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Image Index

Figure 1. Detail of a_vm1480 male slice with a zoom factor of 3. At rigth the image after JPEG compression and at left after wavelet compression. The two image has been compressed at a compression ratio very similar of about 80:1. As can be seen the blockiness effect of 8x8 DCT for JPEG is well visible whereas left image appears much better.

Figure 2. A 1-D discrete signal is splitted into a diadic hierarchical decomposition through wavelet transform and subsampling.

Figure 3. Piramid of images with relative subbands. HH is horizontal high-pass/vertical high-pass, HL is horizontal high-pass/vertical low-pass, LH is horizontal low-pass/vertical high-pass. The subband LL is iteratively splitted as shown. For color images (three channels) there are three piramid like that one.

Figure 4. Wavelet transform of the 256by256 image with HAAR wavelet for 3 level of diadic decomposition. The image is a part of the slice a_vm1480. At each level of decomposition the image if filtered and subsampled of a factor 2. Right down HH1: 128by128 image is the horizontal high-pass/vertical high-pass detail (diagonal edges are enhanced). Right up HL1: 128by128 image is the horizontal high-pass/vertical low-pass detail (horizontal edges are enhanced). Left down LH1: 128by128 image is the horizontal low-pass/vertical high-pass detail (vertical edges are enhanced). LL1 (horizontal low-pass/vertical low-pass) detail is iteratevely decomposed (left up 128by128 image) for further two levels.

Figure 5. Wavelet coefficient node with the corresponding children in the tree decomposition. Each coefficient (except for the coarsest subband) has four children.

Figure 6. EZW: Building the significance map for the threshold T . The input coefficients are coded based on 4 symbol (pos, neg, isolated zero, zero-tree root).

Figure 7. Compression path: wavelet decomposition and bit-plane coding. The result is the embedded file.

Figure 8. Detail of a_vm1480 slice. EZ wavelet compression for different rates of compression. Till to compression rate under 100 image distortion is tolerable.

Figure 9. The visual comparison in between JPEG and Wavelet compression is shown for a compression rate of 40:1. The displayed images are the negated pixel difference between original image and compressed image. In order to ehnance the effects each color has been expressed on 32 level for each channel. Wavelet behaved better than JPEG (cfr. table I in result section).

Figure 10. 3D image difference, red (up), green (middle) and blue (down) channels, for wavelet compression. Left side shown image difference for a compression ratio of 40:1 whereas in the right side are shown results for a compression ratio of 200:1. The clearer the peak the higher the error.

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