2154 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 16, NO. 8, AUGUST 2007 Table I summarizes the character recognition and error rate results. A substitution error happens when the OCR wrongly classifies the nu- meral character, while a rejection error happens when the OCR rejects its low confidence classification of a numeral character. The ICSSG algorithm performed significantly better than other segmentation algo- rithms. It resulted in the highest recognition rate, and the lowest sub- stitution and rejection rates, which means that it consistently preserved the handwritten characters. The execution times of the algorithms on a Pentium 4 processor (2.6 GHz) are also reported in the table. The proposed algorithm’s time is shorter than other algorithms that use local window operations, which seem to slow their execution. IV. CONCLUSION In this paper, we presented ICSSG, an algorithm for handwritten character segmentation that tracks the characters’ growth at equally spaced thresholds. The iterative thresholding reduces the effect of information loss associated with image binarization. It also acts as an intermediate stage between processing gray-level images and pro- cessing binary images, in term of complexity and range of information availability. Processing a binary image is simple, but uses a limited amount of information, while processing gray-level images is more complex, but has access to more information. ICSSG preserves the characters’ skeletal structure by preventing the interference of pixels that cause the flooding of adjacent characters’ segments. Experimental results showed significant improvement in OCR recognition rate compared to other well-established segmentation algorithms. REFERENCES [1] M. Cheriet, J. N. Said, and C. Y. Suen, “A recursive thresholding tech- nique for image segmentation,” IEEE Trans. Image Process., vol. 7, no. 6, pp. 918–921, Jun. 1998. [2] A. Dawoud and M. 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Baret, “Handwriting recognition as an application of regularities and singularities in line picture,” in Frontiers in Hand- writing Recognition. Montréal, QC, Canada: Concordia Univ., 1990, 23–36. [9] Y. Solihin and C. G. Leedham, “A new class of global thresholding techniques for handwriting images,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 8, pp. 761–768, Aug. 1999. [10] T. Suzuki and S. Mori, “Structural description of the line images by the cross section sequence graph,” Int. J. Pattern Recognit. Artif. Intell., vol. 7, pp. 1055–1076, 1993. [11] O. D. Trier and A. K. Jain, “Goal-directed evaluation of binarization methods,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 17, no. 12, pp. 1191–1201, Dec. 1995. [12] S. D. Yanowitz and A. M. Bruckstein, “A new method for image seg- mentation,” Comput. Vis. Graph. Image Process., vol. 46, pp. 82–95, 1989. [13] M. Zhao, Y. Yang, and H. Yan, “An adaptive thresholding method for binarization of blueprint images,” Pattern Recognit. Lett., vol. 21, no. 927–943, 2000. Estimating Planar Surface Orientation Using Bispectral Analysis Hany Farid and Jana Koˇ secká Abstract—In this correspondence, we propose a direct method for esti- mating the orientation of a plane from a single view under perspective pro- jection. Assuming that the underlying planar texture has random phase, we show that the nonlinearities introduced by perspective projection lead to higher order correlations in the frequency domain. We also empirically show that these correlations are proportional to the orientation of the plane. Minimization of these correlations, using tools from polyspectral analysis, yields the orientation of the plane. We show the efficacy of this technique on synthetic and natural images. Index Terms—Shape from texture. I. INTRODUCTION Many visual cues reveal the 3-D structure of a scene and relative pose of the camera with respect to the scene. While many of these cues are present in multiple views (disparity, optical flow), several others are already present in a single view. Gibson suggested, for example, the use of texture gradients and vanishing lines [7], while others proposed the use of shading gradients, e.g., [4], [9], and [16]. Since then, several different computational models based on these mechanisms have been proposed. These techniques differ in the assumptions made about the scene appearance and structure, the types of measurements used, and the computational methods employed for estimating shape or pose. Feature-based techniques use elementary geometric features (points, lines, circles) and additional assumptions (orthogonality, co-planarity, eccentricity) to estimate the projective mapping between the world and the image plane, e.g., [1], [12]. These methods are most applicable when the desired features are easily extracted from the image. The class of techniques termed “shape from texture” have also been popular, particularly when explicit features are not readily available in an image [10]. One class of techniques directly use filtered outputs of the image intensities. As with the feature-based techniques, certain as- sumptions are made regarding the spatial texture properties. The most standard assumption is one of homogeneity. With this assumption, the 3-D structure is estimated by first measuring local deformations of the texture, and then explicitly parameterizing them in terms of surface slant and tilt. In this setting, both orthographic and perspective pro- jections models have been considered, e.g., [5] and [19]. Additional assumptions of isotropy, e.g., [6], and symmetry can also be made. In these cases, the observed violation of the assumed statistical proper- ties of texture elements, characterized by their gradient orientations, Manuscript received October 4, 2005; revised April 22, 2007. H. Farid was supported in part by an Alfred P. Sloan Fellowship, in part by a National Science Foundation CAREER Award (IIS-99-83806), and in part by a departmental Na- tional Science Foundation Infrastructure Grant (EIA-98-02068). J. Koˇ secká was supported by a National Science Foundation CAREER Award (IIS-03-4774). The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Anil Kokaram. H. Farid is with the 6211 Sudikoff Laboratory, Computer Science Depart- ment, Dartmouth College, Hanover, NH 03755 USA (e-mail: farid@cs.dart- mouth.edu). J. Kosecka is with the Department of Computer Science, George Mason Uni- versity, Fairfax, VA 22030 USA. Digital Object Identifier 10.1109/TIP.2007.899629 1057-7149/$25.00 © 2007 IEEE