Color Image Wavelet Compression Using Vector Morphology Martha Saenz † , 5XúHQÖktem ‡ , Karen Egiazarian ‡ , Edward J. Delp † † Video and Image Processing Laboratory Purdue University West Lafayette, Indiana 47906 USA ‡ Signal Processing Laboratory Tampere University of Technology, 33101 Tampere, Finland † This work was partially supported by a grant from the Rockwell Foundation to EJD. Address all correspondence to E. J. Delp at ace@ecn.purdue.edu ABSTRACT In this paper we explore a wavelet compression scheme for color images that uses binary vector morphology to aid in the encoding of the locations of the wavelet coefficients. This is accomplished by predicting the significance of coefficients in the sub-bands. This approach fully exploits the correlation between color components and the correlation between and within sub- bands of the wavelet coefficients. This compression scheme produces images that are comparable in quality to those of color zerotree tree encoders at the same data rate but is computationally less complex. 1. INTRODUCTION The wavelet transform has been successfully used in image coding since it allows localization in both the space and frequency domains [1, 2, 3]. Coders can then exploit the characteristics of the wavelet coefficients to achieve better efficiency. Successful approaches such as the zero- tree method introduced in 1993 by Shapiro [3], exploit the fact that the wavelet coefficients are correlated across sub-bands. This takes advantage of the inter-band dependencies of the wavelet coefficients, based on observation that there is a high correlation between the magnitudes of the coefficients from different sub-bands, corresponding to the same spatial location of the image. In [4, 5] intra-band dependencies of the wavelet coefficients are also exploited. There is concentration of energy around a neighborhood of the coefficients in a given sub-band when edges occur in the image, thus allowing for the prediction of the locations of these clusters within the sub-band. To exploit these dependencies, the prediction is done using a region growing approach. The inter-band dependencies are exploited by using morphology based prediction. The performance of this method is comparable to that of zerotree coders but is less complex. This work was extended and improved in [6] by the use of wavelet packets. Both of the techniques were developed for gray- scale images. In this paper we extend this approach to color images by concentrating on the use of predictors for sub-bands across different color components based on binary vector morphology. Section 2 of this paper describes the principles behind binary morphology and how it can be extended to binary vectors. In Section 3, these filters are then used to encode the location of significant wavelet coefficient. Section 4 presents our experimental results. 2. BINARY MORPHOLOGY Morphological filters are nonlinear signal operators that locally modify the geometrical features of a signal. Given a binary image X, and a 2-D binary structuring element B, the dilated image is defined as the union of all the pixels that fall under B when it is centered at each pixel in X [7]. The eroded image is similarly defined as the intersection of pixels that fall under B when centered at each pixel in X. Given a vector valued binary image Y, morphological filtering can be defined by using component-wise operators [8]. In this case, the structuring element can then be different for each component. The concept of morphological vector filters can be extended by using a scalar valued function that maps each vector y i to a scalar value d i . In our case, for a three component binary valued vector the mapping is d:{0,1} 3 Å ℜ [9]. Dilation is then the binary valued vector under the structuring element that has maximum d, and erosion would similarly, be the vector with the minimum d. Observe that different choices of d can potentially lead to different results. The