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I.D. Svalbe, "Natural Representations for Straight Lines and the Hough Transform on Discrete Arrays," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 9, pp. 941950, September, 1989.  
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@article{ 10.1109/34.35497, author = {I.D. Svalbe}, title = {Natural Representations for Straight Lines and the Hough Transform on Discrete Arrays}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {11}, number = {9}, issn = {01628828}, year = {1989}, pages = {941950}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.35497}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Natural Representations for Straight Lines and the Hough Transform on Discrete Arrays IS  9 SN  01628828 SP941 EP950 EPD  941950 A1  I.D. Svalbe, PY  1989 KW  straight lines; discrete sampled data points; digital image; line quantization; linedetection sensitivity; natural set; discrete imaging array; computerised picture processing; transforms VL  11 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
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 linedetection 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 straightline 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.
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