Analysis of Interferometric Images Using the Hough Transform

The Hough transform is adapted to determine fringe spacings and orientations of noisy interferometric images consisting of one or more superimposed Young’s fringe patterns. These measurements are used to calculate the deformation of concrete under stress, and are part of an investigation into the impact of traffic flow on bridge stability. Introduction: A specklegram is a double-exposed negative produced from two speckle patterns of a specimen, such as a concrete column, taken before and after deformation. It consists of corresponding point pairs separated by a distance which is the product of the deformation and the magnification of the system. When the negative is illuminated with an unexpanded laser beam, Young’s fringes are produced which are analyzed to determine their spacing. Each measurement is part of a map of displacement or deformation. Method: Image analysis techniques are commonly used in fringe analysis, for instance Fourier transforms, autocorrelation and intensity maximisation along radial strips [1,2]. These methods may not be suitable when the quality of the data is low. The Hough transform [3] is a good alternative because it operates well even when data is noisy or missing. It is used for detecting and locating lines, circles and other shapes and accumulates evidence for image features by a voting scheme; more precisely it refers to any algorithm which generates a parameter space with the intention of finding peaks representing properties of the original data. Young’s fringes, also called cos2 fringes, are characterised by an orientation (θ), frequency (ω) and phase (φ) (Figure 1). The orientation can vary between 0° and 180° (due to symmetry); the phase between 0° and 360° and the frequency range is related to the expected fringe spacing measurements. The required precision of these parameters determines the quantisation of its axis in Hough space: coarser for speed and finer for accuracy. The intensity offset (I) and amplitude (α) can be determined by appropriate normalisation of the data. A Hough transform line finder is used by Pieralli [4]. The fringe image is binarised and the HT applied to find the peaks of polar coordinates space thereby locating the fringes. Similarly, Shapiro et al. [5] use the same representation to analyze grey-level images. The parameter space contains a row of peaks at the desired orientation each separated by a fringe spacing. This is obtained by applying a Fourier transform to extract the dominant frequency. Our parameterization does not require an additional FT to be applied. A fringe image consists of parallel lines of constant intensity, and the continuous HT arbitrarily chooses high intensities as significant, ignoring valuable data. Another disadvantage of the continuous HT is that low intensity values, actually belonging to the troughs of the fringes, do not contribute towards the parameter space. Our approach weights all data equally. The conventional Hough transform method scans an image, and for each local region or image pixel, determines the elements to increment in parameter space. At the end of this process the parameters identifying the element with the largest number of votes best characterise the shape. Our approach performs the reverse of this process and is a variant of template matching. It creates the Hough space by scanning through all parameter values and finding the number of votes for each element. Instead of data