2006 # Image Analysis and Reconstruction using a Wavelet Transform Constructed from a Reducible Representation of the Euclidean Motion Group

**Abstract:** £ he xetherlnds yrgniztion for ienti eserh is grtefully knowledged for nnil supportF I P R. Duits, M. Felsberg, G.H. Granlund , B.M. ter Haar Romeny Abstract snspired y the erly visul system of mny mmmlins we onsider the onstrution ofE nd reonstrution fromE n orienttion sore U f X R P ¢ S I 3 C s lol orienttion representtion of n imgeD f X R P 3 RF he mpping f U 3 U f is wvelet trnsform orresponding to reduile representtion of the iuliden motion group onto L P @R P A nd oriented wvelet P L P @R P AF his wvelet…

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(140 citation statements)

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“…The orientation score transform is a wavelet-type transform [8], in which an image is filtered by a set of rotated anisotropic wavelets, i.e. cake wavelets [4].…”

confidence: 99%

“…The orientation score transform is a wavelet-type transform [8], in which an image is filtered by a set of rotated anisotropic wavelets, i.e. cake wavelets [4].…”

confidence: 99%

“…We adapt the group theoretical approach developed for the Euclidean motion groups in the recent works [9,18,12,13,15,11], thus illustrating the scope of the methods devised for general Lie groups in [10] in signal and image processing. Reassignment will be seen to be a special case of left-invariant convection.…”

confidence: 99%

“…. , a 2d ) T and/or conductivity matrix D. We will use ideas similar to our previous work on adaptive diffusions on invertible orientation scores [17], [12], [11], [13] (where we employed evolution equations for the 2D-Euclidean motion group). We use the absolute value to adapt the diffusion and convection to avoid oscillations.…”

confidence: 99%

“…For some choices of K there exists a stable inverse transformation [6], which is obtained by either convolving U (·, θ) with the mirrored conjugate kernel of K followed by integration over θ, or simply by f = 2π 0 U (x, θ)dθ. 1 The space of orientation scores of images V = {U f |f ∈ L2(R 2 )} is a vector subspace of L2(SE (2)).…”

confidence: 99%

“…A related type of data are orientation scores [5] [6], where orientation is made an explicit dimension. Orientation scores arise naturally in high angular resolution diffusion imaging, but can also be created out of an image by applying a wavelet transform [6]. Both tensor images and orientation scores have in common that they contain richer information on local orientation.…”

confidence: 99%