No Arabic abstract
Stress, edge crossings, and crossing angles play an important role in the quality and readability of graph drawings. Most standard graph drawing algorithms optimize one of these criteria which may lead to layouts that are deficient in other criteria. We introduce an optimization framework, Stress-Plus-X (SPX), that simultaneously optimizes stress together with several other criteria: edge crossings, minimum crossing angle, and upwardness (for directed acyclic graphs). SPX achieves results that are close to the state-of-the-art algorithms that optimize these metrics individually. SPX is flexible and extensible and can optimize a subset or all of these criteria simultaneously. Our experimental analysis shows that our joint optimization approach is successful in drawing graphs with good performance across readability criteria.
We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing.
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic quartic differential with finite trajectories. In this work, a surface quadrilateral layout is alternatively characterized as a special immersion of a cut representation of the surface into the Euclidean plane. We call this a quad layout immersion. This characterization, while posed in smooth topology, naturally generalizes to piecewise-linear representations. As such, it mathematically describes and generalizes integer grid maps, which are common in computer graphics settings. Finally, the utility of the representation is demonstrated by computationally extracting quadrilateral layouts on surfaces of interest.
Force-directed layout methods constitute the most common approach to draw general graphs. Among them, stress minimization produces layouts of comparatively high quality but also imposes comparatively high computational demands. We propose a speed-up method based on the aggregation of terms in the objective function. It is akin to aggregate repulsion from far-away nodes during spring embedding but transfers the idea from the layout space into a preprocessing phase. An initial experimental study informs a method to select representatives, and subsequent more extensive experiments indicate that our method yields better approximations of minimum-stress layouts in less time than related methods.
Given an initial placement of a set of rectangles in the plane, we consider the problem of finding a disjoint placement of the rectangles that minimizes the area of the bounding box and preserves the orthogonal order i.e. maintains the sorted ordering of the rectangle centers along both $x$-axis and $y$-axis with respect to the initial placement. This problem is known as Layout Adjustment for Disjoint Rectangles(LADR). It was known that LADR is $mathbb{NP}$-hard, but only heuristics were known for it. We show that a certain decision version of LADR is $mathbb{APX}$-hard, and give a constant factor approximation for LADR.
Detecting dense landmarks for diverse clothes, as a fundamental technique for clothes analysis, has attracted increasing research attention due to its huge application potential. However, due to the lack of modeling underlying semantic layout constraints among landmarks, prior works often detect ambiguous and structure-inconsistent landmarks of multiple overlapped clothes in one person. In this paper, we propose to seamlessly enforce structural layout relationships among landmarks on the intermediate representations via multiple stacked layout-graph reasoning layers. We define the layout-graph as a hierarchical structure including a root node, body-part nodes (e.g. upper body, lower body), coarse clothes-part nodes (e.g. collar, sleeve) and leaf landmark nodes (e.g. left-collar, right-collar). Each Layout-Graph Reasoning(LGR) layer aims to map feature representations into structural graph nodes via a Map-to-Node module, performs reasoning over structural graph nodes to achieve global layout coherency via a layout-graph reasoning module, and then maps graph nodes back to enhance feature representations via a Node-to-Map module. The layout-graph reasoning module integrates a graph clustering operation to generate representations of intermediate nodes (bottom-up inference) and then a graph deconvolution operation (top-down inference) over the whole graph. Extensive experiments on two public fashion landmark datasets demonstrate the superiority of our model. Furthermore, to advance the fine-grained fashion landmark research for supporting more comprehensive clothes generation and attribute recognition, we contribute the first Fine-grained Fashion Landmark Dataset (FFLD) containing 200k images annotated with at most 32 key-points for 13 clothes types.