What is the dimensionality of a Hough accumulator array if circles of all sizes

Question

What is the dimensionality of a Hough accumulator array if circles of all sizes are to be determined in a tu o-dimensional image? List all necessary accumulator array variables. Let an image consist of object and a back ground. Let the mean gray level and variance of the background be u: = 30. c: = 900, and the mean gray level and variance of the object be mu_2 = 90. sigma^2_2 = 400. Sketch the grayscale histogram and determine the optimal threshold assuming that the object occupy (i) 30% (ii) 60% of the image area.

Explanation / Answer

A) The Hough transform is a feature extraction technique used in image analysis, computer vision, and digital image processing.[1]The purpose of the technique is to find imperfect instances of objects within a certain class of shapes by a voting procedure. This voting procedure is carried out in a parameter space, from which object candidates are obtained as local maxima in a so-called accumulator space that is explicitly constructed by the algorithm for computing the Hough transform

necessary accumulator array variables

An array is like a group of variables with one name. All of the values stored within the array are called elements and are of the same datatype. You access the individual elements within an array by using a subscript. A subscript, also known as an index, is a number that identifies a specific element within the array.

Subscript numbering begins at 0 and so the subscript of the first element in an array is 0 and the subscript of the last element in an array is one less than the total number of elements in the array.

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