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We investigate the maximum likelihood metameres of local pure 2nd order structure in natural images. Using the shape index, we re-parameterise the 2nd order structure and gain a one-parameter index which offers a qualitative description of local pure 2nd order image structure. Inspired by Koenderink and previous work within Geometric Texton Theory the maximum likelihood metameres are calculated for a quantised version of the shape index. Results are presented and discussed for natural images, Gaussian noise images, and Brownian or pink noise images. Furthermore, we present statistics for the shape index, principal direction, and curvedness of natural images. Finally, the results are discussed in the terms of their applicability to Geometric Texton Theory. [ABSTRACT FROM AUTHOR]

Image analysis methods that use histograms defined over non-zerosized local neighbourhoods have been proposed [1-4]. To better understand such methods, one can study the histograms of infinitesimal neighbourhoods. In this paper we show how the properties of such histograms can be derived through limit arguments. We show that in many cases the properties of these histograms are given by simple expressions in terms of spatial derivatives at the point analyzed. [ABSTRACT FROM AUTHOR]

We present theoretical and computational results that develop Koenderink΄s theory of feature analysis in human vision [1,7]. Employing a scale space framework, the method aims to classify image points into one of a limited number of feature categories on the basis of local derivative measurements up to some order. At the heart of the method is the use of a family of functions, members of which can be used to account for any set of image measurements. We will show how certain families of simple functions naturally induce a categorical structure onto the space of possible measurements. We present two such families suitable for 1D images measured up to 2nd order, and various results relevant to similar analysis of 2D images. [ABSTRACT FROM AUTHOR]

We review a previously presented proposal - Geometric Texton Theory (GTT) - that feature categories naturally arise through consideration of the maximum likelihood explanations for image measurements by gaussian derivative filters. We present results relevant to this proposal for the case of 1-D measurement by filters of 0th, 1st and 2nd order. The results are consistent with GTT. [ABSTRACT FROM AUTHOR]

Using a consistent adaptive smoothing formulation we show that both nonlinear diffusion and adaptive smoothing can be extended to an arbitrary window, a process called broad kernel filtering. Based on this idea, this paper presents a unified treatment of a number of well known nonlinear techniques for filtering. We show that bilateral filtering represents a particular choice of weights in the extended diffusion process, that is obtained from geometrical considerations. We then show that kernel density estimation applied in the joint spatial-range domain yields a powerful processing paradigm - the mean shift procedure, related to bilateral filtering but having additional flexibility. This establishes an attractive relationship between the theory of statistics and that of diffusion and energy minimization. We experimentally compare the discussed methods and give insights on their performance. [ABSTRACT FROM AUTHOR]

Local scale information extracted from visual data in a bottom-up manner constitutes an important cue for a large number of visual tasks. This article presents a framework for how the computation of such scale descriptors can be performed in real time on a standard computer. The proposed scale selection framework is expressed within a novel type of multi-scale representation, referred to as hybrid multi-scale representation, which aims at integrating and providing variable trade-offs between the relative advantages of pyramids and scale-space representation, in terms of computational efficiency and computational accuracy. Starting from binomial scale-space kernels of different widths, we describe a family pyramid representations, in which the regular pyramid concept and the regular scale-space representation constitute limiting cases. In particular, the steepness of the pyramid as well as the sampling density in the scale direction can be varied. It is shown how the definition of γ-normalized derivative operators underlying the automatic scale selection mechanism can be transferred from a regular scale-space to a hybrid pyramid, and two alternative definitions are studied in detail, referred to as variance normalization and lp-normalization. The computational accuracy of these two schemes is evaluated, and it is shown how the choice of sub-sampling rate provides a trade-off between the computational efficiency and the accuracy of the scale descriptors. Experimental evaluations are presented for both synthetic and real data. In a simplified form, this scale selection mechanism has been running for two years, in a real-time computer vision system. [ABSTRACT FROM AUTHOR]

Scale-space feature hierarchies can be conveniently represented as graphs, in which edges are directed from coarser features to finer features. Consequently, feature matching (or view-based object matching) can be formulated as graph matching. Most approaches to graph matching assume a one-to-one correspondence between nodes (features) which, due to noise, scale discretization, and feature extraction errors, is overly restrictive. In general, a subset of features in one hierarchy, representing an abstraction of those features, may best match a subset of features in another. We present a framework for the many-to-many matching of multi-scale feature hierarchies, in which features and their relations are captured in a vertex-labeled, edge-weighted graph. The matching algorithm is based on a metric-tree representation of labeled graphs and their low-distortion metric embedding into normed vector spaces. This two-step transformation reduces the many-to-many graph matching problem to that of computing a distribution-based distance measure between two such embeddings. To compute the distance between two sets of embedded, weighted vectors, we use the Earth Mover's Distance under transformation. To demonstrate the approach, we target the domain of multi-scale, qualitative shape description, in which an image is decomposed into a set of blobs and ridges with automatic scale selection. We conduct an extensive set of view-based matching trials, and compare the results favorably to matching under a one-to-one assumption. [ABSTRACT FROM AUTHOR]

We study the connections between discrete one-dimensional schemes for nonlinear diffusion and shift-invariant Haar wavelet shrinkage. We show that one step of (stabilised) explicit discretisation of nonlinear diffusion can be expressed in terms of wavelet shrinkage on a single spatial level. This equivalence allows a fruitful exchange of ideas between the two fields. In this paper we derive new wavelet shrinkage functions from existing diffusivity functions, and identify some previously used shrinkage functions as corresponding to well known diffusivities. We demonstrate experimentally that some of the diffusion-inspired shrinkage functions are among the best for translation-invariant multiscale wavelet shrinkage denoising. [ABSTRACT FROM AUTHOR]

The Hermite transform allows to locally approximate an image by a linear combination of polynomials. For a given scale σ and position ξ, the polynomial coefficients are closely related to the differential jet (set of partial derivatives of the blurred image) for the same scale and position. By making use of a classical formula due to Mehler (late 19th century), we establish a linear relationship linking the differential jets at two different scales σ and positions ξ involving Hermite polynomials. Pattern registration and matching applications are suggested. We introduce a Gaussian windowed correlation function K(v) for locally matching two images. When taking the mutual translation parameter v as independent variable, we express the Hermite coefficients of K(v) in terms of the Hermite coefficients of the two images being matched. This new result bears similarity with the Wiener-Khinchin theorem which links the Fourier transform of the conventional (flat-windowed) correlation function with the Fourier spectra of the images being correlated. Compared to the conventional correlation function, ours is more suited for matching localized image features. The mathematical tools we propose are shown to have attractive computational features. Numerical simulations using synthetic 1D and 2D test patterns demonstrate the advantages of our proposals for signal and image matching in terms of accuracy and low algorithm complexity. [ABSTRACT FROM AUTHOR]

We extend a symmetric parametric curve matching algorithm designed for recognition and morphometry by incorporating Gaussian smoothing and curvature scale-space. A general statement of the matching theory and the properties of the associated algorithm is given. Gaussian smoothing is used to assist in approximating the continuous solution from the discrete solution given by dynamic programming. The method is then investigated in a multi-scale framework, which has the advantage of reducing the effects of noise and occlusion. A novel scale-space derived energy functional that incorporates geometric information from many scales at once is proposed. The related issue of selecting a smoothing kernel for a given matching problem is also explored, resulting in a topologically based method of scale-selection. This application requires estimating the matching between the fine and coarse scale versions of the same curve. We provide a tool for finding this inter-scale, intra-curve correspondence, based on tracking curvature extrema through scales. These novel algorithms are demonstrated on both 2D and 3D data. [ABSTRACT FROM AUTHOR]

Object detection and localization are common tasks in image analysis. Correlation based detection algorithms are known to work well, when dealing with objects with known geometry in Gaussianly distributed additive noise. In the Bayes' view, correlation is linearly related to the logarithm of the probability density, and optimal object detection is obtained by the integral of the exponentiated squared correlation under appropriate normalization. Correlation with a model is linear in the input image, and can be computed effectively for all possible positions of the model using Fourier based linear filtering techniques. It is therefore interesting to extend the application to objects with many but small degrees of freedom in their geometry. These geometric variations deteriorate the linear correlation signal, both regarding its strength and localization with multiple peaks from a single object. Localization is typically preferred over detection, and Bayesian localization may be obtained as local integration of the probability density. In this work, Gaussian kernels of the exponentiated correlation are studied, and the use of Linear Scale-Space allows us to extend the Bayes detection with a well-posed localization, to extend the usage of correlation to a larger class of shapes, and to argue for the use of mathematical morphology with quadratic structuring elements on correlation images. [ABSTRACT FROM AUTHOR]

Morphological and linear scale spaces are well-established instruments in image analysis. They display interesting analogies which make a deeper insight into their mutual relation desirable. A contribution to the understanding of this relation is presented here. We embed morphological dilation and erosion scale spaces with paraboloid structure functions into families of scale spaces which are found to include linear Gaussian scale space as limit cases. The scale-space families are obtained by deforming the algebraic operations underlying the morphological scale spaces within a family of algebraic operations related to lp norms and generalised means. Alternatively, the deformation of the morphological scale spaces can be described in terms of grey-scale isomorphisms. We discuss aspects of the newly constructed scale space families such as continuity, invariance, and separability, and the limiting procedure leading to linear scale space. This limiting procedure requires a suitable renormalisation of the scaling parameter. In this sense, our approach turns out to be complementary to that proposed by L. Florack et al. in 1999 which comprises a continuous deformation of linear scale space including morphological scale spaces as limit cases provided an appropriate renormalisation. [ABSTRACT FROM AUTHOR]

Gaussian scale space is properly defined and well-developed for images completely knownand defined on the d dimensional Euclidean space ℝd. However, as soon as image information is only partly available, say, on a subset V of ℝd, the Gaussian scale space paradigm is not readily applicable and one has to resort to different approaches to come to a scale space on V. Examples are the theory dealing with scale space on ℤd ⊂ ℝd, i.e., discrete scale space; the approach based on the heat equation satisfying certain boundary conditions; and the ad hoc approaches dealing with (hyper)rectangular images, e.g. zero-padding of the area outside of V, or periodic continuation of the image. We propose to solve the foregoing problem for general V from a Bayesian viewpoint. Assuming that the observed image is obtained by linearly sampling a real underlying image that is actually defined on the complete d dimensional Euclidean space, we can infer this latter image and from that image build the scale space. Re-sampling this scale space then gives rise to the scale space on V. Necessary for inferring the underlying image is knowledge on the linear apertures (or receptive field) used for sampling this image, and information on the prior over the class of all images. [ABSTRACT FROM AUTHOR]

In this article we learn significant local appearance features for visual classes. Generic feature detectors are obtained by unsupervised learning using clustering. The resulting clusters, referred to as "classtons", identify the significant class characteristics from a small set of sample images. The classton channels mark these characteristics reliably using a probabilistic cluster representation. The classtons demonstrate good generalisation with respect to viewpoint changes and previously unseen objects. In all experiments, the classton channels of similar images have the same spatial relations. Learning of these relations allows to generate a classification model that combines the generalisation ability from the classtons and the discriminative power from the spatial relations. [ABSTRACT FROM AUTHOR]

Compression systems like JPEG include optional pre-processing with filtering to avoid compression artefacts. At higher compression ratios a stronger filtering is needed that impacts the large scale image content. To preserve the large scale information we have previously proposed to use non-linear diffusion as a pre-processing for filtering out small scale details irrelevant at a given compression ratio and acting as noise. Now we compare typical diffusion processes applied before the blockwise DCT compression using the peak signal to noise ration (PSNR) as an objective quality measure. We give a simple measure of artefact reduction in terms of PSNR, and show that a considerable artefact reduction is achieved by pre-processing at the same bit rate as and with no greater error than the original compression. We did tests to see if the above artefact reduction implies a better subjective impression of quality. The images processed with the PSNR-based algorithm had nearly the same but greater PSNR value as the original compression. Subjects preferred noisy image content to the lack of small scale details, so the subjective preference of the images with reduced artefact is worse that of the original compression. Results suggest however that non-linear diffusion is more efficient for artefact reduction than non-adaptive smoothing like Gaussian filtering in terms of the subjective preference. [ABSTRACT FROM AUTHOR]

We present a novel approach to shape representation that describes a shape using a set of histograms derived at salient points within the shape. A computationally efficient multiresolution pyramidal framework is used to generate a dense gradient vector field whose characteristics can be altered through the use of a scale parameter α. This parameter regulates the proportion of low and high spatial frequency components used in creating the vector field and can be set such that minor boundary distortions do not significantly change the representation of the shape. Local maximas of the directional disparity measure in the vector field are used for locating shape axes, from where polar sampling of the vector field is then used to build scale and rotational invariant histograms that describes subparts of the shape. A saliency measure based on the size of a part is introduced to provide appropriate weighting to each part during the shape matching process. Experimental results involving silhouettes images are presented to demonstrate the effectiveness of the proposed gradient vector field histograms for similarity-based shape retrieval. [ABSTRACT FROM AUTHOR]

Recursive filters are commonly used in scale space construction for their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of reflectively extended images for filters with symmetric denominator. We begin with an analysis of reflective extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on reflective domains as a linear but time-varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring the same order of computation as the standard recursive filtering. We give experimental evidence to verify these claims. [ABSTRACT FROM AUTHOR]

Structural variability present in biomedical images is known to aggravate the segmentation process. Statistical models of appearance proved successful in exploiting the structural variability information in the learning set to segment a previously unseen medical image more reliably. In this paper we show that biomedical image segmentation with statistical models of appearance can be improved in terms of accuracy and efficiency by a multiresolution approach. We outline two different multiresolution approaches. The first demonstrates a straightforward extension of the original statistical model and uses a pyramid of statistical models to segment the input image on various resolution levels. The second applies the idea of direct coefficient propagation through the Gaussian image pyramid and uses only one statistical model to perform the multiresolution segmentation in a much simpler manner. Experimental results illustrate the scale of improvement achieved by using the multiresolution approaches described. Possible further improvements are discussed at the end. [ABSTRACT FROM AUTHOR]

Estimation of a digital curve's curvature at any given point is needed for many tasks in computer vision, be it differential invariants or curvature scale space. However, curvature estimation is known to be very susceptible to noise on the contour. We shall show how noise on the contour affects the relative accuracy of the curvature computation. One interesting result is that, contrary to intuition, the accurate calculation of the curvature for low-curvature regions is in fact impossible for common image-sizes, while reasonable results may under favourable conditions be obtained for higher-curvature regions. [ABSTRACT FROM AUTHOR]

This article presents a fully automatic method for segmenting the brain from other tissue in a 3-D MR image of the human head. The method is a an extension and combination of previous techniques, and consists of the following processing steps: (i) After an initial intensity normalization, an affine alignment is performed to a standard anatomical space, where the unsegmented image can be compared to a segmented standard brain. (ii) Probabilistic diffusion, guided by probability measures between white matter, grey matter and cerebrospinal fluid, is performed in order to suppress the influence of extra-cerebral tissue. (iii) A multi-scale watershed segmentation step creates a slightly over-segmented image, where the brain contour constitutes a subset of the watershed boundaries. (iv) A segmentation of the over-segmented brain is then selected by using spatial information from the pre-segmented standard brain in combination with additional stages of probabilistic diffusion, morphological operations and thresholding. The composed algorithm has been evaluated on 50 T1-weighted MR volumes, by visual inspection and by computing quantitative measures of (i) the similarity between the segmented brain and a manual segmentation of the same brain, and (ii) the ratio of the volumetric difference between automatically and manually segmented brains relative to the volume of the manually segmented brain. The mean value of the similarity index was 0.9961 with standard deviation 0.0034 (worst value 0.9813, best 0.9998). The mean percentage volume error was 0.77 % with standard deviation 0.69 % (maximum percentage error 3.81 %, minimum percentage error 0.05 %). [ABSTRACT FROM AUTHOR]

We consider a problem intimately related to the creation of maxima under Gaussian blurring: the number of modes of a Gaussian mixture in D dimensions. To our knowledge, a general answer to this question is not known. We conjecture that if the components of the mixture have the same covariance matrix (or the same covariance matrix up to a scaling factor), then the number of modes cannot exceed the number of components. We demonstrate that the number of modes can exceed the number of components when the components are allowed to have arbitrary and different covariance matrices. We will review related results from scale-space theory, statistics and machine learning, including a proof of the conjecture in 1D. We present a convergent, EM-like algorithm for mode finding and compare results of searching for all modes starting from the centers of the mixture components with a brute-force search. We also discuss applications to data reconstruction and clustering. [ABSTRACT FROM AUTHOR]

Here we present a segmentation algorithm that uses multiscale diffusion with the Mumford-Shah model. The image data inside and outside a surface is smoothed by minimizing an energy functional using a partial differential equation that results in a trade-off between smoothing and data fidelity. We propose a scale-space approach that uses a good deal of diffusion as its coarse scale space and that gradually reduces the diffusion to get a fine scale space. So our algorithm continually moves to a particular diffusion level rather than just using a set diffusion coefficient with the Mumford-Shah model. Each time the smoothing is decreased, the data fidelity term increases and the surface is moved to a steady state. This method is useful in segmenting biomedical images acquired using high-resolution confocal fluorescence microscopy. Here we tested the method on images of individual dendrites of neurons in rat visual cortex. These dendrites are studded with dendritic spines, which have very small heads and faint necks. The coarse scale segments out the dendrite and the brighter spine heads, while avoiding noise. Backing off the diffusion to a medium scale fills in more of the structure, which gets some of the brighter spine necks. The finest scale fills in the small and detailed features of the spines that are missed in the initial segmentation. Because of the thin, faint structure of the spine necks, we incorporate into our level set framework a topology preservation method for the surface which aids in segmentation and keeps a simple topology. [ABSTRACT FROM AUTHOR]

We present a novel variational approach for segmenting the image plane into a set of regions of piecewise constant motion on the basis of only two consecutive frames from an image sequence. To this end, we formulate the problem of estimating a motion field in the framework of Bayesian inference. Our model is based on a conditional probability for the spatio-temporal image gradient, given a particular velocity vector, and on a prior on the estimated motion field favoring motion boundaries of minimal length. The corresponding negative log likelihood is a functional which depends on motion vectors for a set of regions and on the boundary separating these regions. It can be considered an extension of the Mumford-Shah functional from intensity segmentation to motion segmentation. We propose an implementation of this functional by a multiphase level set framework. Minimizing the functional with respect to its dynamic variables results in an evolution equation for a vector-valued level set function and in an eigenvalue problem for the motion vectors. Compared to most alternative approaches, we jointly solve the problems of segmentation and motion estimation by minimizing a single functional. Numerical results both for simulated ground truth experiments and for real-world sequences demonstrate the capacity of our approach to segment several — possibly multiply connected — objects based on their relative motion. [ABSTRACT FROM AUTHOR]

The characteristic (or intrinsic) scale of a local image pattern is the scale parameter at which the Laplacian provides a local maximum. Nearly every position in an image will exhibit a small number of such characteristic scales. Computing a vector of Gaussian derivatives (a Gaussian jet) at a characteristic scale provides a scale invariant feature vector for tracking, matching, indexing and recognition. However, the computational cost of directly searching the scale axis for the characteristic scale at each image position can be prohibitively expensive. We describe a fast method for computing a vector of Gaussian derivatives that are normalised to the characteristic scale at each pixel. This method is based on a scale equivariant half-octave binomial pyramid. The characteristic scale for each pixel is determined by an interpolated maximum in the Difference of Gaussian as a function of scale. We show that interpolation between pixels across scales can be used to provide an accurate estimate of the intrinsic scale at each image point. We present an experimental evaluation that compares the scale invariance of this method to direct computation using FIR filters, and to an implementation using recursive filters. With this method we obtain a scale normalised Gaussian Jet at video rate for a 1/4 size PAL image on a standard 1.5 Ghz Pentium workstation. [ABSTRACT FROM AUTHOR]

This paper presents a new filterbank-based iris recognition method that effectively extracts the spatial and directional features of iris patterns on multiple scales, then performs matching. First, the proposed method localizes the iris area from an input image and establishes a region of interest (ROI) for feature extraction. Second, the iris features are extracted on multiple scales from the ROI and a feature vector generated using a band pass filter and directional filter bank (DFB), which decomposes the image into several directional subband outputs. Finally, iris pattern matching robust to various rotations of the input is performed based on finding the Hamming distance between the corresponding feature vectors. Experimental results demonstrate that the proposed method is both effective in extracting directional and multiresolutional features from iris patterns and robust to input image rotation due to head tilt. [ABSTRACT FROM AUTHOR]

Traditionally, image blurring by diffusion is done in Euclidean space, in an image-based coordinate system. This will blur edges at object boundaries, making segmentation difficult. Geometry-driven diffusion 1 uses a geometric model to steer the blurring, so as to blur along the boundary (to overcome noise) but edge-detect across the object boundary. In this paper, we present a scale-space on image profiles taken about the object boundary, in an object-intrinsic coordinate system. The profiles are sampled from the image in the fashion of Active Shape Models 2, and a scale-space is constructed on the profiles, where diffusion is run only in directions tangent to the boundary. Features from the scale-space are then used to build a statistical model of the image structure about the boundary, trained on a population of images with corresponding geometric models. This statistical image match model can be used in an image segmentation framework. Results are shown in 2D on synthetic and real-world objects; the methods can also be extended to 3D. [ABSTRACT FROM AUTHOR]

Sieves and their variants are established processors for simplifying greyscale images. Because combined outputs of these filters satisfy the scale-space causality property they are often referred to as scale-space filters although they have quite different characteristics compared to systems based around diffusion. In this paper we implement several possible extensions of sieves for colour images which include: applying the processor on separate channels; and enforcing an ordering on the colour vectors. We show that a new definition, based on convex hulls in colour space, can lead to an effective algorithm. As with the greyscale method, the colour sieve produces a tree-based representation of image that form the first step to a meaningful hierarchical decomposition. [ABSTRACT FROM AUTHOR]

This paper reports a novel Multiscale Attention-based Pre-Segmentation method (MAPS) which is built around the multi-feature, multiscale, saliency-based model of visual attention. From the saliency map, provided by the attention algorithm, MAPS first derives the spatial locations of salient regions that will be considered further in the segmentation process. Then, the salient scale and the salient feature of each salient region is determined by exploring the scale and feature spaces computed by the model of attention. A first and rough multiscale segmentation of the salient regions is performed on the corresponding salient scale. This innovative presegmentation but yet uncomplete procedure is followed by some refined segmentation that operates in the salient feature at full resolution. [ABSTRACT FROM AUTHOR]