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Directional edge and texture representations for image processing

By Zhen Yao


An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

Topics: QA76
Year: 2007
OAI identifier:

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  1. 3D Fourier based discrete Radon transform. doi
  2. (2003). A class of discrete multiresolution random fields and its application to image segmentation. doi
  3. (1986). A computational approach to edge detection. doi
  4. A generalized wavelet transform for Fourier analysis: the multiresolutiop Fourier transform and its application to image and audio signal analysis. doi
  5. (1990). A hierarchical approach to line extraction based on the Hough transform. doi
  6. (2000). A lapped directional transform for spectral image analysis and its application to restoration and enhancement. doi
  7. A multiresolution wedgelet transform for image processing. doi
  8. (1999). A new approach to linear filtering and prediction problems. 71urisac. tions of the ASME -
  9. A new denoising mothod witil coIltourlot transform. Lecture notes in control and information sciences,
  10. (1996). A new, fast, and efficient image codec based on set partitioing in hierarchical trees. doi
  11. (2007). A review of bandlet methods for geometrical image representation. doi
  12. A survey of the Hough transform. doi
  13. (1989). A theory for multiresolution signal decomposition: The wavelet repru-sentation. doi
  14. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. doi
  15. A two-component model of texture for analysis anti synthesis. doi
  16. (1995). Adapting to unknown smoothness via wavelet shrinkage. doi
  17. (2004). Adaptive wavelet restoration of noisy video sequences. doi
  18. (2000). Adaptive wavelet thresholding for image tle. noising and compression. doi
  19. (2001). An information-maximization appraoch to blind separation and blind deconvolution. doi
  20. (2005). and A Zibulevsky. Improved denoising of images using njo(l. elling of a redundant contourlet transform. doi
  21. (1999). Are edges incomplete?
  22. Bandelet image approximation and comprmioll. doi
  23. (1993). Best wavelet packet bases in a rate distortion -sense. doi
  24. (1997). Brushlets: a tool for directional image allal)-sis alitl image compression. Applied and Computational Harmonic Analysis, doi
  25. (2001). Brushlets: Steerable Wavelet Packets. doi
  26. (1982). Computer Vision. doi
  27. (1994). Curve extraction in images using a multiresolution framework. doi
  28. (2000). Curvelets -a suprisingly effective nonadaptive rep.. resentation for objects with edges. In
  29. (2007). Curvelets and wave atoms for mirror-extended images. doi
  30. (2006). Custom-built moments for edgc location. doi
  31. Denoising in digital speckle pattern interferonictry using wave atoms. doi
  32. (2005). Development of efficient algorithms for geometrical repm-t-11ta. tion based on arclet decomposition. Master's thesis, Technische UjjivLrsjtiit Njiinchen,
  33. (2003). Digital implementation of ridgelet packets. doi
  34. (2006). Directional wavelet analysis with Fourier-type bases for image processing. In doi
  35. (2005). Discrete bandelets with geometric orthogonal filters. doi
  36. (1974). Discrete cosine transform. doi
  37. (1993). Embedded image coding using zerotree of wavelet coefficients. doi
  38. Emergence of simple-cell receptive field properities by learning a sparse code for natural images. doi
  39. Estimation of the mean of a multivariate normal distribution. doi
  40. (1949). Extrapolation, Interpolation, and Smoothing of Stationary Time Series. doi
  41. Fast adaptive wavelet I)a(: L-et 111jagL, compression.
  42. (2006). Fast discrete curvelet transforms. doi
  43. Fast slant stack: A notion of Radon transform for data in a Cartesian grid which is rapidly computible, alge212 BIBLIOGRAPHY 213 braically exact, geometrically faithful and invertible. to appear in
  44. (1981). Generalising the Hough transform. doi
  45. (2006). Geometrical grouplets. Journal of Applied and Computational Harmonic Analysis, doi
  46. (2007). Geometrical image estilliatiol, with orthogonal bandlet bases. doi
  47. (2003). Gray and color image contrast enhancement by the curvelet transform. doi
  48. Ideal spatial adaptation via wavelet shrinkage. doi
  49. Image compression based on multi-scale edge compensation. doi
  50. (2002). Image compression with adaptive local cosines: A comparative sttitly. doi
  51. (2000). Image compression with geometrical wavelcts. presented at IEEE ICIP, doi
  52. (2005). Image decomposition via the combination of sparse representations and a variational approach. doi
  53. (2005). Image denoising using multiscale directional cosine bases. doi
  54. (2003). Image denoising using scale mixture of Gaussians in the wavelet domain. doi
  55. Image denoising with complex ridgelets. doi
  56. (2007). Image denoising with directional bases. in pnxrrd. doi
  57. (1993). Image feature analysis using the Multiresolution Fourier Transfom. PhD thesis,
  58. (1998). Image Processing and Data Analysis: The Multiscale Approach. doi
  59. Image representation based on the affine symmetry group. doi
  60. (1993). Image representation via a finite Radon transform doi
  61. (1996). Image Segmentation and Uncertainty. doi
  62. (1990). Improving an extended Hough transform. doi
  63. Improving the Hough transform gathering process fo affine transformations. doi
  64. (2005). In search of a general picture Processing operator. Computcr Gruph. ics and Image Processing,
  65. (2001). Independent Component Analysis. doi
  66. Inferring surfaces from images. doi
  67. Lapped transforms for efficient transform/subband coding. doi
  68. Local cosine transform -a method for the reduction of the blocking effect in doi
  69. (1992). Local sine and cosine bases of Coffinan and Meyer and the construction of smooth wavelets. doi
  70. Modeling textures with total variation minimization and oscillating patterns in image processing. doi
  71. (2002). Multilayered image representation: Appli. cation to image compression. doi
  72. (1988). Multiresolution image modelling and estimation. doi
  73. (2005). Multivariate statistical modeling of images with the curvelet transform. doi
  74. (2002). New tight frames of curvelets and optimal representations of objects with C2 smooth singularities. doi
  75. Noise suppression by spectral magnitude estimation. doi
  76. (2007). Orthogonal bandlet bases for geometric images approxima. tion.
  77. Oscillating patterns in image processing and non linear evolution equations. doi
  78. (2004). Planelets: A new analysis tool for planar feature extraction.
  79. (1993). Ractal image coding: A review. doi
  80. (2004). Radon/ridgelet signature for image authentication. doi
  81. (2002). Rate-distortion optimized image compression using wedgelets. doi
  82. Rate-distortion optimized tree structured compression algorithms. doi
  83. Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. doi
  84. Remarques sur Panalyse, de Fourier & fen6tre.
  85. (2001). Ridge functions and orthonormal ridgelets. doi
  86. (2006). Ridgelet bi-frame. doi
  87. (2005). Ridgelet-based signatures for natural image classifl. cation. doi
  88. (1999). Ridgelets and the representation of mutilated Sobolev functions. doi
  89. Ridgelets: a key to higher-dimensional intermittency? doi
  90. (1998). Ridgelets: Theory and applications.
  91. (2004). Robust digital watermarking in the ridgelet domain. doi
  92. (2007). Robust modelling of local image structures and its application to medical imagery. doi
  93. (1990). Scale-space and edge detection using anisotropic (liffusioll. doi
  94. (1999). Shiftable multiscale transforms. doi
  95. (1984). Signal Analysis. doi
  96. (2005). Sparse geometric image representations witIl bandelets. doi
  97. (2006). Spaxse directional image representations using the discrete shearlet transform. doi
  98. Stochastic relaxation, Gibbs distributions and tho Ba)Wiall restoration of images. doi
  99. Textons, the elements of texture perception and their interactions. doi
  100. (1994). Texture Analysis and Synthesis using the Multiresolution Fourier 7ýnnsform. PhD thesis,
  101. (1971). The Binford-Horn linefinder.
  102. (1982). The contourlet transform for image de-noising using cycle spinning. doi
  103. (2003). The contourlet transform: an efficient directional multiresolution image representation. doi
  104. (2002). The curvelet transform for image denoising. doi
  105. (2004). The curvelet transform for image fusion. doi
  106. (1991). The JPEG still picture compression standard. doi
  107. (1989). The Laplacian pyramid as a compact image code. doi
  108. (2006). The nonsubsampled contotirlet transform: Theory, Design and Applications. doi
  109. (1999). The pseu. dopolar FFT and its applications.
  110. The uncertainty principle in image processing. doi
  111. Theory of communication. doi
  112. (1995). Translation invariant denoising. doi
  113. Tree approximation and optimal encoding. doi
  114. (1972). Use of the Hough transform to detect lines and curves in pictures. doi
  115. Very high quality image restoration by combining wavelets and curvelets. doi
  116. (2007). Wave atoms and sparsity of oscillatory patterns. Applied Computational Harmonic Analysis, doi
  117. (2003). Wavelet footprints: Theory, algorithm and applications. doi
  118. (1992). Wavelet transform maxima and multiscale e(jgs.
  119. (1999). Wedgelets: Nearly-minimax estimation of edges. doi
  120. (2006). Why simple shrinkage is still relevant for redundant representations? doi

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