Natural representations for straight lines and the Hough transform on discrete arrays
- 1 January 1989
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Ieee Transactions On Pattern Analysis and Machine Intelligence
- Vol. 11 (9), 941-950
- https://doi.org/10.1109/34.35497
Abstract
The grid of discrete sampled data points in a digital image supports a limited set of lines at angles and displacements 'natural' to that grid. The effect of this implicit line quantization on the parametrization of the Hough transform is presented. The function describing the discrete Hough transforms line-detection sensitivity is derived. Expressions for the orientation, frequency, and popularity of lines in the natural set are given. The results obtained are of importance to data arrays of small size. The distribution of lines in the natural set is also important as it determines the precision and reliability with which straight lines can be measured on a discrete imaging array. From the natural line set concept, a general (a,d) slope/offset straight-line parametrization is developed for which the Hough transform is compact and fast to compute, and which is as easy to interpret as the class (p, theta ) parametrization.Keywords
This publication has 19 references indexed in Scilit:
- Improved localization in a generalized Hough scheme for the detection of straight edgesImage and Vision Computing, 1987
- Contribution to the Prediction of Performances of the Hough TransformIeee Transactions On Pattern Analysis and Machine Intelligence, 1986
- Accuracy issues in measuring quantized images of straight-line featuresPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1986
- Spirograph Theory: A Framework for Calculations on Digitized Straight LinesIeee Transactions On Pattern Analysis and Machine Intelligence, 1984
- Discrete Representation of Straight LinesIeee Transactions On Pattern Analysis and Machine Intelligence, 1984
- Inherent Bias and Noise in the Hough TransformIeee Transactions On Pattern Analysis and Machine Intelligence, 1983
- Discretization errors in the Hough transformPattern Recognition, 1981
- Geometric Constructions for Predicting Hough Transform PerformanceIeee Transactions On Pattern Analysis and Machine Intelligence, 1979
- On the detection of structures in noisy picturesPattern Recognition, 1977
- Use of the Hough transformation to detect lines and curves in picturesCommunications of the ACM, 1972