The Hough Transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve. This paper generalizes the Hough Transform to detect arbitrary shapes in grey-level images. The original Hough Transform was used for detecting analytic curves like lines, circles, and parabolas, but it was limited to binary edge images. The generalized Hough Transform uses edge information to define a mapping from the orientation of an edge point to a reference point of the shape. This mapping allows the detection of instances of that particular shape in an image. Variations in the shape, such as rotations, scale changes, or figure-ground reversals, correspond to straightforward transformations of this mapping. The most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler, component shapes. This makes the generalized Hough Transform a universal transform that can be used to find arbitrarily complex shapes. The paper describes the Hough Transform for analytic curves, including the ellipse, and discusses the generalization of the algorithm to arbitrary shapes. It also presents the R-table, a table used to detect instances of a shape in an image. The R-table is constructed by examining the boundary points of the shape and quantizing the gradient direction. The generalized Hough Transform can be used to detect composite shapes by combining the R-tables of simpler shapes. The paper also discusses incrementation strategies, including weighting locally consistent information and using pairs of edge pixels to reduce the effort in parameter space. The algorithm is described as a parallel algorithm that can be used to detect shapes in images. The paper concludes that the generalized Hough Transform is a powerful tool for detecting arbitrary shapes in images.The Hough Transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve. This paper generalizes the Hough Transform to detect arbitrary shapes in grey-level images. The original Hough Transform was used for detecting analytic curves like lines, circles, and parabolas, but it was limited to binary edge images. The generalized Hough Transform uses edge information to define a mapping from the orientation of an edge point to a reference point of the shape. This mapping allows the detection of instances of that particular shape in an image. Variations in the shape, such as rotations, scale changes, or figure-ground reversals, correspond to straightforward transformations of this mapping. The most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler, component shapes. This makes the generalized Hough Transform a universal transform that can be used to find arbitrarily complex shapes. The paper describes the Hough Transform for analytic curves, including the ellipse, and discusses the generalization of the algorithm to arbitrary shapes. It also presents the R-table, a table used to detect instances of a shape in an image. The R-table is constructed by examining the boundary points of the shape and quantizing the gradient direction. The generalized Hough Transform can be used to detect composite shapes by combining the R-tables of simpler shapes. The paper also discusses incrementation strategies, including weighting locally consistent information and using pairs of edge pixels to reduce the effort in parameter space. The algorithm is described as a parallel algorithm that can be used to detect shapes in images. The paper concludes that the generalized Hough Transform is a powerful tool for detecting arbitrary shapes in images.