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Register a new userLCuts: Linear Clustering of Bacteria using Recursive Graph Cuts
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Added by
Jie Wang
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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Bacterial biofilm segmentation poses significant challenges due to lack of apparent structure, poor imaging resolution, limited contrast between conterminous cells and high density of cells that overlap. Although there exist bacterial segmentation algorithms in the existing art, they fail to delineate cells in dense biofilms, especially in 3D imaging scenarios in which the cells are growing and subdividing in a complex manner. A graph-based data clustering method, LCuts, is presented with the application on bacterial cell segmentation. By constructing a weighted graph with node features in locations and principal orientations, the proposed method can automatically classify and detect differently oriented aggregations of linear structures (represent by bacteria in the application). The method assists in the assessment of several facets, such as bacterium tracking, cluster growth, and mapping of migration patterns of bacterial biofilms. Quantitative and qualitative measures for 2D data demonstrate the superiority of proposed method over the state of the art. Preliminary 3D results exhibit reliable classification of the cells with 97% accuracy.
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These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary background on graphs and graph Laplacians. I then explain in detail how the eigenvectors of the graph Laplacian can be used to draw a graph. This is an attractive application of graph Laplacians. The main thrust of this paper is the method of normalized cuts. I give a detailed account for K = 2 clusters, and also for K > 2 clusters, based on the work of Yu and Shi. Three points that do not appear to have been clearly articulated before are elaborated: 1. The solutions of the main optimization problem should be viewed as tuples in the K-fold cartesian product of projective space RP^{N-1}. 2. When K > 2, the solutions of the relaxed problem should be viewed as elements of the Grassmannian G(K,N). 3. Two possible Riemannian distances are available to compare the closeness of solutions: (a) The distance on (RP^{N-1})^K. (b) The distance on the Grassmannian. I also clarify what should be the necessary and sufficient conditions for a matrix to represent a partition of the vertices of a graph to be clustered.
Vector space representations of words capture many aspects of word similarity, but such methods tend to make vector spaces in which antonyms (as well as synonyms) are close to each other. We present a new signed spectral normalized graph cut algorithm, signed clustering, that overlays existing thesauri upon distributionally derived vector representations of words, so that antonym relationships between word pairs are represented by negative weights. Our signed clustering algorithm produces clusters of words which simultaneously capture distributional and synonym relations. We evaluate these clusters against the SimLex-999 dataset (Hill et al.,2014) of human judgments of word pair similarities, and also show the benefit of using our clusters to predict the sentiment of a given text.
We propose a new segmentation model combining common regularization energies, e.g. Markov Random Field (MRF) potentials, and standard pairwise clustering criteria like Normalized Cut (NC), average association (AA), etc. These clustering and regularization models are widely used in machine learning and computer vision, but they were not combined before due to significant differences in the corresponding optimization, e.g. spectral relaxation and combinatorial max-flow techniques. On the one hand, we show that many common applications using MRF segmentation energies can benefit from a high-order NC term, e.g. enforcing balanced clustering of arbitrary high-dimensional image features combining color, texture, location, depth, motion, etc. On the other hand, standard clustering applications can benefit from an inclusion of common pairwise or higher-order MRF constraints, e.g. edge alignment, bin-consistency, label cost, etc. To address joint energies like NC+MRF, we propose efficient Kernel Cut algorithms based on bound optimization. While focusing on graph cut and move-making techniques, our new unary (linear) kernel and spectral bound formulations for common pairwise clustering criteria allow to integrate them with any regularization functionals with existing discrete or continuous solvers.
An assumption widely used in recent neural style transfer methods is that image styles can be described by global statics of deep features like Gram or covariance matrices. Alternative approaches have represented styles by decomposing them into local pixel or neural patches. Despite the recent progress, most existing methods treat the semantic patterns of style image uniformly, resulting unpleasing results on complex styles. In this paper, we introduce a more flexible and general universal style transfer technique: multimodal style transfer (MST). MST explicitly considers the matching of semantic patterns in content and style images. Specifically, the style image features are clustered into sub-style components, which are matched with local content features under a graph cut formulation. A reconstruction network is trained to transfer each sub-style and render the final stylized result. We also generalize MST to improve some existing methods. Extensive experiments demonstrate the superior effectiveness, robustness, and flexibility of MST.
We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undirected graph on $n$ vertices up to a $1+epsilon$ error must use $Omega(nlog n/epsilon^2)$ bits of space in the worst case, improving the $Omega(n/epsilon^2)$ bound of Andoni et al. and matching the best known upper bound achieved by spectral sparsifiers. Our proof is based on a rigidity phenomenon for cut (and spectral) approximation which may be of independent interest: any two $d-$regular graphs which approximate each others cuts significantly better than a random graph approximates the complete graph must overlap in a constant fraction of their edges.
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