Length measurements in digital images by using an anchored discrete convolution algorithm

Abstract

A digital image could be used as a source of data for various dimensional measurements. After acquiring the digital image of the measured object, the object contour is determined. The contour is composed of a sequence of distinct pixels which contain centre points. This is a representation of a digital curve or digital arc from which the object length or the perimeter could be determined. In order to calculate the approximate length of the object, we introduce a new algorithm called an anchored discrete convolution. The algorithm is based on a discrete convolution by using different convolution masks and points anchored in the pixels. Unfortunately, the use of an ordinary convolution distorts the curve shape and introduces large errors in length calculation. In our case the anchoring limits the point shifting into the pixel area during the calculation of the curve length. In this paper different convolution masks are used on an experimental digital curve in order to evaluate the presented algorithm as a measuring tool. In addition, different real objects were optically scanned and the perimeters of the objects were determined from the acquired images.