Left-invariant evolutions of wavelet transforms on the similitude group

U. Sharma, R. Duits

Research output: Book/ReportReportAcademic

86 Downloads (Pure)


Enhancement of multiple-scale elongated structures in noisy image data is relevant for many biomedical applications but commonly used PDE-based enhancement techniques often fail at crossings in an image. To get an overview of how an image is composed of local multiple-scale elongated structures we construct a multiple scale orientation score, which is a continuous wavelet transform on the similitude group, SIM(2). Our unitary transform maps the space of images onto a reproducing kernel space defined on SIM(2), allowing us to robustly relate Euclidean (and scaling) invariant operators on images to left-invariant operators on multiple-scale orientation scores. Rather than often used wavelet (soft-)thresholding techniques, we employ the group structure in the wavelet domain to arrive at left-invariant evolutions and flows (diffusion), for contextual crossing preserving enhancement of multiple scale elongated structures in noisy images. We present experiments that display benefits of our work compared to recent PDE techniques acting directly on the images and to our previous work on left-invariant diffusions on orientation scores defined on Euclidean motion group.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages43
Publication statusPublished - 2013

Publication series

ISSN (Print)0926-4507

Fingerprint Dive into the research topics of 'Left-invariant evolutions of wavelet transforms on the similitude group'. Together they form a unique fingerprint.

Cite this