A Distance Measure and a Feature Likelihood Map Concept for Scale-Invariant Model Matching

This paper presents two approaches for evaluating multi-scale feature-based object models. Within the first approach, a scale-invariant distance measure is proposed for comparing two image representations in terms of multi-scale features. Based on this measure, the maximisation of the likelihood of parameterised feature models allows for simultaneous model selection and parameter estimation.The idea of the second approach is to avoid an explicit feature extraction step and to evaluate models using a function defined directly from the image data. For this purpose, we propose the concept of a feature likelihood map, which is a function normalised to the interval [0, 1], and that approximates the likelihood of image features at all points in scale-space.To illustrate the applicability of both methods, we consider the area of hand gesture analysis and show how the proposed evaluation schemes can be integrated within a particle filtering approach for performing simultaneous tracking and recognition of hand models under variations in the position, orientation, size and posture of the hand. The experiments demonstrate the feasibility of the approach, and that real time performance can be obtained by pyramid implementations of the proposed concepts.     

Feature Detection with Automatic Scale Selection

The fact that objects in the world appear in different ways depending on the scale of observation has important implications if one aims at describing them. It shows that the notion of scale is of utmost importance when processing unknown measurement data by automatic methods. In their seminal works, Witkin (1983) and Koenderink (1984) proposed to approach this problem by representing image structures at different scales in a so-called scale-space representation. Traditional scale-space theory building on this work, however, does not address the problem of how to select local appropriate scales for further analysis. This article proposes a systematic methodology for dealing with this problem. A framework is presented for generating hypotheses about interesting scale levels in image data, based on a general principle stating that local extrema over scales of different combinations of -normalized derivatives are likely candidates to correspond to interesting structures. Specifically, it is shown how this idea can be used as a major mechanism in algorithms for automatic scale selection, which adapt the local scales of processing to the local image structure.Support for the proposed approach is given in terms of a general theoretical investigation of the behaviour of the scale selection method under rescalings of the input pattern and by integration with different types of early visual modules, including experiments on real-world and synthetic data. Support is also given by a detailed analysis of how different types of feature detectors perform when integrated with a scale selection mechanism and then applied to characteristic model patterns. Specifically, it is described in detail how the proposed methodology applies to the problems of blob detection, junction detection, edge detection, ridge detection and local frequency estimation.In many computer vision applications, the poor performance of the low-level vision modules constitutes a major bottleneck. It is argued that the inclusion of mechanisms for automatic scale selection is essential if we are to construct vision systems to automatically analyse complex unknown environments.     

Scale-Space Image Analysis Based on Hermite Polynomials Theory

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. For multi-dimensional images, anisotropic excursions in scale-space can be handled in this way. Pattern registration and matching applications are suggested.We introduce a Gaussian windowed correlation function K (ν) for locally matching two images. When taking the mutual translation parameter ν as an independent variable, we express the Hermite coefficients of K (ν)interms 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.Numerical simulations using 2D test images illustrate the potentials of our proposals for signal and image matching in terms of accuracy and algorithmic complexity.First online version published in June, 2005     

Temporal Scale Spaces

In this paper we discuss how to define a scale space suitable for temporal measurements. We argue that such a temporal scale space should possess the properties of: temporal causality, linearity, continuity, positivity, recursitivity as well as translational and scaling covariance. It is shown that these requirements imply a one parameter family of convolution kernels. Furthermore it is shown that these measurements can be realized in a time recursive way, with the current data as input and the temporal scale space as state, i.e. there is no need for storing earlier input. This family of measurement processes contains the diffusion equation on the half line (that represents the temporal scale) with the input signal as boundary condition on the temporal axis. The diffusion equation is unique among the measurement processes in the sense that it is preserves positivity (in the scale domain) and is locally generated. A numerical scheme is developed and relations to other approaches are discussed.First online version published in June, 2005     

基于高斯尺度空间的放射性能谱平滑滤波

结合放射性能谱的统计特性,提出了一种基于高斯尺度空间的平滑滤波方法.构造由高斯函数构成的尺度空间,将能谱在该空间内进行多次投影,并在投影中调整高斯函数的权重以实现能谱平滑滤波.选取的标准方差σ和尺度j较小时(如σ=0.2～0.6,j=0),每次平滑后峰形畸变小,适于对弱峰的平滑;选取σ和j较大时(如σ=0.6～1.0,j=1,2,3),可使统计涨落得到较大抑制,并使谱峰成形加快,适于统计涨落较大且谱峰较明显的能谱平滑.结果表明,该方法可灵活地选择标准方差σ和尺度空间Vj,以适应平滑精度和处理速度的要求,且计算简便,是一种性能良好的平滑滤波方法.     

一个基于各向异性的热传导方程导出的图像锐化算子

Ｗｉｔｋｉｎ等人的迟度空间滤波办法是对原图像一个逐渐平滑的过程,这个过程可以用传统的热传导方程来描述,假设“热量”由低温向高温外流动,导出一个各向异性的反向热传导方程。将它用于图像处理,通过选择合适的各向异性函数,使得在盛兴趣的边缘处“热量”由低温向高温处流动,即“灰度”从“     

A Minimum Cost Approach for Segmenting Networks of Lines

The extraction and interpretation of networks of lines from images yields important organizational information of the network under consideration. In this paper, a one-parameter algorithm for the extraction of line networks from images is presented. The parameter indicates the extracted saliency level from a hierarchical graph. Input for the algorithm is the domain specific knowledge of interconnection points. Graph morphological tools are used to extract the minimum cost graph which best segments the network.We give an extensive error analysis for the general case of line extraction. Our method is shown to be robust against gaps in lines, and against spurious vertices at lines, which we consider as the most prominent source of error in line detection. The method indicates detection confidence, thereby supporting error proof interpretation of the network functionality. The method is demonstrated to be applicable on a broad variety of line networks, including dashed lines. Hence, the proposed method yields a major step towards general line tracking algorithms.     

Cartesian differential invariants in scale-space

We present a formalism for studying local image structure in a systematic, coordinate-independent, and robust way, based on scale-space theory, tensor calculus, and the theory of invariants. We concentrate ondifferential invariants. The formalism is of general applicability to the analysis of grey-tone images of various modalities, defined on aD-dimensional spatial domain.We propose a diagrammar of differential invariants and tensors, i.e., a diagrammatic representation of image derivatives in scale-space together with a set of simple rules for representing meaningful local image properties. All local image properties on a given level of inner scale can be represented in terms of such diagrams, and, vice versa, all diagrams represent coordinate-independent combinations of image derivatives, i.e., true image properties.