Geometric and Semantic Structures for Two- and Three-Dimensional Shape Understanding

二维和三维形状理解的几何和语义结构

• 批准号: 1953052
• 负责人: Kathryn Leonard
• 金额: $ 16万
• 依托单位: Occidental College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-06-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1953052&HistoricalAwards=false
• 关键词: Geometric; Semantic; Structures; Two; Three

True computer vision will provide end-to-end image analysis, where images are decomposed into objects of interest, those objects are decomposed into parts, and the parts and objects are recognized. Performing integrated tasks with an image, such as shape generation, animation, editing, or partial matching, requires structure-aware shape processing. A full shape structure consists of a decomposition into parts, an understanding of which parts are more significant than others, and an ability to measure similarity of parts moving toward recognition. A pipeline that takes as input two- or three-dimensional images, performs accurate segmentation to determine shapes of interest, extracts a shape structure, then recognizes the parts and the shapes would represent a fundamental step forward in artificial vision. The task is challenging because human visual perception does not follow computational rules. For example, two shapes can both be similar to a third shape without being similar to each other. For another, our understanding of meaning of shapes adds a semantic level to our geometric perception: if someone is seated on an object, we classify that object as a chair regardless of its shape. Any useful shape analysis must explicitly model the interplay between semantics and geometric shape. This project aims to develop the foundational theory of shape structure and provide robust implementations of the resulting techniques while maintaining the connection to human semantic perception through benchmarking to user studies.The Blum medial axis gives a skeletal decomposition of a closed region in Euclidean space. For spatial dimensions 2 and 3, these regions can be interpreted as 2D and 3D shapes, with the skeletal model providing a lower-dimensional representation of the shape. The skeleton, a Whitney stratified set, is a deformation retract of the shape boundary that captures complete geometric information about the boundary of the shape. This project will introduce functions on the medial axis that encode shape geometry in a way that allows for the determination of a parts decomposition and hierarchy within a shape, as well as similarity between parts, for shapes of any finite genus. Based on that analysis, the research will develop formal measures of shape complexity and benchmark results through human perception studies. Finally, the project aims to connect the new shape structure characterization to current approaches using neural networks for image understanding by developing network architectures that learn the geometry of a shape skeleton from its natural or binary image representation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

真正的计算机视觉将提供端到端的图像分析，其中图像被分解为感兴趣的对象，这些对象被分解为部分，并识别零件和对象。用图像执行集成的任务，例如形状生成，动画，编辑或部分匹配，需要结构感知的形状处理。完整的形状结构包括分解成各个部分，了解哪些部分比其他部件更重要，并且能够测量向识别的零件相似性的能力。将作为输入二维图像或三维图像的管道执行精确的分割以确定感兴趣的形状，提取形状结构，然后识别零件，形状和形状将代表人造视觉中的基本步骤。该任务具有挑战性，因为人类视觉感知不遵循计算规则。例如，两个形状都可以类似于第三形状，而彼此相似。另一方面，我们对形状含义的理解为我们的几何感知增添了语义水平：如果某人坐在对象上，我们将该对象分为椅子，无论其形状如何。任何有用的形状分析都必须明确模拟语义和几何形状之间的相互作用。该项目旨在发展形状结构的基础理论，并通过基准与用户研究进行基准保持与人类语义感知的联系，从而提供强大的实现。蓝光内侧轴使欧几里得空间中封闭区域的骨骼分解。对于空间尺寸2和3，这些区域可以解释为2D和3D形状，骨骼模型提供了形状较低维的表示。骨骼是惠特尼分层的集合，是形状边界的变形缩回，可捕获有关形状边界的完整几何信息。该项目将在内侧轴上引入函数，该轴以某种方式编码形状几何形状，该几何形状允许确定零件分解和形状内的零件分解和层次结构，以及零件之间的相似性，用于任何有限属的形状。基于该分析，该研究将通过人类感知研究制定形状复杂性和基准结果的正式度量。最后，该项目旨在通过开发网络体系结构从其自然或二进制图像表示形式的网络体系结构来将新形状结构表征与当前方法联系起来，以了解形状骨架的几何形状。该奖项反映了NSF的法定任务，并被认为是通过该基金会的知识分子的智力和广泛影响来评估的，并被视为值得通过评估的支持。

项目成果

Semi-supervised Nonnegative Matrix Factorization for Document Classification

• DOI: 10.1109/ieeeconf53345.2021.9723109
• 发表时间: 2021-10
• 期刊: 2021 55th Asilomar Conference on Signals, Systems, and Computers
• 作者: Jamie Haddock;Lara Kassab;Sixian Li;Alona Kryshchenko;Rachel Grotheer;Elena Sizikova;Chuntian Wang;Thomas Merkh;R. W. M. A. Madushani;Miju Ahn;D. Needell;Kathryn Leonard