{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:27:57Z","timestamp":1760243277283,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2014,6,17]],"date-time":"2014-06-17T00:00:00Z","timestamp":1402963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Heavy rain deteriorates the video quality of outdoor imaging equipments. In order to improve video clearness, image-based and sensor-based methods are adopted for rain detection. In earlier literature, image-based detection methods fall into spatio-based and temporal-based categories. In this paper, we propose a new image-based method by exploring spatio-temporal united constraints in a Bayesian framework. In our framework, rain temporal motion is assumed to be Pathological Motion (PM), which is more suitable to time-varying character of rain steaks. Temporal displaced frame discontinuity and spatial Gaussian mixture model are utilized in the whole framework. Iterated expectation maximization solving method is taken for Gaussian parameters estimation. Pixels state estimation is finished by an iterated optimization method in Bayesian probability formulation. The experimental results highlight the advantage of our method in rain detection.<\/jats:p>","DOI":"10.3390\/e16063302","type":"journal-article","created":{"date-parts":[[2014,6,17]],"date-time":"2014-06-17T10:57:13Z","timestamp":1403002633000},"page":"3302-3314","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Bayesian Probabilistic Framework for Rain Detection"],"prefix":"10.3390","volume":"16","author":[{"given":"Chen","family":"Yao","sequence":"first","affiliation":[{"name":"The Third Research Institute of Ministry of Public Security, No. 76 Yueyang Road, Shanghai, China"},{"name":"Shanghai Key Laboratory of Digital Media Processing and Transmission, Shanghai, China"}]},{"given":"Ci","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai, China"}]},{"given":"Lijuan","family":"Hong","sequence":"additional","affiliation":[{"name":"The Third Research Institute of Ministry of Public Security, No. 76 Yueyang Road, Shanghai, China"}]},{"given":"Yunfei","family":"Cheng","sequence":"additional","affiliation":[{"name":"The Third Research Institute of Ministry of Public Security, No. 76 Yueyang Road, Shanghai, China"}]}],"member":"1968","published-online":{"date-parts":[[2014,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/TPAMI.1980.4766969","article-title":"A real-time video tracking system","volume":"1","author":"Gilbert","year":"1980","journal-title":"IEEE Trans. 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