Fuzzy Clustering for Image Segmentation Using Generic Shape Information

The performance of clustering algorithms for image segmentation are highly sensitive to the features used and types of objects in the image, which ultimately limits their generalization capability. This provides strong motivation to investigate integrating shape information into the clustering framework to improve the generality of these algorithms. Existing shape-based clustering techniques mainly focus on circular and elliptical clusters and so are unable to segment arbitrarily-shaped objects. To address this limitation, this paper presents a new shape-based algorithm called fuzzy clustering for image segmentation using generic shape information (FCGS), which exploits the B-spline representation of an object's shape in combination with the Gustafson-Kessel clustering algorithm. Qualitative and quantitative results for FCGS confirm its superior segmentation performance consistently compared to well-established shape-based clustering techniques, for a wide range of test images comprising various regular and arbitrary-shaped objects

Image segmentation using fuzzy clustering incorporating spatial information

Effective image segmentation cannot be achieved for a fuzzy clustering algorithm based on using only pixel intensity, pixel locations or a combination of the two. Often if both pixel intensity and pixel location are combined, one feature tends to minimize the effect of other, thus degrading the resulting segmentation. This paper directly addresses this problem by introducing a new algorithm called image segmentation using fuzzy clustering incorporating spatial information (FCSI), which merges the segmented results independently generated by fuzzy clustering-based on pixel intensity and the location of pixels. Qualitative results show the superiority of the FCSI algorithm compared with the fuzzy c-means (FCM) algorithm for all three alternatives, clustering using only pixel intensity, pixel locations and a combination of the two

Fuzzy image segmentation using location and intensity information

The segmentation results of any clustering algorithm are very sensitive to the features used in the similarity measure and the object types, which reduce the generalization capability of the algorithm. The previously developed algorithm called image segmentation using fuzzy clustering incorporating spatial information (FCSI) merged the independently segmented results generated by fuzzy clustering-based on pixel intensity and pixel location. The main disadvantages of this algorithm are that a perceptually selected threshold does not consider any semantic information and also produces unpredictable segmentation results for objects (regions) covering the entire image. This paper directly addresses these issues by introducing a new algorithm called fuzzy image segmentation using location and intensity (FSLI) by modifying the original FCSI algorithm. It considers the topological feature namely, connectivity and the similarity based on pixel intensity and surface variation. Qualitative and quantitative results confirm the considerable improvements achieved using the FSLI algorithm compared with FCSI and the fuzzy c-means (FCM) algorithm for all three alternatives, namely clustering using only pixel intensity, pixel location and a combination of the two, for a range of sample of images

Correlation Clustering with Low-Rank Matrices

Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature focuses on finding approximation algorithms. In this paper we explore how to solve the correlation clustering objective exactly when the data to be clustered can be represented by a low-rank matrix. We prove in particular that correlation clustering can be solved in polynomial time when the underlying matrix is positive semidefinite with small constant rank, but that the task remains NP-hard in the presence of even one negative eigenvalue. Based on our theoretical results, we develop an algorithm for efficiently "solving" low-rank positive semidefinite correlation clustering by employing a procedure for zonotope vertex enumeration. We demonstrate the effectiveness and speed of our algorithm by using it to solve several clustering problems on both synthetic and real-world data

Robust Correlation Clustering

In this paper, we introduce and study the Robust-Correlation-Clustering problem: given a graph G = (V,E) where every edge is either labeled + or - (denoting similar or dissimilar pairs of vertices), and a parameter m, the goal is to delete a set D of m vertices, and partition the remaining vertices V D into clusters to minimize the cost of the clustering, which is the sum of the number of + edges with end-points in different clusters and the number of - edges with end-points in the same cluster. This generalizes the classical Correlation-Clustering problem which is the special case when m = 0. Correlation clustering is useful when we have (only) qualitative information about the similarity or dissimilarity of pairs of points, and Robust-Correlation-Clustering equips this model with the capability to handle noise in datasets. In this work, we present a constant-factor bi-criteria algorithm for Robust-Correlation-Clustering on complete graphs (where our solution is O(1)-approximate w.r.t the cost while however discarding O(1) m points as outliers), and also complement this by showing that no finite approximation is possible if we do not violate the outlier budget. Our algorithm is very simple in that it first does a simple LP-based pre-processing to delete O(m) vertices, and subsequently runs a particular Correlation-Clustering algorithm ACNAlg [Ailon et al., 2005] on the residual instance. We then consider general graphs, and show (O(log n), O(log^2 n)) bi-criteria algorithms while also showing a hardness of alpha_MC on both the cost and the outlier violation, where alpha_MC is the lower bound for the Minimum-Multicut problem

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

ICAP: An Interactive Cluster Analysis Procedure for analyzing remotely sensed data

An Interactive Cluster Analysis Procedure (ICAP) was developed to derive classifier training statistics from remotely sensed data. The algorithm interfaces the rapid numerical processing capacity of a computer with the human ability to integrate qualitative information. Control of the clustering process alternates between the algorithm, which creates new centroids and forms clusters and the analyst, who evaluate and elect to modify the cluster structure. Clusters can be deleted or lumped pairwise, or new centroids can be added. A summary of the cluster statistics can be requested to facilitate cluster manipulation. The ICAP was implemented in APL (A Programming Language), an interactive computer language. The flexibility of the algorithm was evaluated using data from different LANDSAT scenes to simulate two situations: one in which the analyst is assumed to have no prior knowledge about the data and wishes to have the clusters formed more or less automatically; and the other in which the analyst is assumed to have some knowledge about the data structure and wishes to use that information to closely supervise the clustering process. For comparison, an existing clustering method was also applied to the two data sets