{"url":"/method/timecauslimitkernel","slug":"timecauslimitkernel","name":"timecauslimitkernel","full_name":"time-causal limit kernel","full_name_withheld":false,"description_markdown":"The time-causal limit kernel is a temporal smoothing kernel that is (i) time-causal, (ii) time-recursive and (iii) obeys temporal scale covariance. This kernel constitutes the limit case of coupling an infinite number of truncated exponential kernels in cascade, with specifically chosen time constants to obtain temporal scale covariance. For practical purposes, the infinite convolution operation can often be well approximated by a moderate number (4-8) truncated exponential kernels coupled in cascade. The discrete implementation can, in turn, be performed by a set of first-order recursive filters coupled in cascade.","description_state":"present","introduced_year":null,"introduced_by":{"title":"Time-causal and time-recursive spatio-temporal receptive fields","paper":"/paper/time-causal-and-time-recursive-spatio","first_author":"Tony Lindeberg","n_authors":1,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/time-causal-and-time-recursive-spatio"},"source":{"url":"http://arxiv.org/abs/1504.02648v2","title":"Time-causal and time-recursive spatio-temporal receptive fields","url_on_a_paper_host":true},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"Sequential","area_id":"sequential","collection":"Multi-scale analysis","url":"/methods/category/multi-scale-analysis","pwc_aliases":[]}],"n_papers_tagged":3,"archive_num_papers":3,"papers_newest_first":[{"paper":"/paper/a-time-causal-and-time-recursive-analogue-of","title":"A time-causal and time-recursive analogue of the Gabor transform","date":"2023-08-28","arxiv_id":"2308.14512","n_code_links":0,"syntology":null},{"paper":"/paper/a-time-causal-and-time-recursive-scale","title":"A time-causal and time-recursive scale-covariant scale-space representation of temporal signals and past time","date":"2022-02-18","arxiv_id":"2202.09209","n_code_links":1,"syntology":null},{"paper":"/paper/time-causal-and-time-recursive-spatio","title":"Time-causal and time-recursive spatio-temporal receptive fields","date":"2015-04-10","arxiv_id":"1504.02648","n_code_links":0,"syntology":null}],"papers_shown":3,"tasks":[],"tasks_shown":0,"n_tasks":0,"usage_by_year":[{"year":"2015","papers":1},{"year":"2022","papers":1},{"year":"2023","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/timecauslimitkernel"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}