2,018 research outputs found
Multiscale medial shape-based analysis of image objects
pre-printMedial representation of a three-dimensional (3-D) object or an ensemble of 3-D objects involves capturing the object interior as a locus of medial atoms, each atom being two vectors of equal length joined at the tail at the medial point. Medial representation has a variety of beneficial properties, among the most important of which are 1) its inherent geometry, provides an object-intrinsic coordinate system and thus provides correspondence between instances of the object in and near the object(s); 2) it captures the object interior and is, thus, very suitable for deformation; and 3) it provides the basis for an intuitive object-based multiscale sequence leading to efficiency of segmentation algorithms and trainability of statistical characterizations with limited training sets. As a result of these properties, medial representation is particularly suitable for the following image analysis tasks; how each operates will be described and will be illustrated by results: 1) segmentation of objects and object complexes via deformable models; 2) segmentation of tubular trees, e.g., of blood vessels, by following height ridges of measures of fit of medial atoms to target images; 3) object-based image registration via medial loci of such blood vessel trees; 4) statistical characterization of shape differences between control and pathological classes of structures. These analysis tasks are made possible by a new form of medial representation called m-reps, which is described
Characterizing Width Uniformity by Wave Propagation
This work describes a novel image analysis approach to characterize the
uniformity of objects in agglomerates by using the propagation of normal
wavefronts. The problem of width uniformity is discussed and its importance for
the characterization of composite structures normally found in physics and
biology highlighted. The methodology involves identifying each cluster (i.e.
connected component) of interest, which can correspond to objects or voids, and
estimating the respective medial axes by using a recently proposed wavefront
propagation approach, which is briefly reviewed. The distance values along such
axes are identified and their mean and standard deviation values obtained. As
illustrated with respect to synthetic and real objects (in vitro cultures of
neuronal cells), the combined use of these two features provide a powerful
description of the uniformity of the separation between the objects, presenting
potential for several applications in material sciences and biology.Comment: 14 pages, 23 figures, 1 table, 1 referenc
A Scale-Space Medialness Transform Based on Boundary Concordance Voting
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 âside-lobeâ 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
A Framework for Symmetric Part Detection in Cluttered Scenes
The role of symmetry in computer vision has waxed and waned in importance
during the evolution of the field from its earliest days. At first figuring
prominently in support of bottom-up indexing, it fell out of favor as shape
gave way to appearance and recognition gave way to detection. With a strong
prior in the form of a target object, the role of the weaker priors offered by
perceptual grouping was greatly diminished. However, as the field returns to
the problem of recognition from a large database, the bottom-up recovery of the
parts that make up the objects in a cluttered scene is critical for their
recognition. The medial axis community has long exploited the ubiquitous
regularity of symmetry as a basis for the decomposition of a closed contour
into medial parts. However, today's recognition systems are faced with
cluttered scenes, and the assumption that a closed contour exists, i.e. that
figure-ground segmentation has been solved, renders much of the medial axis
community's work inapplicable. In this article, we review a computational
framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009,
2013), that bridges the representation power of the medial axis and the need to
recover and group an object's parts in a cluttered scene. Our framework is
rooted in the idea that a maximally inscribed disc, the building block of a
medial axis, can be modeled as a compact superpixel in the image. We evaluate
the method on images of cluttered scenes.Comment: 10 pages, 8 figure
Multiscale Phenomenology of the Cosmic Web
We analyze the structure and connectivity of the distinct morphologies that
define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF),
we dissect the matter distribution of a cosmological CDM N-body
computer simulation into cluster, filaments and walls. The MMF is ideally
suited to adress both the anisotropic morphological character of filaments and
sheets, as well as the multiscale nature of the hierarchically evolved cosmic
matter distribution. The results of our study may be summarized as follows:
i).- While all morphologies occupy a roughly well defined range in density,
this alone is not sufficient to differentiate between them given their overlap.
Environment defined only in terms of density fails to incorporate the intrinsic
dynamics of each morphology. This plays an important role in both linear and
non linear interactions between haloes. ii).- Most of the mass in the Universe
is concentrated in filaments, narrowly followed by clusters. In terms of
volume, clusters only represent a minute fraction, and filaments not more than
9%. Walls are relatively inconspicous in terms of mass and volume. iii).- On
average, massive clusters are connected to more filaments than low mass
clusters. Clusters with M h have on average
two connecting filaments, while clusters with M
h have on average five connecting filaments. iv).- Density profiles
indicate that the typical width of filaments is 2\Mpch. Walls have less well
defined boundaries with widths between 5-8 Mpc h. In their interior,
filaments have a power-law density profile with slope ,
corresponding to an isothermal density profile.Comment: 28 pages, 22 figures, accepted for publication in MNRAS. For a
high-res version see http://www.astro.rug.nl/~weygaert/webmorph_mmf.pd
Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons
We present a new method for decomposing a 3D voxel shape into disjoint segments using the shapeâs simplified surface-skeleton. The surface skeleton of a shape consists of 2D manifolds inside its volume. Each skeleton point has a maximally inscribed ball that touches the boundary in at least two contact points. A key observation is that the boundaries of the simplified fore- and background skeletons map one-to-one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable properties. Our method segments both noisy shapes and shapes with soft edges which vanish over low-curvature regions. Multiscale segmentations can be obtained by varying the simplification level of the skeleton. We present a voxel-based implementation of our approach and illustrate it on several realistic examples.
Zoom invariant vision of figural shape: The mathematics of cores
Believing that figural zoom invariance and the cross-figural boundary linking implied by medial loci are important aspects of object shape, we present the mathematics of and algorithms for the extraction of medial loci directly from image intensities. The medial loci called cores are defined as generalized maxima in scale space of a form of medial information that is invariant to translation, rotation, and in particular, zoom. These loci are very insensitive to image disturbances, in strong contrast to previously available medial loci, as demonstrated in a companion paper. Core-related geometric properties and image object representations are laid out which, together with the aforementioned insensitivities, allow the core to be used effectively for a variety of image analysis objectives.
Compensated convexity, multiscale medial axis maps and sharp regularity of the squared-distance function
In this paper we introduce a new stable mathematical model for locating and measuring the medial axis of geometric objects, called the quadratic multiscale medial axis map of scale λ, and provide a sharp regularity result for the squared-distance function to any closed nonempty subset K of Rn. Our results exploit properties of the function Clλ (dist2(ă»; K)) obtained by applying the quadratic lower compensated convex transform of parameter λ [K. Zhang, Ann. Inst. H. PoincarÂŽe Anal. Non LinÂŽeaire, 25 (2008), pp. 743â771] to dist2(ă»; K), the Euclidean squared-distance function to K. Using a quantitative estimate for the tight approximation of dist2(ă»; K) by Clλ (dist2(ă»; K)), we prove the C1,1-regularity of dist2(ă»; K) outside a neighborhood of the closure of the medial axis MK of K, which can be viewed as a weak Lusin-type theorem for dist2(ă»; K), and give an asymptotic expansion formula for Clλ (dist2(ă»; K)) in terms of the scaled squared-distance transform to the set and to the convex hull of the set of points that realize the minimum distance to K. The multiscale medial axis map, denoted by Mλ(ă»; K), is a family of nonnegative functions, parametrized by λ > 0, whose limit as λââexists and is called the multiscale medial axis landscape map, Mâ(ă»; K). We show that Mâ(ă»; K) is strictly positive on the medial axis MK and zero elsewhere. We give conditions that ensure Mλ(ă»; K) keeps a constant height along the parts of MK generated by two-point subsets with the value of the height dependent on the scale of the distance between the generating points, thus providing a hierarchy of heights (hence, the word âmultiscaleâ) between different parts of MK that enables subsets of MK to be selected by simple thresholding. Asymptotically, further understanding of the multiscale effect is provided by our exact representation of Mâ(ă»; K). Moreover, given a compact subset K of Rn, while it is well known that MK is not Hausdorff stable, we prove that in contrast, Mλ(ă»; K) is stable under the Hausdorff distance, and deduce implications for the localization of the stable parts of MK. Explicitly calculated prototype examples of medial axis maps are also presented and used to illustrate the theoretical findings
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