APPLICATION OF NEURAL NETWORKS TO WAVELET FILTER SELECTION IN MULTISPECTRAL IMAGE COMPRESSION Arto Kaarna Lappeenranta University of Technology, Department of Information Technology, P.O. Box 20, FIN-53851 Lappeenranta, FINLAND,
[email protected] ABSTRACT The problem of selecting an appropriate wavelet filter is always present in the wavelet based image compression. In this study, we apply neural networks to wavelet filter selection. The purpose is to find a good filter for the compression of each multispectral image. Spectral characteristics from three different images are used in the training phase and then the neural network is used to select a good wavelet filter for each of the images. The results show, that our method finds the most suitable wavelet filter for multispectral image compression with the specific compression method. 1. INTRODUCTION Many applications require multispectral features since RGB features do not describe the real world well enough. Multispectral images are widely used in remote sensing [10] and nowadays, new applications arise in industry due to the development in the spectral imaging systems [3]. The sizes of multispectral images are from tens of megabytes to hundreds of megabytes and in image libraries, there can be hundreds of images. Thus, compression methods for multispectral images must be developed. Both lossy and lossless compression techniques have been suggested. Some methods use different approaches to the spatial and to the spectral data of the multispectral image, whereas some methods exploit the combined data from all three dimensions [4, 5, 8]. Wavelet based image compression can be applied to multispectral images in different ways. The whole image can be compressed using the wavelet transform [4], or the spatial dimension can be compressed by clustering and the spectral dimension by the wavelet transform [5]. In both cases, the problem of selecting the wavelet filter arises. The regularity of a filter is closely related to the vanishing moments of the filter, and thus, the filter selection can be based on the regularity of the filter. This requires similar knowledge about the image to be compressed, but the regularity of the image is seldom known, or the data cannot be characterized by the regularity at all. Other measures are also proposed to describe the usability of wavelet fil-
ters [7, 9]. In this study, we propose a method to select an appropriate wavelet filter, when a multispectral image is compressed in the spatial dimensions by clustering and in the spectral dimension by the wavelet transform. The filter selection is based on neural networks: some spectra from the image are classified and the filter associated to the largest class will be selected to compress every spectrum from the image. The contents of the paper is following: in section 2, we describe the compression method, in section 3, the classification method is explained. The results from the experiments are shown in section 4 and conclusions are drawn in section 5. 2. COMPRESSION OF MULTISPECTRAL IMAGES Usually a multispectral image contains spatial areas of similar spectra and thus, one spectrum can represent the entire area. This spatial redundancy can be reduced by grouping image pixels into numbered clusters. The redundancy in the spectral dimension can be reduced by compressing the spectra with the wavelet transform. The principle of the compression is illustrated in Figure 1. A spectrum is considered to belong to a certain cluster, if the Euclidean distance DE between the cluster c and the spectrum p is smaller than a priori selected threshold. The Euclidean distance is defined as DE = i (pi ci )2 , where pi is component i of the pixel spectrum and ci is component i of the cluster spectrum and the sum is over all spectral bands. In our compression method, each cluster is represented as one spectrum from the original image. In the spectral reduction, the original presentation of one channel for each wavelength is transformed to a smaller base while preserving as much information of the original spectra as possible. Now, the wavelet transform is used in the spectral reduction. With digital signals, the wavelet transform is accomplished using a filter bank with several levels in resolution. The filter bank consists of a low-pass filter and of a high-pass filter and these filters are based on the mother wavelet selected for the transform [1]. Lossy compression is obtained, when only a limited number of coefficients from the decomposition are retained.
pP
M
Indices to clusters Clustering
1
Indices to clusters
Spectral reduction
M
K
Cluster table
1
Original image
R
Reduced cluster table
1 R
Figure 1. Clustering of the image according to similar spectra. Spectral reduction in the cluster table. The number of bands in the original image is M , in the reduced image K , K < M . The number of clusters is R. The reconstruction of the spectra is based on those retained coefficients. 3. CLASSIFICATION AND SELECTION METHODS In this section we describe a method, that selects an appropriate wavelet filter for the compression method described in Section 2. The selection method is based on neural networks, we compare our implementation of selforganization map (SOM) to learning vector quantization (LVQ). In our case, every component from the spectrum is used in training and classification. Another possibility is to calculate some features from the spectra [2] and use only those features in training and classification. Some spectra from three multispectral images are used as a training set and other spectra from the same images are used in testing the quality of the training. The a priori classification of the selected spectra is obtained by compressing the spectra with different compression ratios and with different wavelet filters. Different compression ratios may result to different, best wavelet filters. In the experiments, we used compression ratio CR = 32=8 = 4. The following two algorithms define the selection of the best wavelet filter for the compression of the multispectral images using the compression method explained in Section 2. The Algorithm 1 defines the training set and the classification of each spectrum in the training set. Algorithm 1: classification of the training set. 1. Select the training spectra from the images. 2. Compress the spectra with different wavelet filters with different compression ratios. Now 8 coefficients out of 32 are selected. 3. Calculate the SNR between the compressed and reconstructed spectra. 4. Find the highest SNR and the corresponding wavelet filter for each spectrum. 5. Train the neural network to respond correctly to each spectrum. 6. Store the classification results into a database. The main result from the Algorithm 1 is the classification of the training spectra: each training spectrum is clas-
sified to be included into one class which has one wavelet filter associated. Now, each class contains spectra, which are best compressed with the same wavelet filter. The whole multispectral image can be compressed with one wavelet filter, which is selected by the Algorithm 2. Algorithm 2: selection of the wavelet filter. 1. Select some spectra from a multispectral image, which is to be compressed. 2. Classify the selected spectra using the stored classification results from the Algorithm 1. 3. Create the histogram from the classification of the selected spectra. 4. Find the highest occurrence in the histogram and select the associated wavelet filter to compress every spectrum in the image. The Algorithm 2 is based on the classification results from the Algorithm 1. With new images, only the Algorithm 2 needs to be run, since it can find an appropriate wavelet filter to compress the multispectral image at hand. The execution time of the Algorithm 2 is much lower than that of the Algorithm 1. The quality of the Algorithm 2 depends on the classification results from the Algorithm 1. If several types of spectra from multispectral images are used in the Algorithm 1, then better results can be expected from the Algorithm 2. 4. RESULTS FROM EXPERIMENTS The training set consisted of 3*1024 spectra and the test set also of 3*1024 spectra. The sets were taken from three multispectral images, which were of size 256*256*32 and they were a landscape in AISA format [6], AVIRIS image from the Moffet field [10], and a BRISTOL image of a flower leaf [11]. One spectral band of each image is shown in Figure 2. The wavelets used in the compression were the ChuiLian multiwavelet, the Haar wavelet, the Daubechies wavelets with 4 and 6 taps and two biorthogonal wavelets: the first one had 6 taps in lowpass decomposition and 2 taps in reconstruction and the second one had 9 taps in lowpass decomposition and 7 taps in reconstruction.
Figure 2. The original images. From left to right: AISA, AVIRIS, and BRISTOL. Thus, we had both low and high regularity filters. In Figure 3, the filters are numbered from 1 to 6, respectively. We experienced also with other wavelet filters including both longer orthogonal filters and various biorthogonal filters. With our data sets, the selected six filters outperformed all others included in the initial experiments. The training spectra and the test spectra were classified with the learning vector quantization (LVQ) and with the self-organization map (SOM). The results from the classification with the two methods are shown in Table 1.
AISA 1000 900 800 700 600 500 400 300 200 100 0
1
2
3
4
5
6
5
6
AVIRIS 1000 900 800 700
Table 1. Number and percentage of correctly classified spectra. The total number of spectra in each set is 3*1024=3072.
600 500 400 300 200
method LVQ SOM
training set # % 2596 84.5 2747 89.4
test set # % 2565 83.5 2628 85.5
100 0
1
2
3
4
BRISTOL 1000 900 800 700 600
Since the classification of the training spectra was found, then the classification results could be applied to the whole multispectral images. The Algorithm 2 describes the procedure to select the best wavelet filter for the compression of the whole multispectral images. The classification results from the Algorithm 2 can be displayed using bar-graphs: there is a set of bars for each wavelet filter and the height of the bar shows the number of spectra, that were best compressed with that wavelet filter. 1024 test spectra were selected from each image. The classification results for each test image according to the Algorithm 2 are shown in Figure 3. The bars from left to right in each set are: classification using LVQ (black bar), classification using SOM (gray bar), and the correct classification (white bar). The correct a priori defined classification is included for reference. Now the wavelet filter, which is the most suitable for the compression of the whole image can be found as the highest bar. Thus, the Haar filter, filter number 2, can be expected to perform best with every image. The compression of the three images was performed with each wavelet filter. The results are shown in Table 2.
500 400 300 200 100 0
1
2
3
4
5
6
Figure 3. Classification of the test spectra from the three images. From top to bottom: AISA, AVIRIS, and BRISTOL. Bars from left to right for each filter: LVQ, SOM, and correct classification.
The two algorithms were applied also to two AISA images, 34 AVIRIS images and 29 BRISTOL images. The wavelet filters selected by our method are shown in Table 3, and the compression results with different filters are shown in Table 4. With our compression method, the compression ratio (CR) and the quality of the compression/reconstruction (SNR) depends also on the clustering and on the encoding/decoding method, not only on the wavelet transform used in the spectral reduction.
Table 2. Compression of the three images with the six wavelet filters. wavelet filter CL Haar DB 4 DB 6 Bi6.2 Bi9.7 AISA CR 9.65 SNR 22.46 AVIRIS CR 17.53 SNR 37.36 BRISTOL CR 4.00 SNR 22.08
10.24 10.06 10.15 10.03 10.06 22.60 19.76 17.72 19.48 15.62 17.71 17.69 17.66 17.63 17.69 37.67 36.25 31.68 36.33 28.51 4.06 4.08 4.03 4.01 4.07 22.30 21.05 19.75 20.48 17.89
Table 3. The wavelet filters selected for 2+34+29 images. wavelet filter CL Haar DB 4 DB 6 Bi6.2 Bi9.7 AISA LVQ 0 SOM 0 AVIRIS LVQ 0 SOM 0 BRISTOL LVQ 0 SOM 1
2 2
0 0
0 0
0 0
0 0
34 34
0 0
0 0
0 0
0 0
27 28
1 0
0 0
0 0
1 0
Table 4. Compression of 2+34+29 images with the six wavelet filters. wavelet filter CL Haar DB 4 DB 6 Bi6.2 Bi9.7 AISA CR 9.73 SNR 21.46 AVIRIS CR 24.07 SNR 35.13 BRISTOL CR 4.06 SNR 21.07
10.29 10.14 10.25 10.13 10.14 21.61 19.16 16.92 18.88 14.60 24.21 24.18 24.15 24.13 24.18 35.29 34.40 31.37 34.28 27.57 4.24 4.23 4.20 4.18 4.23 21.33 19.84 18.73 19.69 17.17 5. CONCLUSIONS
We have defined a method to select a good wavelet filter to compress multispectral images. The selection used a priori information from the classification process, and this information was stored in a database. The method was defined precisely and it gave good results with our test images. The selected wavelet filter performed well in the compression of the multispectral images. The classification gave good results, see Table 1: the correct classifications were from 78 % to 88 %. With the three test images, both methods (LVQ and SOM) gave the
correct selection of the wavelet filter, see Figure 3 and Table 2. With AVIRIS-image, the SOM gave slightly better classification results than LVQ. AVIRIS-image could be compressed well also with multiwavelets. The same applied also to AISA-image: the multiwavelets were the second best selection in classification, but the Haar filter was almost always slightly better. With a larger set of images, the Haar filter was selected for almost every image, some variants arose only with the BRISTOL images. Our images had short spectra, and this may favor short filters. Similar results were obtained in [4]. Our method makes strict decisions in selecting the wavelet filter, the difference in the image quality determines, which filter is absolutely best. In practise, these differences can be very small, and, thus, good results can be obtained also with other filters. This can be seen from the results in Table 4, especially with AVIRIS images. References [1] I. Daubechies, Ten Lectures on Wavelets, CBMSNSF, 61, SIAM, USA, 1992. [2] R. M. Haralick, K. Shanmugam, and I. Dinstein, ”Textural Features for Image Classification”, IEEE Trans. on Systems, Man, and Cybernetics, SMC-3, no. 6, pp. 610–621, Nov. 1973. [3] M. Hauta-Kasari, K. Miyazawa, S. Toyooka, and J. Parkkinen, ”Spectral Vision System for Measuring Color Images”, The Journal of the Opt. Soc. of Am. A (JOSA A), vol. 16, no. 10, pp. 2352–2362, Oct. 1999. [4] A. Kaarna and J. Parkkinen, ”Multiwavelets in Spectral Image Compression”, Proceedings of 11’th SCIA, June 7–11, 1999, Kangerlussuaq, Greenland, pp. 327–334. [5] A. Kaarna, P. Zemcik, H. K¨alvi¨ainen, and J. Parkkinen, ”Compression of Multispectral Remote Sensing Images Using Clustering and Spectral Reduction”, IEEE Tr. on Geoscience and Remote Sensing, vol. 38, no. 2, pp. 1073–1082, Mar. 2000. [6] K. M¨akisara, ”The AISA data user’s guide”, VTT Research Notes, Espoo, Finland, 1998. [7] A. H. Tewfik, D. Sihna, and P. Jorgensen, ”On the optimal choice of a wavelet for signal presentation”, IEEE Transactions on Inform. Theory, vol. 38 no. 2, pp. 747–765, Mar. 1992. [8] V.D. Vaughn and T.S. Wilkinson, ”System Considerations for Multispectral Image Compression Designs”, IEEE Sign. Proc. Magazine, pp. 19–31, Jan. 1995. [9] J. D. Villasenor, B. Belzer, and J. Liao, ”Wavelet filter evaluation for image compression”, IEEE Transactions on Image Proc., vol. 4, no. 8, pp. 1053–1060, Aug. 1995. [10] www-site: http://makalu.jpl.nasa.gov/aviris.html [11] www-site: http://www.crs4.it/gjb/ftpJOSA.html
