An Objective Criterion for the Selection of an Optimum DIC Pattern and Subset Size

The grey level co-occurrence matrix (GLCM) is used in this work for quantitative spatial texture description. The two GLCM metrics, offset and contrast, are used to quantify spatial intensity variation. It is shown that the optimal DIC pattern must possess low critical GLCM offset and high nominal GLCM contrast. A very strong correlation between the critical GLCM contrast and the correlation window size is observed. It is shown that displacement resolution of 0.01 pixel can be achieved if the correlation window size is approximately 3 times bigger than the critical GLCM offset. The method has been tested on over 60 structured speckle and non-structured random smoothed patterns. The proposed method is fully automatic and allows for the optimal pattern and the optimal correlation window size to be chosen in a systematic and fully objective manner based the pattern alone, with no need for the trial DIC experiments. Introduction It is well known that performance of DIC algorithms depends strongly on various correlation settings. Of crucial importance is the size of the correlation window (also called subset), because it affects both the accuracy and the resolution. Bigger correlation windows improve the accuracy but reduce the spatial resolution, while smaller correlation windows increase the spatial resolution at the expense of lower accuracy. Therefore a DIC experimentalist is always forced to adopt an optimal correlation subset as a trade-off between the accuracy and the resolution. Since most, if not all, DIC algorithms rely on statistical uniqueness of each correlation subset, the optimal correlation window size depends on image contents. It has been previously observed experimentally that there is a strong positive correlation between the optimal size of the correlation window and the size of characteristic features in images. For example, for some speckle-based patterns the optimal correlation window was previously reported in the order of 3 speckle sizes [1]. However, it is not clear whether this guide is applicable to a wide range of patterns, including non-speckle patterns. The DIC pattern itself is usually chosen based on researcher’s previous experience and with some trial and error measurements. The existing guides for selecting a pattern for a DIC experiment are at best qualitative, and at worst very vague. In the following sections we describe and verify a new quantitative method for pattern selection and for choosing the optimal correlation window based on the grey level co-occurrence matrix (GLCM) approach. First the GLCM is described. Then the critical GLCM offset is introduced and linked to the spatial variation in the image. Then the GLCM metrics which the optimal DIC patterns must possess are described. Finally it is shown how the critical GLCM offset determines the correlation window and displacement resolution. The Grey-Level Co-occurrence Matrix (GLCM) First order statistical pattern characterisation measures, e.g. intensity histogram, can provide some useful information on the contrast and variance. However, first order methods cannot provide any spatial information. The spatial arrangement of the grey level pixels that make up a pattern is commonly referred to as the texture of a pattern. Various texture descriptors are available, e.g. fractal methods, spatial frequency techniques or statistical methods [2]. Proceedings of the XIth International Congress and Exposition June 2-5, 2008 Orlando, Florida USA ©2008 Society for Experimental Mechanics Inc. A common and effective texture descriptor is a second order statistical method known as Grey-Level Co-occurrence Matrix (GLCM) [3]. The GLCM method applies equally well to structured and non-structured patterns. A structured pattern is a pattern that is made up of structural primitives. A typical example of a structured pattern is a speckle pattern. A non-structured pattern has no repeated elements. An example of a non-structured pattern is a gradient image, or, as in this work, a smoothed random distribution of intensity [4]. In the GLCM method the occurrence of two pixel values located a certain distance one from another (offset) is calculated for every possible combination of pixel values. The offset is defined as the distance and direction of occurrence of certain grey values. Different GLCM, capturing different spatial characteristics of an image texture, can be achieved by varying the offset. An element of GLCM matrix is GLCM(i, j) and we use notation GLCM(i, j) = p to mean that there are p occurrences of pixels having intensity value i located a specified offset from pixels having intensity value j. 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 1 0 2 0 1 0 0 0 0 0 0 1 0 0 1 1 0 Fig. 1 gives an illustration of GLCM calculation for the case when offset is one pixel to the right of the pixel in question. In Fig. 1a intensity value 3 appears directly to the right of 1 twice, therefore the component (1,3) in the GLCM is 2. Likewise, the value 4 is directly to the right of 3 in three places so GLCM(3,4)=3. On the other hand the fact that GLCM(1,1)=0 means that there are no two pixels with intensity 1, located side by side. (a) image fragment (b) GLCM Figure 1: Schematic of GLCM calculation showing (a) a 4× 4 pixel image fragment and (b) its GLCM. Smooth images will have similar grey-level values occurring next to one another. Therefore GLCM of smooth images with offset of 1 pixel will have large diagonal terms as shown in Fig. 2b. In contrast, images with non-smooth, discontinuous intensity changes feature very different grey-level values in close proximity. Therefore the GLCM of such images will have higher off-diagonal terms. High off-diagonal GLCM terms can also be achieved by increasing offset on smooth images. As the offset is increased the intensity values are no longer likely to be similar. This leads to lower diagonal, and higher off-diagonal GLCM terms as shown in Fig. 2c. (a) smooth image (b) GLCM, offset is 1 pixels (c) GLCM, offset is 35 pixels Figure 2: Influence of offset on appearance of GLCM, showing (a) an image with gradually varying intensity, (b) its GLCM for offset of 1 pixel, and (c) its GLCM for offset of 35 pixels. The GLCM values are shown in grey scale, lighter colour represents higher values and darker colour represents lower values. Note that smaller offset (b) results in higher GLCM values clustered near the main diagonal, while higher offset (c) results in more high off-diagonal terms. GLCM critical offset The texture of an image can be described by deriving statistical data from the GLCM. The measure used in this work is contrast which is defined as: