Function-described graphs for modelling objects represented by sets of attributed graphs

We present in this article the model function-described graph (FDG), which is a type of compact representation of a set of attributed graphs (AGs) that borrow from random graphs the capability of probabilistic modelling of structural and attribute information. We define the FDGs, their features and two distance measures between AGs (unclassified patterns) and FDGs (models or classes) and we also explain an efficient matching algorithm. Two applications of FDGs are presented: in the former, FDGs are used for modelling and matching 3D-objects described by multiple views, whereas in the latter, they are used for representing and recognising human faces, described also by several views.     

Graph-based tools for microscopic cellular image segmentation

We propose a framework of graph-based tools for the segmentation of microscopic cellular images. This framework is based on an object oriented analysis of imaging problems in pathology. Our graph tools rely on a general formulation of discrete functional regularization on weighted graphs of arbitrary topology. It leads to a set of useful tools which can be combined together to address various image segmentation problems in pathology. To provide fast image segmentation algorithms, we also propose an image simplification based on graphs as a pre processing step. The abilities of this set of image processing discrete tools are illustrated through automatic and interactive segmentation schemes for color cytological and histological images segmentation problems.     

A graph-based framework for sub-pixel image segmentation

Many image segmentation methods utilize graph structures for representing images, where the flexibility and generality of the abstract structure is beneficial. By using a fuzzy object representation, i.e., allowing partial belongingness of elements to image objects, the unavoidable loss of information when representing continuous structures by finite sets is significantly reduced, enabling feature estimates with sub-pixel precision.This work presents a framework for object representation based on fuzzy segmented graphs. Interpreting the edges as one-dimensional paths between the vertices of a graph, we extend the notion of a graph cut to that of a located cut, i.e., a cut with sub-edge precision. We describe a method for computing a located cut from a fuzzy segmentation of graph vertices. Further, the notion of vertex coverage segmentation is proposed as a graph theoretic equivalent to pixel coverage segmentations and a method for computing such a segmentation from a located cut is given. Utilizing the proposed framework, we demonstrate improved precision of area measurements of synthetic two-dimensional objects. We emphasize that although the experiments presented here are performed on two-dimensional images, the proposed framework is defined for general graphs and thus applicable to images of any dimension.     

基于图论和均匀性测度的彩色图像分割算法

Graph-Based方法是基于图论的彩色图像分割算法中比较新颖的一种方法,且分割速度非常快。针对该算法对边缘和纹理处理效果不佳,且分割效果易受阈值影响的局限,改变了其颜色空间,结合拉普拉斯算子将带权图的边分为边缘边和非边缘边,优先处理非边缘边;再引入均匀性测度求取分割效果最佳的阈值。实验结果表明,相对于Graph-Based方法,改进的算法分割效果具有较好的准确性和适应性,更接近于人眼的感觉。     

A graph isomorphism algorithm for object recognition

We present an algorithm to solve the graph isomorphism problem for the purpose of object recognition. Objects, such as those which exist in a robot workspace, may be represented by labelled graphs (graphs with attributes on their nodes and/or edges). Thereafter, object recognition is achieved by matching pairs of these graphs. Assuming that all objects are sufficiently different so that their corresponding representative graphs are distinct, then given a new graph, the algorthm efficiently finds the isomorphic stored graph (if it exists). The algorithm consists of three phases: preprocessing, link construction, and ambiguity resolution. Results from experiments on a wide variety and sizes of graphs are reported. Results are also reported for experiments on recognising graphs that represent protein molecules. The algorithm works for all types of graphs except for a class of highly ambiguous graphs which includes strongly regular graphs. However, members of this class are detected in polynomial time, which leaves the option of switching to a higher complexity algorithm if desired.     

Quotients of Gaussian graphs and their application to perfect codes

A graph-based model of perfect two-dimensional codes is presented in this work. This model facilitates the study of the metric properties of the codes. Signal spaces are modeled by means of Cayley graphs defined over the Gaussian integers and denoted as Gaussian graphs. Codewords of perfect codes will be represented by vertices of a quotient graph of the Gaussian graph in which the signal space has been defined. It will be shown that any quotient graph of a Gaussian graph is indeed a Gaussian graph. This makes it possible to apply previously known properties of Gaussian graphs to the analysis of perfect codes. To illustrate the modeling power of this graph-based tool, perfect Lee codes will be analyzed in terms of Gaussian graphs and their quotients.     

Near-duplicate document image matching: A graphical perspective

A near-duplicate document image matching approach characterized by a graphical perspective is proposed in this paper. Document images are represented by graphs whose nodes correspond to the objects in the images. Consequently, the image matching problem is then converted to graph matching. To deal with the instability of object segmentation, a multi-granularity object tree is constructed for a document image. Each level in the tree corresponds to one possible object segmentation, while different levels are characterized by various object granularities. Some graphs can be generated from the tree and the objects associated with each graph may be of different granularities. Two graphs with the maximum similarity are found from the multi-granularity object trees of the two near-duplicate document images which are to be matched. The encouraging experimental results have demonstrated the effectiveness of the proposed approach.     

一种新的基于图谱理论的图像阈值分割方法

提出了一种新的图像阈值分割方法,该方法采用图谱划分测度作为区分目标和背景的阈值分割准则.采用基于灰度级的权值矩阵来代替通常所用的基于图像像素的权值矩阵来描述图像各像素的关系,因而算法所需的存储空间及实现的复杂性与其他基于图论的图像分割方法相比大大减少,从而有利于应用在各种实时视觉系统(如自动目标识别,ATR).大量的实验结果表明:与现有的阈值分割方法相比,文中提出的方法具有更为优越的分割性能.     

Fast graph similarity search via hashing and its application on image retrieval

Similarity search in graph databases has been widely investigated. It is worthwhile to develop a fast algorithm to support similarity search in large-scale graph databases. In this paper, we investigate a k-NN (k-Nearest Neighbor) similarity search problem by locality sensitive hashing (LSH). We propose an innovative fast graph search algorithm named LSH-GSS, which first transforms complex graphs into vectorial representations based on prototypes in the database and later accelerates a query in Euclidean space by employing LSH. Because images can be represented as attributed graphs, we propose an approach to transform attributed graphs into n-dimensional vectors and apply LSH-GSS to execute further image retrieval. Experiments on three real graph datasets and two image datasets show that our methods are highly accurate and efficient.     

Color image segmentation: advances and prospects

Image segmentation is very essential and critical to image processing and pattern recognition. This survey provides a summary of color image segmentation techniques available now. Basically, color segmentation approaches are based on monochrome segmentation approaches operating in different color spaces. Therefore, we first discuss the major segmentation approaches for segmenting monochrome images: histogram thresholding, characteristic feature clustering, edge detection, region-based methods, fuzzy techniques, neural networks, etc.; then review some major color representation methods and their advantages/disadvantages; finally summarize the color image segmentation techniques using different color representations. The usage of color models for image segmentation is also discussed. Some novel approaches such as fuzzy method and physics-based method are investigated as well.     

Graph Classification by Means of Lipschitz Embedding

In pattern recognition and related fields, graph-based representations offer a versatile alternative to the widely used feature vectors. Therefore, an emerging trend of representing objects by graphs can be observed. This trend is intensified by the development of novel approaches in graph-based machine learning, such as graph kernels or graph-embedding techniques. These procedures overcome a major drawback of graphs, which consists of a serious lack of algorithms for classification. This paper is inspired by the idea of representing graphs through dissimilarities and extends our previous work to the more general setting of Lipschitz embeddings. In an experimental evaluation, we empirically confirm that classifiers that rely on the original graph distances can be outperformed by a classification system using the Lipschitz embedded graphs.     

Object Recognition as Many-to-Many Feature Matching

Object recognition can be formulated as matching image features to model features. When recognition is exemplar-based, feature correspondence is one-to-one. However, segmentation errors, articulation, scale difference, and within-class deformation can yield image and model features which don’t match one-to-one but rather many-to-many. Adopting a graph-based representation of a set of features, we present a matching algorithm that establishes many-to-many correspondences between the nodes of two noisy, vertex-labeled weighted graphs. Our approach reduces the problem of many-to-many matching of weighted graphs to that of many-to-many matching of weighted point sets in a normed vector space. This is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure. Many-to-many vector correspondences established by the Earth Mover’s Distance framework are mapped back into many-to-many correspondences between graph nodes. Empirical evaluation of the algorithm on an extensive set of recognition trials, including a comparison with two competing graph matching approaches, demonstrates both the robustness and efficacy of the overall approach.     

Polyhedral object recognition by indexing

In computer vision, the indexing problem is the problem of recognizing a few objects in a large database of objects while avoiding the help of the classical image-feature-to-object-feature matching paradigm. In this paper we address the problem of recognizing three-dimensional (3-D) polyhedral objects from 2-D images by indexing. Both the objects to be recognized and the images are represented by weighted graphs. The indexing problem is therefore the problem of determining whether a graph extracted from the image is present or absent in a database of model graphs. We introduce a novel method for performing this graph indexing process which is based both on polynomial characterization of binary and weighted graphs and on hashing. We describe in detail this polynomial characterization and then we show how it can be used in the context of polyhedral object recognition. Next we describe a practical recognition-by-indexing system that includes the organization of the database, the representation of polyhedral objects in terms of 2-D characteristic views, the representation of this views in terms of weighted graphs and the associated image processing. Finally, some experimental results allow the evaluation of the system performance.     

基于熵的两区域图像分割

图像分割在多媒体,图像处理,计算机视觉领域扮演着重要角色。提出了基于图像分割熵的二区域图像分割方法。 首先,根据熵的特性:单个随机变量所对应的熵越大,所包含的信息量越大,图像是单一区域时,所含的信息量(熵)较小,引入图像分割熵(ISE)测度,用于度量两区域图像分割准确程度,将两区域图像分割问题转化成ISE最小值问题。然后,采用迭代图切(graph cut)算法给出ISE最小值问题的近似解,实现二区域图像分割。实验结果表明,基于图像分割熵的二区域图像分割方法是可行有效的。     

Non-rigid 3D object retrieval using topological information guided by conformal factors

Combining the properties of conformal geometry and graph-based topological information, a non-rigid 3D object retrieval methodology is proposed, which is both robust and efficient in terms of retrieval accuracy and computation speed. While graph-based methods are robust to non-rigid object deformations, they require intensive computation which can be reduced by the use of appropriate representations, addressed through geometry-based methods. In this respect, we present a 3D object retrieval methodology, which combines the above advantages in a unified manner. Furthermore, we propose a string matching strategy for the comparison of graphs which describe 3D objects.     

Image segmentation with ratio cut

This paper proposes a new cost function, cut ratio, for segmenting images using graph-based methods. The cut ratio is defined as the ratio of the corresponding sums of two different weights of edges along the cut boundary and models the mean affinity between the segments separated by the boundary per unit boundary length. This new cost function allows the image perimeter to be segmented, guarantees that the segments produced by bipartitioning are connected, and does not introduce a size, shape, smoothness, or boundary-length bias. The latter allows it to produce segmentations where boundaries are aligned with image edges. Furthermore, the cut-ratio cost function allows efficient iterated region-based segmentation as well as pixel-based segmentation. These properties may be useful for some image-segmentation applications. While the problem of finding a minimum ratio cut in an arbitrary graph is NP-hard, one can find a minimum ratio cut in the connected planar graphs that arise during image segmentation in polynomial time. While the cut ratio, alone, is not sufficient as a baseline method for image segmentation, it forms a good basis for an extended method of image segmentation when combined with a small number of standard techniques. We present an implemented algorithm for finding a minimum ratio cut, prove its correctness, discuss its application to image segmentation, and present the results of segmenting a number of medical and natural images using our techniques.     

FReBIR: An image retrieval system based on fuzzy region matching

In this paper, we present a method of image indexing and retrieval which takes into account the relative positions of the regions within the image. Indexing is based on a segmentation of the image into fuzzy regions; we propose an algorithm which produces a fuzzy segmentation. The image retrieval is based on inexact graph matching, taking into account both the similarity between regions and the spatial relation between them. We propose, on one hand a solution to reduce the combinatorial complexity of the graph matching, and on the other hand, a measure of similarity between graphs allowing the result images ranking. A relevance feedback process based on region classifiers allows then a good generalization to a large variety of the regions. The method is adapted to partial queries, aiming for example at retrieving images containing a specific type of object. Applications may be of two types, firstly an on-line search from a partial query, with a relevance feedback aiming at interactively leading the search, and secondly an off-line learning of categories from a set of examples of the object. The name of the system is FReBIR for Fuzzy Region-Based Image Retrieval.