Adjoint Map Representation for Shape Analysis and Matching
Adjoint Map Representation for Shape Analysis and Matching
复制标题
用于形状分析和匹配的伴随图表示
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
M. Ovsjanikov
中科院分区：
文献类型：
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作者：
Ruqi Huang;M. Ovsjanikov
In this paper, we propose to consider the adjoint operators of functional maps, and demonstrate their utility in several tasks in geometry processing. Unlike a functional map, which represents a correspondence simply using the pull‐back of function values, the adjoint operator reflects both the map and its distortion with respect to given inner products. We argue that this property of adjoint operators and especially their relation to the map inverse under the choice of different inner products, can be useful in applications including bi‐directional shape matching, shape exploration, and pointwise map recovery among others. In particular, in this paper, we show that the adjoint operators can be used within the cycle‐consistency framework to encode and reveal the presence or lack of consistency between distortions in a collection, in a way that is complementary to the previously used purely map‐based consistency measures. We also show how the adjoint can be used for matching pairs of shapes, by accounting for maps in both directions, can help in recovering point‐to‐point maps from their functional counterparts, and describe how it can shed light on the role of functional basis selection.
DOI：
10.1145/2729972
发表时间：
2015-05
期刊：
ACM Transactions on Graphics (TOG)
影响因子：
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作者：
C. V. Tycowicz;Christian Schulz;H. Seidel;K. Hildebrandt
通讯作者：
C. V. Tycowicz;Christian Schulz;H. Seidel;K. Hildebrandt