Ž . Ž . Figure 3 Measured E-plane y z plane and H-plane x z plane Ž. radiation patterns for the proposed antenna shown in Figure 2. a Ž. Ž. f 1975 MHz. b f 2035 MHz. c f 2085 MHz Figure 4 Measured maximum received power in the broadside direction against frequency for the proposed antenna shown in Figure 2 grated reactive loading has been proposed and successfully implemented. The obtained wide antenna bandwidth is formed by a group of three closely excited resonant modes, and can be as large as 4.5 times that of a simple triangular microstrip antenna. Good radiation characteristics for the frequencies within the operating bandwidth are also ob- served. REFERENCES 1. S.T. Fang, K.L. Wong, and T.W. Chiou, Bandwidth enhancement of inset-microstrip-line-fed equilateral-triangular microstrip an- Ž . tenna, Electron Lett 34 1998 , 21842186. 2. S.E. Davidson, S.A. Long, and W.F. Richards, Dual-band mi- crostrip antennas with monolithic reactive loading, Electron Lett Ž . 21 1985 , 936937. 1999 John Wiley & Sons, Inc. CCC 0895-247799 DESIGN OF ROTATION, ILLUMINATION, AND TEXTURE-INVARIANT COMPOSITE FILTERS FROM RANGE IMAGES USING SIMULATED ANNEALING FOR FACE RECOGNITION Shizhuo Yin, 1 David Duarte, 1 and Purwadi Purwosumarto 1 1 Department of Electrical Engineering The Pennsylvania State University University Park, Pennsylvania 16802 Recei ed 30 April 1999 ABSTRACT: In this paper, the design of composite filters from range images using the simulated annealing technique for robust face recognition is discussed. Due to the use of range images as the training set for the synthesis of composite filters, besides the out-of-plane rotation in ariance, the designed composite filters are also inherently insensiti e to the ariation in the illumination and texture of the object. In addition, since the correlation operation can be done in the 2-D domain, the required processing time for 3-D range data is also substantially reduced. The experimental results show that the maximum responses of the antitarget are always less than the minimum response of the target, e en in the case where multiple faces are in ol ed, which demonstrates the feasibility of the proposed technique. 1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 151155, 1999. Key words: optical filter; optical imaging; 3-D imaging I. INTRODUCTION Ž Methods for face recognition and, in general, object recogni- . tion have been proposed in many different ways that can be . roughly classified into two categories: 1 based on 2-D im- . ages, and 2 based on 3-D images. To recognize the faces from the 2-D images taken from the objects, a variety of approaches were proposed, such as using geometric parameters of distinguishable features 1, gray-level distribution 2 , neural networks 3 , computation from templates and features 4 , parametric eigenspace 5, wavelet filters 6 , the generation of a face space 7 , silhou- ette information 8 , and correlation 9 , just to mention a few. The authors apologize for the possibility of omitting some important references. In the cases where the 3-D information is available, sev- eral different approaches have been employed. One approach involves the use of the profile silhouette to perform the face recognition task 10, 11 . Other approaches do not limit themselves to consider the silhouette information only. For example, range images of face surfaces were proposed for pattern matching 12 , and the use of surface curvature classi- fication for the description and recognition of faces from 3-D data was also discussed 13 . Although the use of 3-D data is alluring due to its ability to solve many constraints of 2-D techniques, it also proves to be somewhat inconvenient. One of the major limitations is that the use of 3-D information may require the use of special computational capabilities due to the amount of data needed to be processed. Furthermore, at a given time, only 2-D images may be available to perform the authentication procedure; even the reference function is a 3-D profile. As an alternative for the use of 3-D data, techniques such as the ones mentioned in 10 and 11 offer a way to reduce the computational expense, but some useful range information may be discarded. In addition, use of the high-speed nature MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 23, No. 3, November 5 1999 151