text in images on Web documents, for effective indexing, semantic analysis and even presentation by non-visual means (e.g., audio). This paper argues that the challenging segmentation stage for such images benefits from a human perspective of colour perception in preference to RGB colour space analysis. The proposed approach enables the segmentation of text in complex situations such as in the presence of varying colour and texture (characters and background). More precisely, characters are segmented as distinct regions with separate chromaticity and/or lightness by performing a layer decomposition of the image. The method described here is a result of the authors’ systematic approach to approximate the human colour perception characteristics for the identification of character regions. In this instance, the image is decomposed by performing histogram analysis of Hue and Lightness in the HLS colour space and merging using information on human discrimination of wavelength and luminance

    Constructing Light Spanners Deterministically in Near-Linear Time

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    Graph spanners are well-studied and widely used both in theory and practice. In a recent breakthrough, Chechik and Wulff-Nilsen [Shiri Chechik and Christian Wulff-Nilsen, 2018] improved the state-of-the-art for light spanners by constructing a (2k-1)(1+epsilon)-spanner with O(n^(1+1/k)) edges and O_epsilon(n^(1/k)) lightness. Soon after, Filtser and Solomon [Arnold Filtser and Shay Solomon, 2016] showed that the classic greedy spanner construction achieves the same bounds. The major drawback of the greedy spanner is its running time of O(mn^(1+1/k)) (which is faster than [Shiri Chechik and Christian Wulff-Nilsen, 2018]). This makes the construction impractical even for graphs of moderate size. Much faster spanner constructions do exist but they only achieve lightness Omega_epsilon(kn^(1/k)), even when randomization is used. The contribution of this paper is deterministic spanner constructions that are fast, and achieve similar bounds as the state-of-the-art slower constructions. Our first result is an O_epsilon(n^(2+1/k+epsilon\u27)) time spanner construction which achieves the state-of-the-art bounds. Our second result is an O_epsilon(m + n log n) time construction of a spanner with (2k-1)(1+epsilon) stretch, O(log k * n^(1+1/k) edges and O_epsilon(log k * n^(1/k)) lightness. This is an exponential improvement in the dependence on k compared to the previous result with such running time. Finally, for the important special case where k=log n, for every constant epsilon>0, we provide an O(m+n^(1+epsilon)) time construction that produces an O(log n)-spanner with O(n) edges and O(1) lightness which is asymptotically optimal. This is the first known sub-quadratic construction of such a spanner for any k = omega(1). To achieve our constructions, we show a novel deterministic incremental approximate distance oracle. Our new oracle is crucial in our construction, as known randomized dynamic oracles require the assumption of a non-adaptive adversary. This is a strong assumption, which has seen recent attention in prolific venues. Our new oracle allows the order of the edge insertions to not be fixed in advance, which is critical as our spanner algorithm chooses which edges to insert based on the answers to distance queries. We believe our new oracle is of independent interest

    Light Spanners

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    A tt-spanner of a weighted undirected graph G=(V,E)G=(V,E), is a subgraph HH such that dH(u,v)≀t⋅dG(u,v)d_H(u,v)\le t\cdot d_G(u,v) for all u,v∈Vu,v\in V. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all edge weights), both being important measures of the spanner's quality -- in this work we focus on the latter. Specifically, it is shown that for any parameters k≄1k\ge 1 and Ï”>0\epsilon>0, any weighted graph GG on nn vertices admits a (2k−1)⋅(1+Ï”)(2k-1)\cdot(1+\epsilon)-stretch spanner of weight at most w(MST(G))⋅OÏ”(kn1/k/log⁥k)w(MST(G))\cdot O_\epsilon(kn^{1/k}/\log k), where w(MST(G))w(MST(G)) is the weight of a minimum spanning tree of GG. Our result is obtained via a novel analysis of the classic greedy algorithm, and improves previous work by a factor of O(log⁥k)O(\log k).Comment: 10 pages, 1 figure, to appear in ICALP 201
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