Topological saliency

Doraiswamy, Harish; Shivashankar, Nithin; Natarajan, Vijay; Wang, Yusu

doi:10.1016/j.cag.2013.04.009

Cited by 16 publications

(10 citation statements)

References 39 publications

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“…We use an approach based on topological saliency [ 27 ] to evaluate relative importance of branches. Let the set B = { b 1 , b 2 , …, b n } be the set of branches in the contour tree, t i is the topological feature created at b i , d ( b i , b j ) is the distance between two branches of b i and b j .…”

Section: Methodsmentioning

confidence: 99%

Topology-aware illumination design for volume rendering

et al. 2016

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BackgroundDirect volume rendering is one of flexible and effective approaches to inspect large volumetric data such as medical and biological images. In conventional volume rendering, it is often time consuming to set up a meaningful illumination environment. Moreover, conventional illumination approaches usually assign same values of variables of an illumination model to different structures manually and thus neglect the important illumination variations due to structure differences.ResultsWe introduce a novel illumination design paradigm for volume rendering on the basis of topology to automate illumination parameter definitions meaningfully. The topological features are extracted from the contour tree of an input volumetric data. The automation of illumination design is achieved based on four aspects of attenuation, distance, saliency, and contrast perception. To better distinguish structures and maximize illuminance perception differences of structures, a two-phase topology-aware illuminance perception contrast model is proposed based on the psychological concept of Just-Noticeable-Difference.ConclusionsThe proposed approach allows meaningful and efficient automatic generations of illumination in volume rendering. Our results showed that our approach is more effective in depth and shape depiction, as well as providing higher perceptual differences between structures.

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Section: Methodsmentioning

confidence: 99%

Topology-aware illumination design for volume rendering

et al. 2016

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“…However, such measures do not explicitly reflect persistence, while both the bottleneck distance between persistence diagrams and the distance between merge trees do. Doraiswamy et al 20 with a proposition of a saliency plot that summarizes relative importance of all topological features, and Bubenik 21 proposed the bottleneck distance for persistence landscapes, a topological descriptor that extends persistence diagrams.…”

Section: Scalar Functionsmentioning

confidence: 99%

“…To determine whether an observed behavior also is evident in other relatively simple Fig. 7: The error measure e B for MoC functions with varying numbers of maxima (3,20,50). As expected, more maxima slow the error decrease rate, as it takes more samples to discover all maxima.…”

Section: Sampling Density and Dimensionalitymentioning

confidence: 99%

Measuring the Error in Approximating the Sub-Level Set Topology of Sampled Scalar Data

Beketayev

Yeliussizov

Morozov

et al. 2018

Int. J. Comput. Geom. Appl.

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This paper studies the influence of the definition of neighborhoods and methods used for creating point connectivity on topological analysis of scalar functions. It is assumed that a scalar function is known only at a finite set of points with associated function values. In order to utilize topological approaches to analyze the scalar-valued point set, it is necessary to choose point neighborhoods and, usually, point connectivity to meaningfully determine critical-point behavior for the point set. Two distances are used to measure the difference in topology when different point neighborhoods and means to define connectivity are used: (i) the bottleneck distance for persistence diagrams and (ii) the distance between merge trees. Usually, these distances define how different scalar functions are with respect to their topology. These measures, when properly adapted to point sets coupled with a definition of neighborhood and connectivity, make it possible to understand how topological characteristics depend on connectivity. Noise is another aspect considered. Five types of neighborhoods and connectivity are discussed: (i) the Delaunay triangulation; (ii) the relative neighborhood graph; (iii) the Gabriel graph; (iv) the [Formula: see text]-nearest-neighbor (KNN) neighborhood; and (v) the Vietoris–Rips complex. It is discussed in detail how topological characterizations depend on the chosen connectivity.

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“…4. For each k-th iteration of step 2 and 3, a leaf edge e k that was removed from the tree is generated.…”

Section: Figmentioning

confidence: 99%

“…However, it cannot distinguish individual contours in an isosurface. Topological saliency [4] and volume saliency [6] can be used to find salient areas, but they cannot generate salient surfaces from volume data. A contour tree (CT) is useful for visualization of contours [3].…”

Section: Introductionmentioning

confidence: 99%

Contour Gradient Tree for Automatic Extraction of Salient Object Surfaces from 3D Imaging Data

Sohn

2015

IEICE Trans. Inf. & Syst.

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SUMMARYIsosurface extraction is one of the most popular techniques for visualizing scalar volume data. However, volume data contains infinitely many isosurfaces. Furthermore, a single isosurface might contain many connected components, or contours, with each representing a different object surface. Hence, it is often a tedious and time-consuming manual process to find and extract contours that are interesting to users. This paper describes a novel method for automatically extracting salient contours from volume data. For this purpose, we propose a contour gradient tree (CGT) that contains the information of salient contours and their saliency magnitude. We organize the CGT in a hierarchical way to generate a sequence of contours in saliency order. Our method was applied to various medical datasets. Experimental results show that our method can automatically extract salient contours that represent regions of interest in the data.

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Topological saliency

Cited by 16 publications

References 39 publications

Topology-aware illumination design for volume rendering

Topology-aware illumination design for volume rendering

Measuring the Error in Approximating the Sub-Level Set Topology of Sampled Scalar Data

Contour Gradient Tree for Automatic Extraction of Salient Object Surfaces from 3D Imaging Data

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