61,050 research outputs found
Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds
The Euclidean scattering transform was introduced nearly a decade ago to
improve the mathematical understanding of convolutional neural networks.
Inspired by recent interest in geometric deep learning, which aims to
generalize convolutional neural networks to manifold and graph-structured
domains, we define a geometric scattering transform on manifolds. Similar to
the Euclidean scattering transform, the geometric scattering transform is based
on a cascade of wavelet filters and pointwise nonlinearities. It is invariant
to local isometries and stable to certain types of diffeomorphisms. Empirical
results demonstrate its utility on several geometric learning tasks. Our
results generalize the deformation stability and local translation invariance
of Euclidean scattering, and demonstrate the importance of linking the used
filter structures to the underlying geometry of the data.Comment: 35 pages; 3 figures; 2 tables; v3: Revisions based on reviewer
comment
A Learning Framework for Morphological Operators using Counter-Harmonic Mean
We present a novel framework for learning morphological operators using
counter-harmonic mean. It combines concepts from morphology and convolutional
neural networks. A thorough experimental validation analyzes basic
morphological operators dilation and erosion, opening and closing, as well as
the much more complex top-hat transform, for which we report a real-world
application from the steel industry. Using online learning and stochastic
gradient descent, our system learns both the structuring element and the
composition of operators. It scales well to large datasets and online settings.Comment: Submitted to ISMM'1
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