On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

Noise-robust method for image segmentation

Segmentation of noisy images is one of the most challenging problems in image analysis and any improvement of segmentation methods can highly influence the performance of many image processing applications. In automated image segmentation, the fuzzy c-means (FCM) clustering has been widely used because of its ability to model uncertainty within the data, applicability to multi-modal data and fairly robust behaviour. However, the standard FCM algorithm does not consider any information about the spatial linage context and is highly sensitive to noise and other imaging artefacts. Considering above mentioned problems, we developed a new FCM-based approach for the noise-robust fuzzy clustering and we present it in this paper. In this new iterative algorithm we incorporated both spatial and feature space information into the similarity measure and the membership function. We considered that spatial information depends on the relative location and features of the neighbouring pixels. The performance of the proposed algorithm is tested on synthetic image with different noise levels and real images. Experimental quantitative and qualitative segmentation results show that our method efficiently preserves the homogeneity of the regions and is more robust to noise than other FCM-based methods

Visual Concepts and Compositional Voting

It is very attractive to formulate vision in terms of pattern theory \cite{Mumford2010pattern}, where patterns are defined hierarchically by compositions of elementary building blocks. But applying pattern theory to real world images is currently less successful than discriminative methods such as deep networks. Deep networks, however, are black-boxes which are hard to interpret and can easily be fooled by adding occluding objects. It is natural to wonder whether by better understanding deep networks we can extract building blocks which can be used to develop pattern theoretic models. This motivates us to study the internal representations of a deep network using vehicle images from the PASCAL3D+ dataset. We use clustering algorithms to study the population activities of the features and extract a set of visual concepts which we show are visually tight and correspond to semantic parts of vehicles. To analyze this we annotate these vehicles by their semantic parts to create a new dataset, VehicleSemanticParts, and evaluate visual concepts as unsupervised part detectors. We show that visual concepts perform fairly well but are outperformed by supervised discriminative methods such as Support Vector Machines (SVM). We next give a more detailed analysis of visual concepts and how they relate to semantic parts. Following this, we use the visual concepts as building blocks for a simple pattern theoretical model, which we call compositional voting. In this model several visual concepts combine to detect semantic parts. We show that this approach is significantly better than discriminative methods like SVM and deep networks trained specifically for semantic part detection. Finally, we return to studying occlusion by creating an annotated dataset with occlusion, called VehicleOcclusion, and show that compositional voting outperforms even deep networks when the amount of occlusion becomes large.Comment: It is accepted by Annals of Mathematical Sciences and Application

Hypergraph Modelling for Geometric Model Fitting

In this paper, we propose a novel hypergraph based method (called HF) to fit and segment multi-structural data. The proposed HF formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph model. In the hypergraph model, vertices represent data points and hyperedges denote model hypotheses. The hypergraph, with large and "data-determined" degrees of hyperedges, can express the complex relationships between model hypotheses and data points. In addition, we develop a robust hypergraph partition algorithm to detect sub-hypergraphs for model fitting. HF can effectively and efficiently estimate the number of, and the parameters of, model instances in multi-structural data heavily corrupted with outliers simultaneously. Experimental results show the advantages of the proposed method over previous methods on both synthetic data and real images.Comment: Pattern Recognition, 201