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Now showing 1 - 6 of 6
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    Attention And Positional Encoding Are (Almost) All You Need For Shape Matching
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Raganato, Alessandro; Pasi, Gabriella; Melzi, Simone; Memari, Pooran; Solomon, Justin
    The fast development of novel approaches derived from the Transformers architecture has led to outstanding performance in different scenarios, from Natural Language Processing to Computer Vision. Recently, they achieved impressive results even in the challenging task of non-rigid shape matching. However, little is known about the capability of the Transformer-encoder architecture for the shape matching task, and its performances still remained largely unexplored. In this paper, we step back and investigate the contribution made by the Transformer-encoder architecture compared to its more recent alternatives, focusing on why and how it works on this specific task. Thanks to the versatility of our implementation, we can harness the bi-directional structure of the correspondence problem, making it more interpretable. Furthermore, we prove that positional encodings are essential for processing unordered point clouds. Through a comprehensive set of experiments, we find that attention and positional encoding are (almost) all you need for shape matching. The simple Transformer-encoder architecture, coupled with relative position encoding in the attention mechanism, is able to obtain strong improvements, reaching the current state-of-the-art.
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    3D Keypoint Estimation Using Implicit Representation Learning
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Zhu, Xiangyu; Du, Dong; Huang, Haibin; Ma, Chongyang; Han, Xiaoguang; Memari, Pooran; Solomon, Justin
    In this paper, we tackle the challenging problem of 3D keypoint estimation of general objects using a novel implicit representation. Previous works have demonstrated promising results for keypoint prediction through direct coordinate regression or heatmap-based inference. However, these methods are commonly studied for specific subjects, such as human bodies and faces, which possess fixed keypoint structures. They also suffer in several practical scenarios where explicit or complete geometry is not given, including images and partial point clouds. Inspired by the recent success of advanced implicit representation in reconstruction tasks, we explore the idea of using an implicit field to represent keypoints. Specifically, our key idea is employing spheres to represent 3D keypoints, thereby enabling the learnability of the corresponding signed distance field. Explicit keypoints can be extracted subsequently by our algorithm based on the Hough transform. Quantitative and qualitative evaluations also show the superiority of our representation in terms of prediction accuracy.
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    Singularity-Free Frame Fields for Line Drawing Vectorization
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Guțan, Olga; Hegde, Shreya; Berumen, Erick Jimenez; Bessmeltsev, Mikhail; Chien, Edward; Memari, Pooran; Solomon, Justin
    State-of-the-art methods for line drawing vectorization rely on generated frame fields for robust direction disambiguation, with each of the two axes aligning to different intersecting curve tangents around junctions. However, a common source of topological error for such methods are frame field singularities. To remedy this, we introduce the first frame field optimization framework guaranteed to produce singularity-free fields aligned to a line drawing. We first perform a convex solve for a roughly-aligned orthogonal frame field (cross field), and then comb away its internal singularities with an optimal transport–based matching. The resulting topology of the field is strictly maintained with the machinery of discrete trivial connections in a final, non-convex optimization that allows non-orthogonality of the field, improving smoothness and tangent alignment. Our frame fields can serve as a drop-in replacement for frame field optimizations used in previous work, improving the quality of the final vectorizations.
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    HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Ludwig, Ingmar; Tyson, Daniel; Campen, Marcel; Memari, Pooran; Solomon, Justin
    We describe HalfedgeCNN, a collection of modules to build neural networks that operate on triangle meshes. Taking inspiration from the (edge-based) MeshCNN, convolution, pooling, and unpooling layers are consistently defined on the basis of halfedges of the mesh, pairs of oppositely oriented virtual instances of each edge. This provides benefits over alternative definitions on the basis of vertices, edges, or faces. Additional interface layers enable support for feature data associated with such mesh entities in input and output as well. Due to being defined natively on mesh entities and their neighborhoods, lossy resampling or interpolation techniques (to enable the application of operators adopted from image domains) do not need to be employed. The operators have various degrees of freedom that can be exploited to adapt to application-specific needs.
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    Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Lachaud, Jacques-Olivier; Coeurjolly, David; Labart, Céline; Romon, Pascal; Thibert, Boris; Memari, Pooran; Solomon, Justin
    The estimation of differential quantities on oriented point cloud is a classical step for many geometry processing tasks in computer graphics and vision. Even if many solutions exist to estimate such quantities, they usually fail at satisfying both a stable estimation with theoretical guarantee, and the efficiency of the associated algorithm. Relying on the notion of corrected curvature measures [LRT22, LRTC20] designed for surfaces, the method introduced in this paper meets both requirements. Given a point of interest and a few nearest neighbours, our method estimates the whole curvature tensor information by generating random triangles within these neighbours and normalising the corrected curvature measures by the corrected area measure. We provide a stability theorem showing that our pointwise curvatures are accurate and convergent, provided the noise in position and normal information has a variance smaller than the radius of neighbourhood. Experiments and comparisons with the state-of-the-art confirm that our approach is more accurate and much faster than alternatives. The method is fully parallelizable, requires only one nearest neighbour request per point of computation, and is trivial to implement.
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    Variational Pruning of Medial Axes of Planar Shapes
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Rong, Peter; Ju, Tao; Memari, Pooran; Solomon, Justin
    Medial axis (MA) is a classical shape descriptor in graphics and vision. The practical utility of MA, however, is hampered by its sensitivity to boundary noise. To prune unwanted branches from MA, many definitions of significance measures over MA have been proposed. However, pruning MA using these measures often comes at the cost of shrinking desirable MA branches and losing shape features at fine scales. We propose a novel significance measure that addresses these shortcomings. Our measure is derived from a variational pruning process, where the goal is to find a connected subset of MA that includes as many points that are as parallel to the shape boundary as possible. We formulate our measure both in the continuous and discrete settings, and present an efficient algorithm on a discrete MA. We demonstrate on many examples that our measure is not only resistant to boundary noise but also excels over existing measures in preventing MA shrinking and recovering features across scales.