{"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/density-modeling-of-images-using-a","title":"Density Modeling of Images using a Generalized Normalization Transformation","arxiv_id":"1511.06281","date":"2015-11-19","proceeding":null,"authors":["Johannes Ballé","Valero Laparra","Eero P. Simoncelli"],"abstract":"We introduce a parametric nonlinear transformation that is well-suited for\nGaussianizing data from natural images. The data are linearly transformed, and\neach component is then normalized by a pooled activity measure, computed by\nexponentiating a weighted sum of rectified and exponentiated components and a\nconstant. We optimize the parameters of the full transformation (linear\ntransform, exponents, weights, constant) over a database of natural images,\ndirectly minimizing the negentropy of the responses. The optimized\ntransformation substantially Gaussianizes the data, achieving a significantly\nsmaller mutual information between transformed components than alternative\nmethods including ICA and radial Gaussianization. The transformation is\ndifferentiable and can be efficiently inverted, and thus induces a density\nmodel on images. We show that samples of this model are visually similar to\nsamples of natural image patches. We demonstrate the use of the model as a\nprior probability density that can be used to remove additive noise. Finally,\nwe show that the transformation can be cascaded, with each layer optimized\nusing the same Gaussianization objective, thus offering an unsupervised method\nof optimizing a deep network architecture.","url_abs":"http://arxiv.org/abs/1511.06281v4","url_pdf":"http://arxiv.org/pdf/1511.06281v4.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":[{"paper_slug":"density-modeling-of-images-using-a","repo_url":"https://github.com/ika-rwth-aachen/point-cloud-compression","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"density-modeling-of-images-using-a","repo_url":"https://github.com/jorge-pessoa/pytorch-gdn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"ica","method_name":"ICA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1511.06281","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}