Segmentation of 3-D Textured Images Using Continuous Wavelet Transform

A (‘oni1non assumpt,ion of the shape from texture problc~ri s that i i perceived imago mainly contains only one type of texture with the sanic’ surface orientation. Unfortuiiatelly. a natural image is often composed of more than onc: t,exures. In order t,o solve the shape from tcxturc problern in a practical manner, we need to segment, 3D textured images. In this paper, we propose a new algorithm for the task. PVe estimate the local surface orientations from the the scales of the ridge points of continuous wavelet transform. Then, the local surface orientations are used as the features for texture segment,ntion. Textured images synthesized from Brodatz’s albu~ri and scvtrral natural images denionstrate the perforniance of our method. 1. I N T R O D U C T I O N Shape from texture is an important problem in recovering 3-D scene information from a single image by using texture cue only [2][5][8][9][12]. In the literature, almost all the shape from texture methods assumo that the projected iniage is mainly composed of only one texture arid therefore the 3-D scgment,ation problem is avoided. However, there are oft,eri more than one texture appearing in our perceived images (see an example s1io~v-n in Fig. 1). In order to solve the shape from texture problem in a practical manner, the 3-D text,ure image segIrientation must be taken int,o account. 3-D textured image segmentation differs from its 2-D counterpart in that the features commonly used in 2-D texture segmentation is no longer suitable, the projection effects should be considered. Krurnm and Shafer [7][8] had firstly presented a 3-D textured image segmcntatiori method. In their algorithm, they estimated the local frontal frequency by applying their shape from texture method to a local patch. The local frontal frequency was used later as the feature for texture segmentation. The accuracy of their algorithm depends on the number of patches and their sizes. Figure 1: A scene contains regions of window, brick wall, arid road. In this paper, we propose a new 3-D textured iniage segmentation method by using local surface orienthtions as feat,iires. Based on oiir prcvious shape from texture methods [5][9], the frequency variations of perspectively projected iniages are charact,erized by the ridge surface of c:ont,iniious wavelet, transform with the scale, tmnslation, and rotation pararritrtcrs. For simplicity, t,hr ridge points are t,he cwnt,iniioiis wavelet, transforni coc+€cients which are tho iriodiiliis local Inaxima among all the scales and direct,ions. iVit,h t,he sc:alt> parameter, we obtain the degree of frcyuency variations, with the rotation parameter, wc’ know at which ion the maximal frequency variations is. The ridge surface of a continuous wavelet transform marks the places in the spatial frequency domain where t,he energy of an image is mostly concentrated [4]. The scales of a ridge surface is derived to 1 ~ : a parabolic function of the slant and the tilt angles. The surface orientation is solved by fitting the scales of t,lie ridgr 235 0-8186-8183-7/97 $10.00