An efficient kernel product for automatic differentiation libraries, with applications to measure transport

Duration: 41 mins 42 secs

Share this media item:

Embed this media item:

<iframe width="_width_" height="_height_" src="https://sms.cam.ac.uk/media/2606745/embed" frameborder="0" scrolling="no" allowfullscreen></iframe>

Choose size:

About this item

Available Formats

About this item

Description:	Feydy, J Monday 13th November 2017 - 11:00 to 11:30


Created:	2017-11-14 09:01
Collection:	Growth form and self-organisation
Publisher:	Isaac Newton Institute
Copyright:	Feydy, J
Language:	eng (English)


Abstract:	Authors : Benjamin Charlier, Jean Feydy, Joan Alexis Glaunès and Alain Trouvé This paper presents a memory-efficient implementation of the kernel matrix-vector product, which is suitable for use with automatic differentiation libraries -- in our case, PyTorch. This piece of software alleviates the major bottleneck of autodiff libraries as far as diffeomorphic image registration is concerned: symbolic python code can now scale up to large point clouds and shapes (100,000+ vertices). To showcase the value of automatic differentiation to the LDDMM community, we introduce the "normalized Hamiltonian" setting and show that it corresponds to a spatially regularized optimal transport of mass distributions: made tractable by autodiff libraries, the kernel normalization trick turns an extrinsic image deformation routine into an intrinsic measure transportation program.

Abstract:

Authors : Benjamin Charlier, Jean Feydy, Joan Alexis Glaunès and Alain Trouvé This paper presents a memory-efficient implementation of the kernel matrix-vector product, which is suitable for use with automatic differentiation libraries -- in our case, PyTorch. This piece of software alleviates the major bottleneck of autodiff libraries as far as diffeomorphic image registration is concerned: symbolic python code can now scale up to large point clouds and shapes (100,000+ vertices). To showcase the value of automatic differentiation to the LDDMM community, we introduce the "normalized Hamiltonian" setting and show that it corresponds to a spatially regularized optimal transport of mass distributions: made tractable by autodiff libraries, the kernel normalization trick turns an extrinsic image deformation routine into an intrinsic measure transportation program.

Available Formats

Format	Quality	Bitrate	Size
MPEG-4 Video	640x360	1.94 Mbits/sec	607.15 MB	View	Download
WebM	640x360	640.9 kbits/sec	195.75 MB	View	Download
iPod Video	480x270	522.28 kbits/sec	159.52 MB	View	Download
MP3	44100 Hz	249.78 kbits/sec	76.35 MB	Listen	Download
Auto *	(Allows browser to choose a format it supports)