{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:54Z","timestamp":1760242794037,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T00:00:00Z","timestamp":1467158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61272051","61370111"],"award-info":[{"award-number":["61272051","61370111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010026","name":"Beijing Higher Education Young Elite Teacher Project","doi-asserted-by":"publisher","award":["YETP0543"],"award-info":[{"award-number":["YETP0543"]}],"id":[{"id":"10.13039\/501100010026","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Fundamental Research Funds for the Central Universities of China","award":["2014JBM028"],"award-info":[{"award-number":["2014JBM028"]}]},{"name":"CCF-Tencent Open Fund"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multiple description (MD) coding is a promising alternative for the robust transmission of information over error-prone channels. In 3D image technology, the depth map represents the distance between the camera and objects in the scene. Using the depth map combined with the existing multiview image, it can be efficient to synthesize images of any virtual viewpoint position, which can display more realistic 3D scenes. Differently from the conventional 2D texture image, the depth map contains a lot of spatial redundancy information, which is not necessary for view synthesis, but may result in the waste of compressed bits, especially when using MD coding for robust transmission. In this paper, we focus on the redundancy removal of MD coding based on the DCT (discrete cosine transform) domain. In view of the characteristics of DCT coefficients, at the encoder, a Lagrange optimization approach is designed to determine the amounts of high frequency coefficients in the DCT domain to be removed. It is noted considering the low computing complexity that the entropy is adopted to estimate the bit rate in the optimization. Furthermore, at the decoder, adaptive zero-padding is applied to reconstruct the depth map when some information is lost. The experimental results have shown that compared to the corresponding scheme, the proposed method demonstrates better rate central and side distortion performance.<\/jats:p>","DOI":"10.3390\/e18070245","type":"journal-article","created":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T17:03:22Z","timestamp":1467219802000},"page":"245","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiple Description Coding Based on Optimized Redundancy Removal for 3D Depth Map"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1972-2751","authenticated-orcid":false,"given":"Sen","family":"Han","sequence":"first","affiliation":[{"name":"Institute of Information Science, Beijing Jiaotong University, No.3 Shang Yuan Cun, Hai Dian, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huihui","family":"Bai","sequence":"additional","affiliation":[{"name":"Institute of Information Science, Beijing Jiaotong University, No.3 Shang Yuan Cun, Hai Dian, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengmeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Information Engineering, North China University of Technology, No.5 Jinyuanzhuang Road, Shijingshan, Beijing 100144, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhu, C., Zhao, Y., Yu, L., and Tanimoto, M. 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