Scale-Space: A Framework for Handling Image Structures at Multiple Scales

This article gives a tutorial overview of essential components of scale-space theory --- a framework for multi-scale signal representation, which has been developed by the computer vision community to analyse and interpret real-world images by automatic methods. 1 The need for multi-scale representation of image data An inherent property of real-world objects is that they only exist as meaningful entities over In: Proc. CERN School of Computing, Egmond aan Zee, The Netherlands, 8--21 September, 1996. certain ranges of scale. A simple example is the concept of a branch of a tree, which makes sense only at a scale from, say, a few centimeters to at most a few meters, It is meaningless to discuss the tree concept at the nanometer or kilometer level. At those scales, it is more relevant to talk about the molecules that form the leaves of the tree, and the forest in which the tree grows, respectively. This fact, that objects in the world appear in different ways depending on the scale of ..

Separable time-causal and time-recursive spatio-temporal receptive fields

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about parameterizing the intermediate temporal scale levels, analysing the resulting temporal dynamics and transferring the theory to a discrete implementation in terms of recursive filters over time.Comment: 12 pages, 2 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1404.203

Provably scale-covariant networks from oriented quasi quadrature measures in cascade

This article presents a continuous model for hierarchical networks based on a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed and it is shown that the resulting representation allows for provable scale and rotation covariance. A prototype application to texture analysis is developed and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.Comment: 12 pages, 3 figures, 1 tabl

Affine Subspace Representation for Feature Description

This paper proposes a novel Affine Subspace Representation (ASR) descriptor to deal with affine distortions induced by viewpoint changes. Unlike the traditional local descriptors such as SIFT, ASR inherently encodes local information of multi-view patches, making it robust to affine distortions while maintaining a high discriminative ability. To this end, PCA is used to represent affine-warped patches as PCA-patch vectors for its compactness and efficiency. Then according to the subspace assumption, which implies that the PCA-patch vectors of various affine-warped patches of the same keypoint can be represented by a low-dimensional linear subspace, the ASR descriptor is obtained by using a simple subspace-to-point mapping. Such a linear subspace representation could accurately capture the underlying information of a keypoint (local structure) under multiple views without sacrificing its distinctiveness. To accelerate the computation of ASR descriptor, a fast approximate algorithm is proposed by moving the most computational part (ie, warp patch under various affine transformations) to an offline training stage. Experimental results show that ASR is not only better than the state-of-the-art descriptors under various image transformations, but also performs well without a dedicated affine invariant detector when dealing with viewpoint changes.Comment: To Appear in the 2014 European Conference on Computer Visio

Effect of Feeding Intensity on Metabolic Maintenance, Reproduction and Welfare in Blue Fox (Vulpes lagopus)

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Extraction of Airways with Probabilistic State-space Models and Bayesian Smoothing

Segmenting tree structures is common in several image processing applications. In medical image analysis, reliable segmentations of airways, vessels, neurons and other tree structures can enable important clinical applications. We present a framework for tracking tree structures comprising of elongated branches using probabilistic state-space models and Bayesian smoothing. Unlike most existing methods that proceed with sequential tracking of branches, we present an exploratory method, that is less sensitive to local anomalies in the data due to acquisition noise and/or interfering structures. The evolution of individual branches is modelled using a process model and the observed data is incorporated into the update step of the Bayesian smoother using a measurement model that is based on a multi-scale blob detector. Bayesian smoothing is performed using the RTS (Rauch-Tung-Striebel) smoother, which provides Gaussian density estimates of branch states at each tracking step. We select likely branch seed points automatically based on the response of the blob detection and track from all such seed points using the RTS smoother. We use covariance of the marginal posterior density estimated for each branch to discriminate false positive and true positive branches. The method is evaluated on 3D chest CT scans to track airways. We show that the presented method results in additional branches compared to a baseline method based on region growing on probability images.Comment: 10 pages. Pre-print of the paper accepted at Workshop on Graphs in Biomedical Image Analysis. MICCAI 2017. Quebec Cit

Segmentation of Loops from Coronal EUV Images

We present a procedure which extracts bright loop features from solar EUV images. In terms of image intensities, these features are elongated ridge-like intensity maxima. To discriminate the maxima, we need information about the spatial derivatives of the image intensity. Commonly, the derivative estimates are strongly affected by image noise. We therefore use a regularized estimation of the derivative which is then used to interpolate a discrete vector field of ridge points ``ridgels'' which are positioned on the ridge center and have the intrinsic orientation of the local ridge direction. A scheme is proposed to connect ridgels to smooth, spline-represented curves which fit the observed loops. Finally, a half-automated user interface allows one to merge or split, eliminate or select loop fits obtained form the above procedure. In this paper we apply our tool to one of the first EUV images observed by the SECCHI instrument onboard the recently launched STEREO spacecraft. We compare the extracted loops with projected field lines computed from almost-simultaneously-taken magnetograms measured by the SOHO/MDI Doppler imager. The field lines were calculated using a linear force-free field model. This comparison allows one to verify faint and spurious loop connections produced by our segmentation tool and it also helps to prove the quality of the magnetic-field model where well-identified loop structures comply with field-line projections. We also discuss further potential applications of our tool such as loop oscillations and stereoscopy.Comment: 13 pages, 9 figures, Solar Physics, online firs

Topological analysis of the vasculature of angiopoietin-expressing tumours through scale-space tracing

This work describes the topological analysis of the vasculature of tumours. The analysis is performed with a scale-space technique, which traces the centrelines of vessels as topological ridges of the image intensities and then obtains a series of measurements, which are used to compare the vasculatures. Besides the measurements directly associated with the centrelines, the scales obtained allow the estimation of width andthusareacoveredwithvessels. Tumours of SW1222 human colorectal carcinoma xenografts were observed when growing in dorsal skin-fold window chambers in mice. Three variants of the tumours expressing either endogenous levels of angiopoietins (WT) or over-expressing either angiopoietin-1 (Ang-1) or angiopoietin-2 (Ang-2) were assessed with/without vascular targeted therapy. The scale-space technique was able to discriminate between the vasculatures of the three different tumour types prior to treatment. Results also suggested that over-expression of Ang-2 was associated with susceptibility of the tumour vasculature to the vascular disrupting agent, combretastatin A4 phosphate (CA4P). Substantiation of this finding would point to the potential of tumour Ang-2 expression as a predictive bio-marker for response to CA4P