The Shape of an Image – A Study of Mapper on Images

We study the topological construction called Mapper in the context of simply connected domains, in particular on images. The Mapper construction can be considered as a generalization for contour, split, and joint trees on simply connected domains. A contour tree on an image domain assumes the height function to be a piecewise linear Morse function. This is a rather restrictive class of functions and does not allow us to explore the topology for most real world images. The Mapper construction avoids this limitation by assuming only continuity on the height function allowing this construction to robustly deal with a significant larger set of images. We provide a customized construction for Mapper on images, give a fast algorithm to compute it, and show how to simplify the Mapper structure in this case. Finally, we provide a simple procedure that guarantees the equivalence of Mapper to contour, join, and split trees on a simply connected domain.

The Shape of an Image: A Study of Mapper on Images
Alejandro Robles, Mustafa Hajij, and Paul Rosen
International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP) 2018

Conferences and Journals

Visualization

March 31 – IEEE VAST/InfoVis/SciVis

April (odd numbered years) – TopoInVis

Late September – IEEE Pacific Visualization

Early December – EG EuroVis

Rolling – IEEE Transactions on Visualization and Computer Graphics (TVCG)

IEEE Vis paper list since 1990 and acceptance rates

late April – IEEE WORKING CONFERENCE ON SOFTWARE VISUALIZATION (VISSOFT 2019)

Graphics/AR/VR

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Virtual Reality Software and Technology (VRST)

Geometry

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Computer Aided Design

January – CAD Conference and Exhibition

Rolling – Computer Aided Design and Applications

A hybrid solution to parallel calculation of augmented join trees of scalar fields in any dimension

Scalar fields are used to describe a variety of data from photographs, to laser scans, to x-ray, CT or MRI scans of machine parts and are invaluable for a variety of tasks, such as fatigue detection in parts. Analyzing scalar fields can be quite challenging due to their size, complexity, and the need to understand both local and global details in context. Join trees are a data structure used to capture the geometric properties of scalar fields, including local minima, local maxima, and saddle points. Unfortunately, computing these trees is expensive, and their incremental construction makes parallel computation nontrivial. We introduce an approach that combines three strategies, pruning, spatial-domain parallelization, and value-domain parallelization, to parallelize join tree construction using OpenCL. The resulting implementation shows a significant speedup, making computation of trees on large data practical on even modest commodity hardware.

A hybrid solution to parallel calculation of augmented join trees of scalar fields in any dimension
P Rosen, J Tu, LA Piegl
Computer-Aided Design and Applications 15 (4), 610-618