Shape Manipulation
Shape-from-Operator: Recovering Shapes from Intrinsic Operators
Davide Boscaini,
Davide Eynard,
Drosos Kourounis,
Michael M. Bronstein,
Davide Boscaini
Università della Svizzera Italiana (USI), Lugano, Switzerland
Search for more papers by this authorDavide Eynard
Università della Svizzera Italiana (USI), Lugano, Switzerland
Search for more papers by this authorDrosos Kourounis
Università della Svizzera Italiana (USI), Lugano, Switzerland
Search for more papers by this authorMichael M. Bronstein
Università della Svizzera Italiana (USI), Lugano, Switzerland
Search for more papers by this authorDavide Boscaini,
Davide Eynard,
Drosos Kourounis,
Michael M. Bronstein,
Davide Boscaini
Università della Svizzera Italiana (USI), Lugano, Switzerland
Search for more papers by this authorDavide Eynard
Università della Svizzera Italiana (USI), Lugano, Switzerland
Search for more papers by this authorDrosos Kourounis
Università della Svizzera Italiana (USI), Lugano, Switzerland
Search for more papers by this authorMichael M. Bronstein
Università della Svizzera Italiana (USI), Lugano, Switzerland
Search for more papers by this authorAbstract
We formulate the problem of shape-from-operator (SfO), recovering an embedding of a mesh from intrinsic operators defined through the discrete metric (edge lengths). Particularly interesting instances of our SfO problem include: shape-from-Laplacian, allowing to transfer style between shapes; shape-from-difference operator, used to synthesize shape analogies; and shape-from-eigenvectors, allowing to generate ‘intrinsic averages’ of shape collections. Numerically, we approach the SfO problem by splitting it into two optimization sub-problems: metric-from-operator (reconstruction of the discrete metric from the intrinsic operator) and embedding-from-metric (finding a shape embedding that would realize a given metric, a setting of the multidimensional scaling problem). We study numerical properties of our problem, exemplify it on several applications, and discuss its imitations.
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