On the gray-scale inverse Hough transform A.L. Kesidis, N. Papamarkos * Electric Circuits Analysis Laboratory, Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100 Xanthi, Greece Received 12 April 1999; received in revised form 22 September 1999; accepted 25 October 1999 Abstract This paper proposes a gray-scale inverse Hough transform (GIHT) algorithm which is combined with a modified gray-scale Hough transform (GHT). Given only the data of the Hough transform (HT) space and the dimensions of the image, the GIHT algorithm reconstructs correctly the original gray-scale image. As a first application, the GIHT is used for line detection and filtering according to conditions associated with the polar parameters, the size and the gray-scale values of the lines. The main advantage of the GIHT is the determination of the image lines exactly as they appear, i.e. pixel by pixel and with the correct gray-scale values. To avoid the quantization effects in the accumulator array of the GHT space, inversion conditions are defined which are associated only with the image size. The GIHT algorithm consists of two phases, which are the collection of gray-scale information stored in the accumulator array and the extraction of the final image according to the filtering conditions. Experimental results confirm the efficiency of the proposed method.  2000 Elsevier Science B.V. All rights reserved. Keywords: Hough transform; Gray-scale Hough transform; Line detection 1. Introduction The Conventional Hough Transform (CHT) is a well- known technique for straight line detection in binary images. It is a voting process where each pixel of the image space votes for several possible patterns (straight lines) passing through that pixel. The votes are stored in an accumulator array, the peak values of which provide the parameters of the lines in the original image. The CHT is commonly used for straight line detection and was first introduced by Hough [1]. Duda and Hart [2] using the polar form of straight lines adapted the HT technique in discrete binary images. The advantages of the HT are associated with its robustness to image noise as well as its discrimination ability against unwanted shapes [3]. However, the HT can determine only the line parameters but not the exact position of the pixels in the lines. Other disadvantages of the HT are associated with its large storage and computational requirements. For this reason many approaches have been proposed in the literature, regarding the reduction of the computation time and memory require- ments while others have focused on the investigation of the nature of the HT space [4–14]. All these methods are appli- cable to binary images. Thus, the application of the CHT to a gray-scale image requires its conversion to a binary image. The main disadvantage of this approach is that the gray-scale information of the source image is lost. Until now, only a few methods have been proposed for using the HT in gray-scale images. Shapiro [15] used a method that replaces the original image by its digital half- toning (DH) equivalent. Specifically, several DH techniques that minimize the integral approximation error of using the DH Hough transform as an approximation of the Radon transform of a gray-scale image are investigated. In an approach proposed by Lo and Tsai [16] a four-dimensional accumulator array is employed. Specifically, each pixel x i ; y i  in the image space is associated with its gray-scale value g i and each accumulator cell Cu j ; r j; g i  in the so-called gray Hough parameter counting space is con- sidered as a function of three parameters r , u and g, where the definitions of r and u are the same as those of the CHT and g represents the gray-scale value. The method allows the extraction of the parameters of gray-scale lines but it is expensive in terms of storage space since it needs higher dimension HT space. This paper proposes a gray-scale inverse Hough transform algorithm, a new method that allows the correct inversion of the HT space. As a first application the GIHT can be used for straight line detection and filtering in gray- scale images. The GIHT algorithm can reconstruct the original image from the GHT space and determine lines Image and Vision Computing 18 (2000) 607–618 0262-8856/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0262-8856(99)00067-0 www.elsevier.com/locate/imavis * Corresponding author. Tel.: +30-541-79585; fax: +30-541-79569. E-mail address: papamark@voreas.ee.duth.gr (N. Papamarkos).