Set redundancy compression

In computer science and information theory, set redundancy compression are methods of data compression that exploits redundancy between individual data groups of a set, usually a set of similar images. It is wide used on medical and satellital images.^[1]^[2]^[3]^[4] The main methods are min-max differential, min-max predictive and centroid method.

Methods

Min-max differential

In the min-max differential (or MMD), for each position (pixel) selects the highest or the lowest. And then in each image is stored the difference of each of their positions with respect to the value previously selected.

References

^ Karadimitriou, Kosmas (August 1996), Set redundancy, the enhanced compression model, andmethods for compressing sets of similar images, CiteSeerX 10.1.1.35.7146, This statistical correlation among similar images is a result of inter-image redundancy. In this study, the term "set redundancy" is introduced to describe this type of redundant information, and is defined as follows: Definition: Set redundancy is the inter-image redundancy that exists in a set of similar images, and refers to the common information found in more than one image in the set. Set redundancy can be used to improve compression. A limit to compression is imposed by the image entropy. In the next section it is shown how set redundancy can be used to decrease the average image entropy in a set of similar images. Ph.D. thesis, Department of Computer Science, Louisiana State University, Baton Rouge, La, USA
^ Ait-Aoudia, Samy; Gabis, Abdelhalim (2005-02-27), "A Comparison of Set Redundancy Compression Techniques" (PDF), EURASIP Journal on Applied Signal Processing, 2006: 092734, Bibcode:2006EJASP2006..234A, doi:10.1155/ASP/2006/92734, retrieved 2012-09-28, Medical imaging applications produce a huge amount of similar images. Storing such amount of data needs gigantic disk space. Thus a compression technique is necessary to reduce space storage. In addition, medical images must be stored without any loss of information since the fidelity of images is critical in diagnosis. This requires lossless compression techniques. Lossless compression is an error-free compression. The decompressed image is the same as the original image. Classical image compression techniques (see [1–5]) concentrate on how to reduce the redundancies presented in an individual image. These compression techniques use the same model of compression as shown in Figure 1. Thismodel ignores an additional type of redundancy that exists in sets of similar images, the "set redundancy." The term "set redundancy" was introduced for the first time by Karadimitriou [6] and defined as follows: "Set redundancy is the interimage redundancy that exists in a set of similar images, and refers to the common information found in more than one image in the set.
^ Ait-Aoudia, Samy; Gabis, Abdelhalim; Naimi, Amina, Compressing Sets of Similar Images (PDF), Applications using these types of data, produce a large amount of similar images. Thus a compression technique is useful to reduce transmission time and space storage. Lossless compression methods are necessary in such critical applications. Set Redundancy Compression (SRC) methods exploit the interimage redundancy and achieve better results than individual image compression techniques when applied to sets of similar images.
^ Karadimitriou, Kosmas; Tyler, John M. (1998), "The Centroid method for compressing sets of similar images", Pattern Recognition Letters, 19 (7): 585–593, Bibcode:1998PaReL..19..585K, CiteSeerX 10.1.1.39.3248, doi:10.1016/S0167-8655(98)00033-6, Karadimitriou (1996) proposed the Enhanced Compression Model as a more appropriate model for compressing sets of similar images. […] Methods that achieve set redundancy reduction are referred to as SRC (Set Redundancy Compression) methods. Two SRC methods are the Min-Max Differential method (Karadimitriou and Tyler, 1996) and the Min-Max Predictive method (Karadimitriou and Tyler, 1997).[…] One of the best application areas for SRC methods is medical imaging. Medical image databases usually store similar images; therefore, they contain large amounts of set redundancy.

[kosmas1-1] Karadimitriou, Kosmas (August 1996), Set redundancy, the enhanced compression model, andmethods for compressing sets of similar images, CiteSeerX 10.1.1.35.7146, This statistical correlation among similar images is a result of inter-image redundancy. In this study, the term "set redundancy" is introduced to describe this type of redundant information, and is defined as follows: Definition: Set redundancy is the inter-image redundancy that exists in a set of similar images, and refers to the common information found in more than one image in the set. Set redundancy can be used to improve compression. A limit to compression is imposed by the image entropy. In the next section it is shown how set redundancy can be used to decrease the average image entropy in a set of similar images. Ph.D. thesis, Department of Computer Science, Louisiana State University, Baton Rouge, La, USA

[gabis1-2] Ait-Aoudia, Samy; Gabis, Abdelhalim (2005-02-27), "A Comparison of Set Redundancy Compression Techniques" (PDF), EURASIP Journal on Applied Signal Processing, 2006: 092734, Bibcode:2006EJASP2006..234A, doi:10.1155/ASP/2006/92734, retrieved 2012-09-28, Medical imaging applications produce a huge amount of similar images. Storing such amount of data needs gigantic disk space. Thus a compression technique is necessary to reduce space storage. In addition, medical images must be stored without any loss of information since the fidelity of images is critical in diagnosis. This requires lossless compression techniques. Lossless compression is an error-free compression. The decompressed image is the same as the original image. Classical image compression techniques (see [1–5]) concentrate on how to reduce the redundancies presented in an individual image. These compression techniques use the same model of compression as shown in Figure 1. Thismodel ignores an additional type of redundancy that exists in sets of similar images, the "set redundancy." The term "set redundancy" was introduced for the first time by Karadimitriou [6] and defined as follows: "Set redundancy is the interimage redundancy that exists in a set of similar images, and refers to the common information found in more than one image in the set.

[gabis2-3] Ait-Aoudia, Samy; Gabis, Abdelhalim; Naimi, Amina, Compressing Sets of Similar Images (PDF), Applications using these types of data, produce a large amount of similar images. Thus a compression technique is useful to reduce transmission time and space storage. Lossless compression methods are necessary in such critical applications. Set Redundancy Compression (SRC) methods exploit the interimage redundancy and achieve better results than individual image compression techniques when applied to sets of similar images.

[kosmas2-4] Karadimitriou, Kosmas; Tyler, John M. (1998), "The Centroid method for compressing sets of similar images", Pattern Recognition Letters, 19 (7): 585–593, Bibcode:1998PaReL..19..585K, CiteSeerX 10.1.1.39.3248, doi:10.1016/S0167-8655(98)00033-6, Karadimitriou (1996) proposed the Enhanced Compression Model as a more appropriate model for compressing sets of similar images. […] Methods that achieve set redundancy reduction are referred to as SRC (Set Redundancy Compression) methods. Two SRC methods are the Min-Max Differential method (Karadimitriou and Tyler, 1996) and the Min-Max Predictive method (Karadimitriou and Tyler, 1997).[…] One of the best application areas for SRC methods is medical imaging. Medical image databases usually store similar images; therefore, they contain large amounts of set redundancy.

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