共查询到20条相似文献,搜索用时 15 毫秒
1.
Tony Lindeberg 《Journal of Mathematical Imaging and Vision》2011,40(1):36-81
This paper describes a generalized axiomatic scale-space theory that makes it possible to derive the notions of linear scale-space,
affine Gaussian scale-space and linear spatio-temporal scale-space using a similar set of assumptions (scale-space axioms). 相似文献
2.
Pseudo-Linear Scale-Space Theory 总被引:2,自引:2,他引:0
It has been observed that linear, Gaussian scale-space, and nonlinear, morphological erosion and dilation scale-spaces generated by a quadratic structuring function have a lot in common. Indeed, far-reaching analogies have been reported, which seems to suggest the existence of an underlying isomorphism. However, an actual mapping appears to be missing.In the present work a one-parameter isomorphism is constructed in closed-form, which encompasses linear and both types of morphological scale-spaces as (non-uniform) limiting cases. The unfolding of the one-parameter family provides a means to transfer known results from one domain to the other. Moreover, for any fixed and non-degenerate parameter value one obtains a novel type of pseudo-linear multiscale representation that is, in a precise way, in-between the familiar ones. This is of interest in its own right, as it enables one to balance pros and cons of linear versus morphological scale-space representations in any particular situation. 相似文献
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The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space 总被引:2,自引:0,他引:2
In this paper we address the topics of scale-space and phase-based image processing in a unifying framework. In contrast to the common opinion, the Gaussian kernel is not the unique choice for a linear scale-space. Instead, we chose the Poisson kernel since it is closely related to the monogenic signal, a 2D generalization of the analytic signal, where the Riesz transform replaces the Hilbert transform. The Riesz transform itself yields the flux of the Poisson scale-space and the combination of flux and scale-space, the monogenic scale-space, provides the local features phase-vector and attenuation in scale-space. Under certain assumptions, the latter two again form a monogenic scale-space which gives deeper insight to low-level image processing. In particular, we discuss edge detection by a new approach to phase congruency and its relation to amplitude based methods, reconstruction from local amplitude and local phase, and the evaluation of the local frequency. 相似文献
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The Topological Structure of Scale-Space Images 总被引:5,自引:0,他引:5
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He Yuchen Kang Sung Ha Morel Jean-Michel 《Journal of Mathematical Imaging and Vision》2022,64(1):41-56
Journal of Mathematical Imaging and Vision - Silhouettes are building elements of logos, graphic symbols and fonts. These shapes can be designed and exchanged in vector form, but more often they... 相似文献
6.
When an image is viewed at varying resolutions, it is known to create discrete perceptual jumps or transitions amid the continuous
intensity changes. In this paper, we study a perceptual scale-space theory which differs from the traditional image scale-space theory in two aspects. (i) In representation, the perceptual scale-space adopts a full generative model. From a Gaussian
pyramid it computes a sketch pyramid where each layer is a primal sketch representation (Guo et al. in Comput. Vis. Image Underst. 106(1):5–19, 2007)—an attribute graph whose elements are image primitives for the image structures. Each primal sketch graph generates the
image in the Gaussian pyramid, and the changes between the primal sketch graphs in adjacent layers are represented by a set
of basic and composite graph operators to account for the perceptual transitions. (ii) In computation, the sketch pyramid and graph operators are inferred, as hidden
variables, from the images through Bayesian inference by stochastic algorithm, in contrast to the deterministic transforms
or feature extraction, such as computing zero-crossings, extremal points, and inflection points in the image scale-space.
Studying the perceptual transitions under the Bayesian framework makes it convenient to use the statistical modeling and learning
tools for (a) modeling the Gestalt properties of the sketch graph, such as continuity and parallelism etc; (b) learning the
most frequent graph operators, i.e. perceptual transitions, in image scaling; and (c) learning the prior probabilities of
the graph operators conditioning on their local neighboring sketch graph structures. In experiments, we learn the parameters
and decision thresholds through human experiments, and we show that the sketch pyramid is a more parsimonious representation
than a multi-resolution Gaussian/Wavelet pyramid. We also demonstrate an application on adaptive image display—showing a large
image in a small screen (say PDA) through a selective tour of its image pyramid. In this application, the sketch pyramid provides
a means for calculating information gain in zooming-in different areas of an image by counting a number of operators expanding
the primal sketches, such that the maximum information is displayed in a given number of frames.
A short version was published in ICCV05 (Wang et al. 2005). 相似文献
7.
Linear Scale-Space Theory from Physical Principles 总被引:2,自引:0,他引:2
Alfons H. Salden Bart M. ter Haar Romeny Max A. Viergever 《Journal of Mathematical Imaging and Vision》1998,9(2):103-139
In the past decades linear scale-space theory was derived on the basis of various axiomatics. In this paper we revisit these axioms and show that they merely coincide with the following physical principles, namely that the image domain is a Galilean space, that the total energy exchange between a region and its surrounding is preserved under linear filtering and that the physical observables should be invariant under the group of similarity transformations. These observables are elements of the similarity jet spanned by natural coordinates and differential energies read out by a vision system.Furthermore, linear scale-space theory is extended to spatio-temporal images on bounded and curved domains. Our theory permits a delay-operation at the present moment which is in agreement with the motion detection model of Reichardt. In this respect our theory deviates from that of Koenderink which requires additional syntactical operators to realise such a delay-operation.Finally, the semi-discrete and discrete linear scale-space theories are derived by discretising the continuous theories following the theory of stochastic processes. The relation and difference between our stochastic approach and that of Lindeberg is pointed out. The connection between continuous and (semi-)discrete sale-space theory for infinitely high scales observed by Lindeberg is refined by applying appropriate scaling limits. It is shown that Lindeberg's requirement of normalisation for one-dimensional discrete Green's functions can be incorporated into our theory for arbitrary dimensional discrete Green's functions, parameter determination can be avoided, and the requirement of operation at even and odd coordinates sum can be guaranteed simultaneously by taking a normalised linear combination of the identity operator and the first step discrete Green's functions. The new discrete Green's functions are still intimately related to the continuous Green's functions and appear to coincide with pyramidal discrete Green's functions. 相似文献
8.
Bo Markussen Kim Steenstrup Pedersen Marco Loog 《Journal of Mathematical Imaging and Vision》2008,31(2-3):207-220
The second-order structure of random images f :? d →? N is studied under the assumption of stationarity of increments, isotropy and scale invariance. Scale invariance is defined via linear scale space theory. The results are formulated in terms of the covariance structure of the jet consisting of the scale space derivatives at a single point. Operators describing the effect in jet space of blurring and scaling are investigated. The theory developed is applicable in the analysis of naturally occurring images of which examples are provided. 相似文献
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Regularization, Scale-Space, and Edge Detection Filters 总被引:2,自引:0,他引:2
Mads Nielsen Luc Florack Rachid Deriche 《Journal of Mathematical Imaging and Vision》1997,7(4):291-307
Computational vision often needs to deal with derivatives ofdigital images. Such derivatives are not intrinsic properties ofdigital data; a paradigm is required to make them well-defined.Normally, a linear filtering is applied. This can be formulated interms of scale-space, functional minimization, or edge detectionfilters. The main emphasis of this paper is to connect these theoriesin order to gain insight in their similarities and differences. We donot want, in this paper, to take part in any discussion of how edgedetection must be performed, but will only link some of the current theories. We take regularization (or functional minimization) as astarting point, and show that it boils down to Gaussian scale-space ifwe require scale invariance and a semi-group constraint to besatisfied. This regularization implies the minimization of afunctional containing terms up to infinite order of differentiation.If the functional is truncated at second order, the Canny-Deriche filter arises. It is also shown that higher dimensional regularizationboils down to a rotated version of the one dimensional case, whenCartesian invariance is imposed and the image is vanishing at theborders. This means that the results from 1D regularization can beeasily generalized to higher dimensions. Finally we show how anefficient implementation of regularization of order n can be made byrecursive filtering using 2n multiplications and additions peroutput element without introducing any approximation. 相似文献
13.
Tony Lindeberg 《Journal of Mathematical Imaging and Vision》2013,46(2):177-210
Scale-invariant interest points have found several highly successful applications in computer vision, in particular for image-based matching and recognition. This paper presents a theoretical analysis of the scale selection properties of a generalized framework for detecting interest points from scale-space features presented in Lindeberg (Int. J. Comput. Vis. 2010, under revision) and comprising: an enriched set of differential interest operators at a fixed scale including the Laplacian operator, the determinant of the Hessian, the new Hessian feature strength measures I and II and the rescaled level curve curvature operator, as well as an enriched set of scale selection mechanisms including scale selection based on local extrema over scale, complementary post-smoothing after the computation of non-linear differential invariants and scale selection based on weighted averaging of scale values along feature trajectories over scale. It is shown how the selected scales of different linear and non-linear interest point detectors can be analyzed for Gaussian blob models. Specifically it is shown that for a rotationally symmetric Gaussian blob model, the scale estimates obtained by weighted scale selection will be similar to the scale estimates obtained from local extrema over scale of scale normalized derivatives for each one of the pure second-order operators. In this respect, no scale compensation is needed between the two types of scale selection approaches. When using post-smoothing, the scale estimates may, however, be different between different types of interest point operators, and it is shown how relative calibration factors can be derived to enable comparable scale estimates for each purely second-order operator and for different amounts of self-similar post-smoothing. A theoretical analysis of the sensitivity to affine image deformations is presented, and it is shown that the scale estimates obtained from the determinant of the Hessian operator are affine covariant for an anisotropic Gaussian blob model. Among the other purely second-order operators, the Hessian feature strength measure I has the lowest sensitivity to non-uniform scaling transformations, followed by the Laplacian operator and the Hessian feature strength measure II. The predictions from this theoretical analysis agree with experimental results of the repeatability properties of the different interest point detectors under affine and perspective transformations of real image data. A number of less complete results are derived for the level curve curvature operator. 相似文献
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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 相似文献
16.
Linear Scale-Space has First been Proposed in Japan 总被引:5,自引:0,他引:5
Joachim Weickert Seiji Ishikawa Atsushi Imiya 《Journal of Mathematical Imaging and Vision》1999,10(3):237-252
Linear scale-space is considered to be a modern bottom-up tool in computer vision. The American and European vision community, however, is unaware of the fact that it has already been axiomatically derived in 1959 in a Japanese paper by Taizo Iijima. This result formed the starting point of vast linear scale-space research in Japan ranging from various axiomatic derivations over deep structure analysis to applications to optical character recognition. Since the outcomes of these activities are unknown to western scale-space researchers, we give an overview of the contribution to the development of linear scale-space theories and analyses. In particular, we review four Japanese axiomatic approaches that substantiate linear scale-space theories proposed between 1959 and 1981. By juxtaposing them to ten American or European axiomatics, we present an overview of the state-of-the-art in Gaussian scale-space axiomatics. Furthermore, we show that many techniques for analysing linear scale-space have also been pioneered by Japanese researchers. 相似文献
17.
The Concordance-based Medial Axis Transform (CMAT) presented in this paper is a multiscale medial axis (MMA) algorithm that computes the medial response from grey-level boundary measures. This non-linear operator responds only to symmetric structures, overcoming the limitations of linear medial operators which create side-lobe responses for symmetric structures and respond to edge structures. In addition, the spatial localisation of the medial axis and the identification of object width is improved in the CMAT algorithm compared with linear algorithms. The robustness of linear medial operators to noise is preserved in our algorithm. The effectiveness of the CMAT is accredited to the concordance property described in this paper. We demonstrate the performance of this method with test figures used by other authors and medical images that are relatively complex in structure. In these complex images the benefit of the improved response of our non-linear operator is clearly visible. 相似文献
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International Journal of Computer Vision - 相似文献
20.
Ives Rey-Otero Jean-Michel Morel Mauricio Delbracio 《Journal of Mathematical Imaging and Vision》2016,56(3):554-572
The most popular image matching algorithm SIFT, introduced by D. Lowe a decade ago, has proven to be sufficiently scale invariant to be used in numerous applications. In practice, however, scale invariance may be weakened by various sources of error inherent to the SIFT implementation affecting the stability and accuracy of keypoint detection. The density of the sampling of the Gaussian scale-space and the level of blur in the input image are two of these sources. This article presents a numerical analysis of their impact on the extracted keypoints stability. Such an analysis has both methodological and practical implications, on how to compare feature detectors and on how to improve SIFT. We show that even with a significantly oversampled scale-space numerical errors prevent from achieving perfect stability. Usual strategies to filter out unstable detections (e.g., poorly contrasted extrema) are shown to be inefficient. We also prove that the effect of the error in the assumption on the initial blur is asymmetric and that the method is strongly degraded in the presence of aliasing or without a correct assumption on the camera blur. This analysis leads to a series of practical recommendations. 相似文献