Satellite Image Compression Using A Universal Codebook: Applications of Direct Classification Technique

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1 Satellite Image Compression Using A Universal Codebook: Applications of Direct Classification Technique Hamdy S. Soliman Mohammed Omari {hss, omari01}@nmt.edu Computer Science Department New Mexico Institute of Mining and Technology Socorro, NM 87801, USA Abstract We present an image compression application that utilizes the neural networks approach of Direct Classification (DC) in the satellite imaging domain. The training of our DC model is based on the winner-take-all mechanism of the Kohonen model, as well as the elasticity/stability feature of the ART1 model. Experimental results show a promising future for our DC model, both at the performance (compression ratio, quality, time) and security levels in compressing geosynchronous-satellite images. I. Introduction In many domains that deal with large-scale images, many applications force the use of image compression in order to reduce the required storage. The best existing compression techniques, with respect to image quality, are the lossless compression methods. Unfortunately, there are serious limitations on how much we can compress an image without losing vital information [4]. In order to balance performance, in both quality and compression ratio, we must use a lossy compression approach, especially when the quality of the output is udged by the human visual/acoustic system, allowing for tolerance. In application domains that use lossy image compression, the tradeoff between compression ratio and distortion of the image has to be balanced so that a higher compression ratio can be achieved with minimal distortion, in order to ensure sufficient accuracy for specific purposes [5]. The application of lossy compression to an image sequence further improves the compression performance, when the degree of image varying dimension is reduced. For example, in the geosynchronous satellite image domain, a huge set of images usually share the same characteristics, since they reflect the geophysical aspects of approximately the same region. This dimension reduction can be utilized in order to increase the compression ratio with good quality of the reconstructed image. Our work investigates the application of the DC model in the geosynchronous satellite images domain. Section II describes the DC algorithm, including the training parameters. In Section III, the tuning of our model in order to handle satellite images is presented. Experimental results are shown in Section IV. Section V is the conclusion. II. Direct Classification Approach Based on the Adaptive Vector Quantization (AVQ) theory, we designed our new Direct Classification neural net engine for image compression/decompression [1]. It follows the winner-take-all feature of the Kohonen model, and the elasticity as well as the single epoch training cycle features of the ART1 model. The advantage of the DC over Kohonen is that the input domain is presented only once to the DC system. Therefore the asymptotic training time complexity is O(n), where n is the size of the input domain of

2 subimages; a huge reduction to the original SOFM 1 time complexity of n 2.The traditional ART1 [6] generates small real numbers in the weight matrix, which might cause deviation of the classification in the event of low system precision. Instead, our DC model develops classes representatives (centers of mass) called centroids, which are of the same type as the input subimages (integer vectors). Our work is in the same area as the well-known Wavelet and JPEG image compression techniques, with a maor difference in the formation of the lookup tables [1]. The manufacturing of the DC s lookup tables is carried out via the training of a hybrid neural model of the SOFM and ART nets, with some modifications. Our model is a vector quantizer (VQ), which encodes subimage vectors via the mapping of many similar k-dimensional input vectors (with respect to a given distortion measure) into one representative codeword (centroid) vector [3]. The similarity measure of vectors X and Y is based on the distance X-Y (distortion) between X and Y. A collection of centroids is to be stored in a lookup table (codebook), which is utilized later at the decompression phase, in the lookup process. The manufacturing and the nature of the codebook are the key distinctions of our work from peer mechanisms. The next sections explain in detail the DC training, compression and decompression process. A. Training/Compression Phase Step1: Parameters Setup. CS, codebook size (maximum number of entries). IT, intensity threshold representing the maximum difference between two corresponding vector coordinates. TSS, Training set threshold (size) representing the maximum number of subimages allowed to adust the center of mass of their cluster. Step 2: Initialization COE 0; Codebook occupied entries. SCS i φ; i th set of classified subimages, i =1, 2,, CS Step 3: Divide the input images into subimages of equal size (n 2 ). Step 4: Present an input subimage S to the system. Step 5: For each center of mass C i, generate a distance vector D i : D i S - C i, for i = 1, 2,, COE Step 6: Compute ND i, the number of D i s coordinates exceeding IT. Step 7: Form PWC, a set of possible winner centroids, whose ND=0. Step 8: If PWC is empty go to Step 8-a. Otherwise, select the best-match centroid C from PWC according to the mean square criterion: D D min i=1,2,..., PWC ( ) i Go to Step 9. Step 8-a: If the codebook is full (COE = CS), assign PWC to be the whole codebook (all centroids) and go back to Step 8. Otherwise, add a new cluster, containing only the subimage S: COE COE + 1 SCS COE SCS COE {S} 1 Self Organization Feature Map

3 C COE S COE Step 9: If SCE = TSS go to Step 10. Otherwise, adust the center of mass C : SCS * C + S C SCS + 1 Add the subimage S to the cluster of C: SCS SCS {S} Step 10: (Compression sub-phase) save the index to be the corresponding entry of S in the compressed file: win S Step 11: If there are more subimages to train, go to Step 4. Step 12: Save the winner indices (win S s) and the codebook entries (C i s) into the compressed file. Step 13: Compress the compressed file further using LZW, GZIP, WINZIP, etc. The above algorithm is suitable for local codebooks (one codebook per image). In case of training a universal codebook (one codebook per many images), the training phase and the compression phase are separated. The training phase will be performed excluding steps 10, 12, and 13 from the above algorithm, and adding a final step of saving the centroids in a separate codebook file. The compression phase is also performed as described above, except for centroid adustment (Steps 8-a and 9), and without saving the centroids as in Step 12. B. Decompression Phase Step1: Load the compressed file. Decompress it using LZW, GZIP, WINZIP, etc. Retrieve the indices and the codebook. Step 2: Select, in order, an index i from the indices tables. Step 3: Using i as an address, access the corresponding codebook entry to obtain a centroid and store it in the same order of index i into the decompressed file. Step 4: If there are more indices, go to Step 2. C. Codebook Size Assuming that the size of the codebook is CS, and the size of the subimage is n, the initial compression ratio achieved is n/(log2 CS). In our DC model, the codebook size is the maor factor controlling the quality of the image and the compression ratio. Figure 1 clearly shows that the larger the codebook, the better the quality. However, a larger codebook requires a longer bit representation of the indices centroids, resulting in a lower compression ratio. Also, experimental results show that the compression time depends directly on the codebook size. Such dependency is due to the time spent in searching for the closest centroid to an input subimage.

4 Codebook Size (CS) Quality (PSNR db) Compression ratio Figure 1: Compression performance, varying the codebook size. D. Training Set Size In the DC training phase, the training set size threshold TSS represents the maximum number of inputs allowed to adust a specific centroid; only the first TSS members (subimages) can modify the center of mass. Figure 2 clearly shows that the size of the training set (controlled by TSS) dramatically affects the quality of the decompressed image. However, the time and the compression ratio remained nearly the same Training Set Size (TSS) Quality (PSNR db) Figure 2: Compression performance, varying the training set size. E. Intensity Threshold In order to achieve better quality, the input subimage vector is compared to the previously formed centroids to select the closest (most similar) as its representative. The IT threshold controls the comparison between corresponding coordinate bytes of the subimage and each compared centroid. Figure 3 shows that the quality increases around mid-values (e.g.: 15, 20), but not at high or low values. However, the compression ratio increases as IT threshold increases.

5 Quality (PSNR db) Compression Ratio Intensity Threshold (IT) Figure 3: Compression performance varying the intensity threshold (IT). Finding a balance among the aforementioned three parameters (CS, TSS, IT) for optimal performance is a function of the complexity of the image. A very complicated image requires a large codebook, in order to maintain good quality. However, a small codebook is sufficient to handle simple images with acceptable quality. III. Geosynchronous-Satellite Image Domain: DC Specification Due to the great overhead of the extra codebook per image and the codebooks overlap, we utilize the universal codebook approach in the compressing/decompressing process. Therefore, all images of the same region were used to train one universal codebook, yielding an increase in the compression ratio. The image quality will depend on the precision of the codebook training. A rich and long universal codebook will include the most important centroids, for good recovered image quality. Theoretically, the generated universal codebook will not be counted against the compression ratio; instead, it will be stored at the sender and receiver sites. We carried out many experiments using different satellite images in order to train several universal codebooks. The result of growing huge universal codebooks is a larger image index size, yielding a lower compression ratio. To solve the problem, we divide the image into regions with each having its own small codebook. The total universal codebook is the integration of all such regional small codebooks. Every image is divided into regions (1000 regions), where the i th region trains the i th regional codebook. Such a mechanism allows every regional codebook to learn about similar smaller regions from different images; small numbers of centroids are stored, which are yet enough for good image quality. The small size of the regional codebook helped also in decreasing the local search time (15min to train 100 images, and 6 to 15 sec to compress/decompress an input image). We utilized intensity graphs and pixel value distributions in order to find a balance of the training parameters CS, TSS and IT that achieve good performance, balancing high image quality and compression ratio. Experimental results showed such a balance at TSS=200, IT=15, and CS= 256.

6 IV. Results There are two sets of experimental results for our DC model. A set of results was obtained from the compression/decompression of the same set of images used to train the universal codebook, and images outside the training set. In processing the training set images, we obtained a 70% increase of the compression ratio over the peer Wavelet/JPEG models, for the same quality. But, for images outside the training set, we obtained acceptable quality (above 30 db S/N ratio), with a slight increase (about 30%) in the compression ratio over existing peer mechanisms. (Universal codebook training using 100 satellite images) Trained images Non-trained images Image Compression Quality Compression Quality Image ratio (PSNR db) ratio (PSNR db) Sat1.ppm Sat101.ppm Sat2.ppm Sat102.ppm Sat3.ppm Sat103.ppm V. Conclusion Our new DC neural model for image compression combines the advantages of the Kohonen SOFM networks, with some useful characteristics of the ART network. The DC neural net model can be utilized to train a universal codebook (for a single homogenous domain of images) faster and with better performance (compression ratio and quality), even for images from outside the training domain. In secure satellite applications (e.g., the military domain), we increase the bandwidth utilization via image compression, saving the encryption/decryption times of the transmitted images. References [1] H.S. Soliman, M. Omari. Hybrid ART/Kohonen Neural Model for Document Image Compression. ANNIE 2002, University of Missouri-Rolla, MO, November [2] H.S. Soliman, M. Omari. Universal Codebook versus Local Codebook: Applications of Image Compression Using AVQ Theory. ANNIE 2002, University of Missouri-Rolla, MO, November [3] T. Kohonen. A Program Package for the Correct Application of Learning Vector Quantization Algorithms, IEEE International Joint Conference on Neural Networks [4] O. Koshelva and V. Kreinovich. On the Optimal Choice of Quality Metric in Image Compression. Fifth IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI 02). [5] L. Ke and M. W. Marcellin. Near Lossless Image Compression: Minimum-Entropy, Constrained-Error DPCM. Proceedings of the 1995 International Conference on Image Processing (ICIP 95). [6] Jack M. Zurada. Introduction to Artificial Neural Systems. PWS Publishing Company, 1995.