{"id":147347,"date":"2008-01-01T00:00:00","date_gmt":"2008-01-01T00:00:00","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/learning-the-2-d-topology-of-images\/"},"modified":"2018-10-16T20:21:53","modified_gmt":"2018-10-17T03:21:53","slug":"learning-the-2-d-topology-of-images","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/learning-the-2-d-topology-of-images\/","title":{"rendered":"Learning the 2-D Topology of Images"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We study the following question: is the two-dimensional structure of images a very strong prior or is it something that can be learned with a few examples of natural images? If someone gave us a learning task involving images for which the two-dimensional topology of pixels was not known, could we discover it automatically and exploit it? For example suppose that the pixels had been permuted in a fixed but unknown way, could we recover the relative two-dimensional location of pixels on images? The surprising result presented here is that not only the answer is yes but that about as few as a thousand images are enough to approximately recover the relative locations of about a thousand pixels. This is achieved using a manifold learning algorithm applied to pixels associated with a measure of distributional similarity between pixel intensities. We compare different topology extraction approaches and show how having the two-dimensional topology can be exploited.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study the following question: is the two-dimensional structure of images a very strong prior or is it something that can be learned with a few examples of natural images? If someone gave us a learning task involving images for which the two-dimensional topology of pixels was not known, could we discover it automatically and [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"NIPS2007","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"NIPS2007","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Yoshua Bengio, Pascal Lamblin, Marc Joliveau , Bal\u00e1zs 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