Feature Extraction Capability of Some Discrete Transforms Ja-Ling Wu and Wei-JOU Duh Department of Computer Science and Information Engineering, National Taiwan University, 10764, Taipei, Taiwan, R.O.C. Abstract Feature extraction is a fundamental operation of classification and pattern recognition. There are var- ious strategies for one- and multi-dimensional feature extraction. The transform domain features are very effective when the patterns are characterized by their spectral properties. A wellknown successful example is the speech recognition. In this paper the feature ex- traction capability of discrete cosine transform (DCT), Walsh-Hadamard transform (WHT), discrete Hartley transform (DHT) and their sign transformations are in- vestigated and compared for the recognition of two &- mensional binary patterns. It is shown, in this paper, that the noise immunity of the transform based feature extraction is rather promising. 1 Selection of Transforms The appliance of unitary transforms to feature extrac- tion had been discussed in [1,2]. Since the characteris- tics of speech signals are represented by their spectral properties, the adoption of unitary transformsfor speech recognition is very intuitive and effective [5]. There are several ways to extract features of 2- D patterns, such as amplitude features, histogram fe& tures, transform domain features and shape features. Some comparisons of various properties among the dis- crete Fourier transform (DFT), the Karhunen-Ldve trans form (KLT), the WHT and the Haar transform (HT) were given in [l]. M is well known that KLT is the opti- mum choice for signal decorrelation in the sense of mean square error and the DCT performs closest to the KLT for highly correlated inputs. Hence, the feature extrac- tion capability of the DCT is interesting. The DCT was first proposed in 1974 [3] and was proven to be of closest performance to the KLT for Markov-I signal class [4]. Thus it is natural to use DCT for feature extraction, classification and pattern recogni- tion. The previous works [l] shown that the DFT per- forms better than other unitary tra.ns€ormsin pattern classification applications. Since the transform kernel of DHT is very similar to that of DFT, the performance of the DHT is believed to be comparable to that of the DFT. Recently, Ersoy had proposed a new two - stage representation of the DFT [5]. In his work the compu- tation of the DFT was decomposed into pre- and post - processing stages by using MWius inversion formula [6]. The pre-processing stage of the two-stage DFT consists of fl, ktj and their combinations; the post- processing stage consists of several independent con- volvers or correlators of smaller sizes. The two-stage representation of the DFT is not only a fast algorithm but also provides a new tool for feature extraction. The simple pre-processing stage can be treated as a new transform called discrete rectangular wave transform (DRWT). Ersoy et al. have used the DRWT in speech recognition [7] and image recognition [8,9] and the results are re- markable. From the derivation of the two-stage DFT (51, the sine and cosine function can be represented in number- theoretic bases. It is clear from [5] that the DRWT is, in fact, the sign transformation of the DFT. Some sim- ilar works of the two-stage representations of the DHT [lo] and DCT [ll] were also given. Following the fea- ture extraction concepts of the DRWT [7,8,9], the sign transformations of the DHT and DCT are also taken into consideration in the pattern recognition applica- tions. Therefore, the feature extraction capability of five different discrete transforms, including the WHT, DHT, DCT, DHT-sign and DCT-sign, are investigated in detail. CH 30064/91/0000-2649 $1.00 0 IEEE