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Image texture provides a rich visual description of the surfaces in the scene. Many texture signatures based on various statistical descriptions and various local measurements have been developed. Existing signatures, in general, are not invariant to 3D geometric transformations, which is a serious limitation for many applications. In this paper we introduce a new texture signature, called the multifractal spectrum (MFS). The MFS is invariant under the bi-Lipschitz map, which includes view-point changes and non-rigid deformations of the texture surface, as well as local affine illumination changes. It provides an efficient framework combining global spatial invariance and local robust measurements. Intuitively, the MFS could be viewed as a "better histogram" with greater robustness to various environmental changes and the advantage of capturing some geometrical distribution information encoded in the texture. Experiments demonstrate that the MFS codes the essential structure of textures with very low dimension, and thus represents an useful tool for texture classification.

In this paper, we present feature/detail preserving models for color image smoothing and segmentation using the Hamiltonian quaternion framework. First, we introduce a novel quaternionic Gabor filter (QGF) which can combine the color channels and the orientations in the image plane. We show that these filters are optimally localized both in the spatial and frequency domains and provide a good approximation to quaternionic quadrature filters. Using the QGFs, we extract the local orientation information in the color images. Second, in order to model this derived orientation information, we propose continuous mixtures of appropriate exponential basis functions and derive analytic expressions for these models. These analytic expressions take the form of spatially varying kernels which, when convolved with a color image or the signed distance function of an evolving contour (placed in the color image), yield a detail preserving smoothing and segmentation, respectively. Several examples on widely used image databases are shown to depict the performance of our algorithms.

Representing texture images statistically as histograms over a discrete vocabulary of local features has proven widely effective for texture classification tasks. Images are described locally by vectors of, for example, responses to some filter bank; and a visual vocabulary is defined as a partition of this descriptor-response space, typically based on clustering. In this paper, we investigate the performance of an approach which represents textures as histograms over a visual vocabulary which is defined geometrically, based on the Basic Image Features of Griffin and Lillholm (Proc. SPIE 6492(09):1---11, 2007), rather than by clustering. BIFs provide a natural mathematical quantisation of a filter-response space into qualitatively distinct types of local image structure. We also extend our approach to deal with intra-class variations in scale. Our algorithm is simple: there is no need for a pre-training step to learn a visual dictionary, as in methods based on clustering, and no tuning of parameters is required to deal with different datasets. We have tested our implementation on three popular and challenging texture datasets and find that it produces consistently good classification results on each, including what we believe to be the best reported for the KTH-TIPS and equal best reported for the UIUCTex databases.

This paper presents a probabilistic framework based on Bayesian theory for the performance prediction and selection of an optimal segmentation algorithm. The framework models the optimal algorithm selection process as one that accounts for the information content of an input image as well as the behavioral properties of a particular candidate segmentation algorithm. The input image information content is measured in terms of image features while the candidate segmentation algorithm's behavioral characteristics are captured through the use of segmentation quality features. Gaussian probability distribution models are used to learn the required relationships between the extracted image and algorithm features and the framework tested on the Berkeley Segmentation Dataset using four candidate segmentation algorithms.

Since their introduction as a means of front propagation and their first application to edge-based segmentation in the early 90's, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of region-based level set segmentation methods and clarify how they can all be derived from a common statistical framework. Region-based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edge-based schemes such as the classical Snakes, region-based methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly well-suited for local optimization methods such as the level set method. We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals. We point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.

We present a coupled minimization problem for image segmentation using prior shape and intensity profile. One part of the model minimizes a shape related energy and the energy of geometric active contour with a parameter that balances the influence from these two. The minimizer corresponding to a fixed parameter in this minimization gives a segmentation and an alignment between the segmentation and prior shape. The second part of this model optimizes the selection of the parameter by maximizing the mutual information of image geometry between the prior and the aligned novel image over all the alignments corresponding to different parameters in the first part. By this coupling the segmentation arrives at higher image gradient, forms a shape similar to the prior, and captures the prior intensity profile. We also propose using mutual information of image geometry to generate intensity model from a set of training images. Experimental results on cardiac ultrasound images are presented. These results indicate that the proposed model provides close agreement with expert traced borders, and the parameter determined in this model for one image can be used for images with similar properties.

We describe a shape from texture method that constructs an estimate of surface geometry using only the deformation of individual texture elements. Our method does not need to use either the boundary of the observed surface or any assumption about the overall distribution of elements.The method assumes that surface texture elements are drawn from a number of different types, each of fixed shape. Neither the shape of the elements nor the number of types need be known in advance. We show that, with this assumption and assuming a generic, scaled orthographic view and texture, each type of texture element can be reconstructed in a frontal coordinate system from image instances. Interest-point methods supply a method of simultaneously obtaining instances of each texture element automatically and defining each type of element. Furthermore, image instances that have been marked in error can be identified and ignored using the Expectation-Maximization algorithm. A further EM procedure yields a surface reconstruction and a relative irradiance map from the data. We provide numerous examples of reconstructions for images of real scenes, show a comparison between our reconstruction and range maps, and demonstrate that the reconstructions display geometric and irradiance phenomena that can be observed in the original image.

We address the issue of low-level segmentation of vector-valued images, focusing on the case of color natural images. The proposed approach relies on the formulation of the problem in the metric framework, as a Voronoi tessellation of the image domain. In this context, a segmentation is determined by a distance transform and a set of sites. Our method consists in dividing the segmentation task in two successive sub-tasks: pre-segmentation and hierarchical representation. We design specific distances for both sub-problems by considering low-level image attributes and, particularly, color and lightness information. Then, the interpretation of the metric formalism in terms of boundaries allows the definition of a soft contour map that has the property of producing a set of closed curves for any threshold. Finally, we evaluate the quality of our results with respect to ground-truth segmentation data.

We propose a novel classifier that both classifies surface texture and simultaneously estimates the unknown illumination conditions. A new formal model of the dependency of texture features on lighting direction is developed which shows that their mean vectors are trigonometric functions of the illuminations' tilt and slant angles. This is used to develop a probabilistic description of feature behaviour which forms the basis of the new classifier. Given a feature set from an image of an unknown texture captured under unknown illumination conditions the algorithm first estimates the most likely illumination direction for each possible texture class. These estimates are used to calculate the class likelihoods and the classification is made accordingly. The ability of the classifier to estimate illuminant direction, and to assign the correct class, was tested on 55 real texture samples in two stages. The classifier was able to accurately estimate both the tilt and the slant angles of the light source for the majority of textures and gave a 98% classification rate.

Curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances, hence can not account for higher order nature of the textural characteristics of image regions. In addition, the object delineation by active contour methods, results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases. Polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding. The key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process. This model can robustly capture texture boundaries by way of higher-order statistics of the data and using an information-theoretic measure and with its nature of the ordinary differential equations. This new variational texture segmentation model, is unsupervised since no prior knowledge on the textural properties of image regions is used. Another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles. This is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners.

This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm runs in time nearly linear in the number of graph edges and is also fast in practice. An important characteristic of the method is its ability to preserve detail in low-variability image regions while ignoring detail in high-variability regions.

This paper provides an algorithm for partitioning grayscale images into disjoint regions of coherent brightness and texture. Natural images contain both textured and untextured regions, so the cues of contour and texture differences are exploited simultaneously. Contours are treated in the intervening contour framework, while texture is analyzed using textons. Each of these cues has a domain of applicability, so to facilitate cue combination we introduce a gating operator based on the texturedness of the neighborhood at a pixel. Having obtained a local measure of how likely two nearby pixels are to belong to the same region, we use the spectral graph theoretic framework of normalized cuts to find partitions of the image into regions of coherent texture and brightness. Experimental results on a wide range of images are shown.

This paper addresses the problem of characterizing the set of all images of a rigid set of m points and n lines observed by a weak perspective or paraperspective camera. By taking explicitly into account the Euclidean constraints associated with calibrated cameras, we show that the corresponding image space can be represented by a six-dimensional variety embedded in {\cal R}^{2(m+n)} and parameterized by the image positions of three reference points. The coefficients defining this parameterized image variety (or PIV for short) can be estimated from a sample of images of a scene via linear and non-linear least squares. The PIV provides an integrated framework for using both point and line features to synthesize new images from a set of pre-recorded pictures (image-based rendering). The proposed technique does not perform any explicit three-dimensional scene reconstruction but it supports hidden-surface elimination, texture mapping and interactive image synthesis at frame rate on ordinary PCs. It has been implemented and extensively tested on real data sets.

We extend the geometric framework introduced in Sochen et al. (IEEE Trans. on Image Processing, 7(3):310–318, 1998) for image enhancement. We analyze and propose enhancement techniques that selectively smooth images while preserving either the multi-channel edges or the orientation-dependent texture features in them. Images are treated as manifolds in a feature-space. This geometrical interpretation lead to a general way for grey level, color, movies, volumetric medical data, and color-texture image enhancement. We first review our framework in which the Polyakov action from high-energy physics is used to develop a minimization procedure through a geometric flow for images. Here we show that the geometric flow, based on manifold volume minimization, yields a novel enhancement procedure for color images. We apply the geometric framework and the general Beltrami flow to feature-preserving denoising of images in various spaces. Next, we introduce a new method for color and texture enhancement. Motivated by Gabor's geometric image sharpening method (Gabor, Laboratory Investigation, 14(6):801–807, 1965), we present a geometric sharpening procedure for color images with texture. It is based on inverse diffusion across the multi-channel edge, and diffusion along the edge.

Herein we propose a complete procedure to analyze and classify the texture of an image. We apply this scheme to solve a specific image processing problem: urban areas detection in satellite images. First we propose to analyze the texture through the modelling of the luminance field with eight different chain-based models. We then derived a texture parameter from these models. The effect of the lattice anisotropy is corrected by a renormalization group technique coming from statistical physics. This parameter, which takes into account local conditional variances of the image, is compared to classical methods of texture analysis. Afterwards we develop a modified fuzzy Cmeans algorithm that includes an entropy term. The advantage of such an algorithm is that the number of classes does not need to be known a priori. Besides this algorithm provides us with further information, i.e. the probability that a given pixel belongs to a given cluster. Finally we introduce this information in a Markovian model of segmentation. Some results on SPOT5 simulated images, SPOT3 images and ERS1 radar images are presented. These images are provided by the French National Space Agency (CNES) and the European Space Agency (ESA).

This article presents a statistical theory for texture modeling. This theory combines filtering theory and Markov random field modeling through the maximum entropy principle, and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view. Our theory characterizes the ensemble of images I with the same texture appearance by a probability distribution f(I) on a random field, and the objective of texture modeling is to make inference about f(I), given a set of observed texture examples.In our theory, texture modeling consists of two steps. (1) A set of filters is selected from a general filter bank to capture features of the texture, these filters are applied to observed texture images, and the histograms of the filtered images are extracted. These histograms are estimates of the marginal distributions of f( I). This step is called feature extraction. (2) The maximum entropy principle is employed to derive a distribution p(I), which is restricted to have the same marginal distributions as those in (1). This p(I) is considered as an estimate of f( I). This step is called feature fusion. A stepwise algorithm is proposed to choose filters from a general filter bank. The resulting model, called FRAME (Filters, Random fields And Maximum Entropy), is a Markov random field (MRF) model, but with a much enriched vocabulary and hence much stronger descriptive ability than the previous MRF models used for texture modeling. Gibbs sampler is adopted to synthesize texture images by drawing typical samples from p(I), thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled. Experiments on a variety of 1D and 2D textures are described to illustrate our theory and to show the performance of our algorithms. These experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework.