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WAVELET TRANSFORM FOR IMAGE ANALYSIS AND IMAGE ENCRYPTION Dr. Christoph Busch Fraunhofer-Institut for Computer Graphics (IGD), Germany IMAVIWA (IMAge Visualization with Wavelets) makes use of the wavelet transform to provide a wide variety of useful tools for image processing tasks. It helps you find out the opportunities that wavelet transform offers to image processing. Wavelet transform is a succesful way to decompose and analyse data. A signal is transformed using appopriate basis functions, called wavelets. Basis functions can be computed by dilation and translation from a single prototype. The essential advantages of wavelet transform are hierarchical organization of data, concentration of information, interaction and evaluation.
Overview IMAVIWA (IMAge Visualization with Wavelets) makes use of the wavelet transform to provide a wide variety of useful tools for image processing tasks. It helps you find out the opportunities that wavelet transform offers to image processing. IMAVIWA therefore contains a number of orthogonal and biorthogonal basis functions and makes the selection of suitable wavelets very easy. Wavelet Transform Wavelet transform is a succesful way to decompose and analyse data. A signal is transformed using appopriate basis functions, called wavelets. Basis functions can be computed by dilation and translation from a single prototype. Wavelet transform is superiour to the well known fourier transform because it allows multiple views of the input data. The essential advantages of wavelet transform are:
Level-of-Detail Control The wavelet transform is localized in frequency and space. This makes possible a level-of-detail control of interactions with the wavelet representation which can be limited in space in the original signal as well as in frequency to selected frequency bands. Application: Image Encryption The space localization property makes the wavelet transform an ideal tool for partial image encryption (local blurring). The encryption of a part of the signal (or image) is achieved by separation of space dependent coefficients from the pyramid decomposition of the image. The elimination in selected decomposition layers leads to local modifications in certain frequency bands of the original image. Application: Image Compression Image compression can be achieved by eliminating non-significant coefficients of the pyramid decomposition. This is done by first transforming the image, followed by scalar- and vectorquantization and run-length coding of the wavelet representation which leads to high compression rates at relatively small loses. Application: Edge detection A careful interpretation of the detail coefficients in the wavelet representatin leads to the sharp variation points (edges) of the signal. This holds for all layers of the pyramid decomposition and is used by IMAVIWA for edge detection. The scalling of a given edge in the original image is a direct result of a certain iteration depth. Contact Dr. Christoph Busch, Fraunhofer-Institut for Computer Graphics (IGD), Rundeturmstr. 6, D-64283 Darmstadt, Germany. Email: busch@igd.fhg.de
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