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# Image feature extraction method and image compression method

Foreign code F110005494 K07605WO Sep 6, 2011 United States of America 37605907 20090324064 8160368 Feb 2, 2007 Dec 31, 2009 Apr 17, 2012 JP2007051831 WO2008015799 Feb 2, 2007 Feb 7, 2008 P2006-211219 (Aug 2, 2006) JP 2007WO-JP51831 (Feb 2, 2007) WO Image feature extraction method and image compression method (US8160368)The image feature extraction method of the present invention includes: the step of performing k2 dividing process at least once on a given image so as to convert the given image into a multi-divided image, where the k2 dividing process comprises the steps of: a) creating matrix T based on image matrix X; b) computing singular values of the matrix T; c) determining whether or not minj|σj－σj－1|>ε; d) if the result of the determination in the step c) is “No”, returning to the step c) subsequent to computing the singular values of the enlarged matrix Tα; e) if the result of the determination in the step c) is “Yes”, obtaining U which satisfies T=USVT; f) obtaining matrix T1=UTT; and g) creating image matrix X1 based on matrix T1. [claim1]1. An image feature extraction method for extracting a feature of an image, comprising the step of performing k2 (k is an arbitrary integer greater than or equal to 2) dividing process at least once on a given image so as to convert the given image into a multi-divided image, wherein the k2 dividing process comprises the steps of: a) creating matrix T based on image matrix X; b) computing singular values sigma 1, sigma 2, . . . , sigma k^2 of the matrix T, where sigma 1 >= sigma 2 >= . . . >= sigma k^2; c) determining whether or not minj|sigma j-sigma j-1|>epsilon , where epsilon shows a constant greater than or equal to machine epsilon; d) if the result of the determination in the step c) is "No" returning to the step c) subsequent to computing the singular values of enlarged matrix Talpha ; e) if the result of the determination in the step c) is "Yes", obtaining U which satisfies T=USVT, where S=diag (sigma 1, sigma 2, . . . , sigma k^2), U is an orthogonal matrix and V is an orthogonal matrix; f) obtaining matrix T1=UTT; and g) creating image matrix X1 based on matrix T1, wherein the computing the singular values of the enlarged matrix Talpha in the step d) comprises the steps of: creating enlarged matrix Talpha based on matrix T and a frame added to at least a portion of at least one side of image matrix X, the frame having a size of at least k pixels and k pixels; and computing singular values sigma 1, sigma 2, . . . , sigma k^2 of the enlarged matrix Talpha , where sigma 1 >= sigma 2 >= . . . >= sigma k^2.[claim2]2. An image feature extraction method for extracting a feature of an image, comprising the step of performing k2 (k is an arbitrary integer greater than or equal to 2) dividing process at least once on a given image so as to convert the given image into a multi-divided image, wherein the k2 dividing process comprises the steps of: a) creating matrix T based on image matrix X; b) obtaining a singular value decomposition of the matrix T, T=USVT, where S=diag (sigma 1, sigma 2, . . . , sigma k^2), sigma 1, sigma 2, . . . , sigma k^2 are singular values of T satisfying sigma 1 >= sigma 2 >= . . . >= sigma k^2, U is an orthogonal matrix and V is an orthogonal matrix; c) determining whether or not minj|sigma j-sigma j-1|>epsilon , where epsilon shows a constant greater than or equal to machine epsilon; d) if the result of the determination in the step c) is "No", returning to the step c) subsequent to performing singular value decomposition of enlarged matrix Talpha ; e) if the result of the determination in the step c) is "Yes", obtaining matrix T1=UTT; and f) obtaining matrix T1=UTT based on matrix T1, wherein the performing singular value decomposition of enlarged matrix Talpha comprises the steps of: creating enlarged matrix Talpha based on matrix T and a frame added to at least a portion of at least one side of image matrix X, the frame having a size of at least k pixels and k pixels; and obtaining the singular value decomposition of the enlarged matrix Talpha , Talpha =USVT, where S=diag (sigma 1, sigma 2, . . . , sigma k^2), sigma 1, sigma 2, . . . , sigma k^2 is a singular value of Talpha which satisfies sigma 1 >= sigma 2 >= . . . >= sigma k^2, U is an orthogonal matrix, and V is an orthogonal matrix.[claim3]3. An image feature extraction method according to claim 1, wherein the image is a gray scale image or a color image.[claim4]4. An image feature extraction method according to claim 2, wherein the image is a gray scale image or a color image.[claim5]5. An image feature extraction method according to claim 1, wherein the singular value decompositions of the T and the Talpha are performed by floating point arithmetic.[claim6]6. An image feature extraction method according to claim 2, wherein the singular value decompositions of the T and the Talpha are performed by floating point arithmetic.[claim7]7. An image feature extraction method according to claim 1, wherein the singular value decompositions of the T and the Talpha are performed by integer arithmetic.[claim8]8. An image feature extraction method according to claim 2, wherein the singular value decompositions of the T and the Talpha are performed by integer arithmetic.[claim9]9. An image feature extraction method according to claim 1, wherein a known k2 dividing process is used together with the k2 dividing process, so that the given image matrix X is converted into a multi-divided image.[claim10]10. An image feature extraction method according to claim 2, wherein a known k2 dividing process is used together with the k2 dividing process, so that the given image matrix X is converted into a multi-divided image.[claim11]11. An image compression method for compressing an image, comprising the steps of: performing k2 (k is an arbitrary integer greater than or equal to 2) dividing process at least once on a given image so as to convert the given image into a multi-divided image; and performing a data compression process on the multi-divided image so as to create a compressed image, wherein the k2 dividing process comprises the steps of: a) creating matrix T based on image matrix X; b) computing singular values sigma 1, sigma 2, . . . , sigma k^2 of the matrix T, where sigma 1 >= sigma 2 >= . . . >= sigma k^2; c) determining whether or not minj|sigma j-sigma j-1|>epsilon , where epsilon shows a constant greater than or equal to machine epsilon; d) if the result of the determination in the step c) is "No", returning to the step c) subsequent to computing the singular values of the enlarged matrix Talpha ; e) if the result of the determination in the step c) is "Yes", obtaining U which satisfies T=USVT, where S=diag (sigma 1, sigma 2, . . . , sigma k^2), U is an orthogonal matrix and V is an orthogonal matrix; f) obtaining matrix T1=UTT; and g) creating image matrix X1 based on matrix T1, wherein the computing the singular values of the enlarged matrix Talpha in the step d) comprises the steps of: creating enlarged matrix Talpha based on matrix T and a frame added to at least a portion of at least one side of image matrix X, the frame having a size of at least k pixels and k pixels; and computing singular values sigma 1, sigma 2, . . . , sigma k^2 of the enlarged matrix Talpha , where sigma 1 >= sigma 2 >= . . . >= sigma k^2.[claim12]12. An image compression method for compressing an image, comprising the steps of: performing k2 (k is an arbitrary integer greater than or equal to 2) dividing process at least once on a given image so as to convert the given image into a multi-divided image; and performing a data compression process on the multi-divided image so as to create a compressed image, wherein the k2 dividing process comprises the steps of: a) creating matrix T based on image matrix X; b) obtaining a singular value decomposition of the matrix T, T=USVT, where S=diag (sigma 1, sigma 2, . . . , sigma k^2), sigma 1, sigma 2, . . . , sigma k^2 are singular values of T satisfying sigma 1 >= sigma 2 >= . . . >= sigma k^2, U is an orthogonal matrix and V is an orthogonal matrix; c) determining whether or not minj|sigma j-sigma j-1|>epsilon , where epsilon shows a constant greater than or equal to machine epsilon; d) if the result of the determination in the step c) is "No", returning to the step c) subsequent to performing singular value decomposition of enlarged matrix Talpha ; e) if the result of the determination in the step c) is "Yes", obtaining matrix T1=UTT; and f) obtaining matrix T1=UTT based on matrix T1, wherein the performing singular value decomposition of enlarged matrix Talpha comprises the steps of: creating enlarged matrix Talpha based on matrix T and a frame added to at least a portion of at least one side of image matrix X, the frame having a size of at least k pixels and k pixels; and obtaining the singular value decomposition of the enlarged matrix Talpha , Talpha =USVT, where S=diag (sigma 1, sigma 2, . . . , sigma k^2), sigma 1, sigma 2, . . . , sigma k^2 is a singular value of Talpha which satisfies sigma 1 >= sigma 2 >= . . . >= sigma k^2, U is an orthogonal matrix, and V is an orthogonal matrix.[claim13]13. An image compression method according to claim 11, wherein the image is a gray scale image or a color image.[claim14]14. An image compression method according to claim 12, wherein the image is a gray scale image or a color image.[claim15]15. An image compression method according to claim 11, wherein the singular value decompositions of the T and the Talpha are performed by floating point arithmetic.[claim16]16. An image compression method according to claim 12, wherein the singular value decompositions of the T and the Talpha are performed by floating point arithmetic.[claim17]17. An image compression method according to claim 11, wherein the singular value decomposition of the T and the Talpha are performed by integer arithmetic.[claim18]18. An image compression method according to claim 12, wherein the singular value decomposition of the T and the Talpha are performed by integer arithmetic.[claim19]19. An image compression method according to claim 11, wherein a known k2 dividing process is used together with the k2 dividing process, so that the given image matrix X is converted into a multi-divided image.[claim20]20. An image compression method according to claim 12, wherein a known k2 dividing process is used together with the k2 dividing process, so that the given image matrix X is converted into a multi-divided image. NAKAMURA YOSHIMASA IWASAKI MASASHI OBATA MASAHIKO KONDO KOICHI SASADA SHOHEI DOSHISHA JAPAN SCIENCE AND TECHNOLOGY AGENCY G06K   9/36      Image preprocessing, i.e. processing the image information without deciding about the identity of the image G06K   9/46      Extraction of features or characteristics of the image G06K   9/56      using a local operator, i.e. means to operate on an elementary image point in terms of the immediate surroundings of this point PRESTO The Innovation of Simulation Technology and the Construction of Foundations for its Practical Use AREA      