This paper presents a method for retinal vasculature extraction based on biologically inspired multi-orientation analysis. We apply multi-orientation analysis via so-called invertible orientation scores, modeling the cortical columns in the visual system of higher mammals. This allows us to generically deal with many hitherto complex problems inherent to vessel tracking, such as crossings, bifurcations, parallel vessels, vessels of varying widths and vessels with high curvature. Our approach applies tracking in invertible orientation scores via a novel geometrical principle for curve optimization in the Euclidean motion group SE(2). The method runs fully automatically and provides a detailed model of the retinal vasculature, which is crucial as a sound basis for further quantitative analysis of the retina, especially in screening applications.
£ he xetherlnds yrgniztion for ienti eserh is grtefully knowledged for nnil supportF I P R. Duits, M. Felsberg, G.H. Granlund , B.M. ter Haar Romeny Abstract snspired y the erly visul system of mny mmmlins we onsider the onstrution ofE nd reonstrution fromE n orienttion sore U f X R P ¢ S I 3 C s lol orienttion representtion of n imgeD f X R P 3 RF he mpping f U 3 U f is wvelet trnsform orresponding to reduile representtion of the iuliden motion group onto L P @R P A nd oriented wvelet P L P @R P AF his wvelet trnsform is speil se of reently developed generliztion of the stndrd wvelet theory nd hs the prtil dvntge over the usul wvelet pprohes in imge nlysis @onstruted y irreduile representtions of the similitude groupA tht it llows stle reonstrution from one @single sleA orienttion soreF ine our wvelet trnsform is unitry mpping with stle inverseD we diretly relte opertions on orienttion sores to opertions on imges in roust mnnerF purthermoreD y geometril exmintion of the iuliden motion group G a R P o TD whih is the domin of our orienttion soresD we dedue tht n opertor¨on orienE ttion sores must e left invrint to ensure tht the orresponding opertor I ¨ on imges is iuliden invrintF es n exmple we onsider ll liner seond order left invrint evolutions on orienttion sores orresponding to stohsti proesses on GF es n pplition we detet elongted strutures in @medilA imges nd utomtilly lose the gps etween themF pinllyD we onsider roust orienttion estimtes y mens of hnnel representtionsD where we omine roust orienttion estimtion nd lerning of wvelets resulting in n utoEssoitive proessing of orienttion feturesF rere liner verging of the hnnel repE resenttion is equivlent to roust orienttion estimtion nd n dpttion of the wvelet to the sttistis of the onsidered imge lss leds to n utoEssoitive ehvior of the systemF
Abstract. We consider alternative scale space representations beyond the well-established Gaussian case that satisfy all "reasonable" axioms. One of these turns out to be subject to a first order pseudo partial differential equation equivalent to the Laplace equation on the upper half planeWe investigate this so-called Poisson scale space and show that it is indeed a viable alternative to Gaussian scale space. Poisson and Gaussian scale space are related via a one-parameter class of operationally well-defined intermediate representations generated by a fractional power of (minus) the spatial Laplace operator.
A representation of local image structure is proposed which takes into account both the image's spatial structure at a given location, as well as its "deep structure", that is, its local behaviour as a function of scale or resolution (scale-space). This is of interest for several low-level image tasks. The proposed basis of scale-space, for example, enables a precise local study of interactions of neighbouring image intensities in the course of the blurring process. It also provides an extrapolation scheme for local image data, obtained at a given spatial location and resolution, to a finite scale-space neighbourhood. This is especially useful for the determination of sampling rates and for interpolation algorithms in a multilocal context. Another, particularly straightforward application is image enhancement or deblurring, which is an instance of data extrapolation in the high-resolution direction.A potentially interesting feature of the proposed local image parametrisation is that it captures a trade-off between spatial and scale extrapolations from a given interior point that do not exceed a given tolerance. This trade-off suggests the possibility of a fairly coarse scale sampling at the expense of a dense spatial sampling (large relative spatial overlap of scale-space kernels).The central concept developed in this paper is an equivalence class called the multiscale local jet, which is a hierarchical, local characterisation of the image in a full scale-space neighbourhood. For this local jet, a basis of fundamental polynomials is constructed that captures the scale-space paradigm at the local level up to any given order.
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