{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/time-causal-and-time-recursive-spatio","title":"Time-causal and time-recursive spatio-temporal receptive fields","arxiv_id":"1504.02648","date":"2015-04-10","proceeding":null,"authors":["Tony Lindeberg"],"abstract":"We present an improved model and theory for time-causal and time-recursive\nspatio-temporal receptive fields, based on a combination of Gaussian receptive\nfields over the spatial domain and first-order integrators or equivalently\ntruncated exponential filters coupled in cascade over the temporal domain.\n  Compared to previous spatio-temporal scale-space formulations in terms of\nnon-enhancement of local extrema or scale invariance, these receptive fields\nare based on different scale-space axiomatics over time by ensuring\nnon-creation of new local extrema or zero-crossings with increasing temporal\nscale. Specifically, extensions are presented about (i) parameterizing the\nintermediate temporal scale levels, (ii) analysing the resulting temporal\ndynamics, (iii) transferring the theory to a discrete implementation, (iv)\ncomputing scale-normalized spatio-temporal derivative expressions for\nspatio-temporal feature detection and (v) computational modelling of receptive\nfields in the lateral geniculate nucleus (LGN) and the primary visual cortex\n(V1) in biological vision.\n  We show that by distributing the intermediate temporal scale levels according\nto a logarithmic distribution, we obtain much faster temporal response\nproperties (shorter temporal delays) compared to a uniform distribution.\nSpecifically, these kernels converge very rapidly to a limit kernel possessing\ntrue self-similar scale-invariant properties over temporal scales, thereby\nallowing for true scale invariance over variations in the temporal scale,\nalthough the underlying temporal scale-space representation is based on a\ndiscretized temporal scale parameter.\n  We show how scale-normalized temporal derivatives can be defined for these\ntime-causal scale-space kernels and how the composed theory can be used for\ncomputing basic types of scale-normalized spatio-temporal derivative\nexpressions in a computationally efficient manner.","url_abs":"http://arxiv.org/abs/1504.02648v2","url_pdf":"http://arxiv.org/pdf/1504.02648v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[],"methods":[{"method_slug":"timecauslimitkernel","method_name":"timecauslimitkernel"}],"datasets_introduced":[],"methods_introduced":[{"slug":"timecauslimitkernel","name":"timecauslimitkernel","full_name":"time-causal limit kernel"}],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}