Modified Surface Fitting Algorithm using Digital Image Correlation for Effective Displacement Analysis

Modified Surface Fitting Algorithm using Digital Image Correlation for Effective Displacement Analysis

S.Agnes Shifani¹, M.S. Godwin Premi²

¹Research Scholar, Department of ECE, Sathyabama Institute of Science and Technology, Chennai

¹Professor, School of EEE, Sathyabama Institute of Science and Technology, Chennai

shifaniece2110@gmail.com, msgodwinpremi@gmail.com

Abstract

Displacement analysis utilizing surface fitting algorithm (SFA) is an essential technique in digital image correlation additionally with robust in computational complexity without noise interference in real time applications.  There is a need in expanding and improving the accuracy of existing surface fitting algorithm (E-SFA). In order to achieve this modified surface fitting algorithm (M-SFA) is proposed. Integrated interpolation technique utilized to search the pixel position and its corresponding gray level value in the displacement matrix and also obtain the weight co-efficient of the particular pixel. The proposed M-SFA is highly suitable in finding the initial displacement accuracy of the subpixel. The simulation results obtained in linear and nonlinear displacement shows that the calculation time is same but the calculation accuracy is increased in proposed M-SFA than the E-SFA

Keywords: Surface fitting, Bilinear interpolation, Nearest neighbor, ZMNCC, Displacement

1. Introduction

Surfaces are utilized in a structural displaying condition to represent various highlights of the sample. Surface fitting is the way toward acquiring surface conditions from distorted picture in a structure that is appropriate for later calculations. Surface Fitting Algorithm (SFA) for nonstop relocation is a significant strategy for computerized picture relationship with less noise capacity and computational productivity focal points in reasonable applications. An assortment of surface-fitting procedures exist to be specific polynomial strategy, Spline Laplacian technique, Kriging strategy, Least square fitting strategy utilizing cubic-b-spline, Finite component approach technique and the decision of system relies on the application and information assortment scheme [1].

Surface fitting systems can be extensively characterized into two classes: interpolation and approximation. As the name infers, interpolation schemes bring about surfaces that add the deliberate information at every datum point. Inexact methods, then again, locate a best coordinating point. Interpolation is utilized when the capacity esteems at the deliberate focuses are known to a high accuracy and it is alluring that these qualities be safeguarded by the fitted capacity [2]. Bilinear interpolation and adjacent interpolation are utilized to examine the gray level at any whole number pixel location in the dislodgment grid and the weight constant is given. The distance-weighted technique is utilized to estimate the actual initial dislodgment estimation of the continuity [3].

One class of subpixel DIC calculation fits a constant surface to the discrete correlation esteems discovered utilizing the DIC calculation, to fill the qualities between pixels close to the best coordinating point [4]. The beginning stage of the calculation is the Zero Mean Square Normalized Cross Correlation (ZMNCC) values for the best coordinating point and its eight closest neighbors, these are accessible as a result of the DIC calculation. The most extreme purpose of the fitted constant relationship surface gives the subpixel displacement [5]

Different surface fitting methods are utilized to fit the relationship surface. In four distinctive surface fittings calculations are utilized to fit the relationship surface to acquire the subpixel removal. The outcomes show binary quadratic surface fitting is quickest while the bi-quadratic Lagrange surface fitting technique gives the best precision. The fitting of the relationship surface as an explanatory capacity has likewise been utilized in subpixel DIC calculations. The correlation coefficient surface fitting techniques are generally agreeable to basic execution as they require scarcely any calculations; as an outcome, the time required to figure the subpixel displacement is moderately little [6]. Subsequently, one of the correlation coefficient surface fitting techniques is read further for auxiliary usage. The bi-quadratic Lagrange surface fitting technique, which gives preferred outcomes over the other surface fitting strategies, is picked [7]. By and large, the correlation coefficient surface fitting strategies give great outcomes to an example experiencing inflexible body interpretation. Be that as it may, the correlation coefficient surface fitting calculations don’t think about change looking like the distorted subset; this presents some error in the subpixel displacement estimations when disfigurement is huge

Surface fitting is a strategy of characterising enormous measure of information into a brief structure which is helpful for later calculations. A surface fitting issue can be presented in the figure 1,

Figure 1: Gridded data Collection

Let R be a domain in the (x, y) plane, and assume F is a genuine esteemed capacity characterized on D. Assume we know the qualities F (xi, yi) = Fi for some arrangement of focuses (xi, yi,) (I = 1, 2, . . ., N) situated in D. Find a function f characterized on D which sensibly approximates F. The space might be a rectangular lattice, wherein case the issue arrangement could be disentangled. In any case, for more real time applications D might be sporadic shape and the information is dispersed all through D. At the point when the measure of information is enormous, surface fitting can get mistaken and computationally costly. Be that as it may, so as to improve the calculation exactness and extend its application run, M-SFA is executed, which is appropriate for deciphering the preliminary estimation of uninterrupted dislodgment [9].

2. REVIEW ON REPRESENTATION AND CLASSIFICATION OF SURFACES

                This area depicts the absolute most basic representation and classification of surfaces. They are referenced underneath

• Grid
• Triangular mesh
• Subdivision surface
• Parametric surfaces
• Curved patches

1. Grid: This is a discrete rendition of an express surface.. Grids are generally simple to register yet since they are discrete one need to utilize an interjection strategy to acquire focuses on a superficial level between the lattice focuses. So as to display small details one needs to utilize a thick grid with poor compactness or to utilize a progressive grid. Grids are regularly utilized as a middle of the representation while building increasingly complex representations [10].

1. Triangular mesh: A level triangular work comprises of the 3D directions of a lot of focuses on a superficial level, and a structure that describes how these points associated in triangles. The mesh represents to a ceaseless however nonsmooth surface. The thickness of triangles in various regions on a superficial level can be differed on request to accomplish good approximations of the physical surface in zones with fine details or high arch without losing a lot of its compactness. Triangular meshes are a mainstream portrayal of surfaces with complex, and from the earlier obscure, topology. The straightforwardness of level triangular meshes emerges from the way that three focuses in 3-D are met by an exceptional plane, given that the focuses don’t lie on a straight line [11].

1. Subdivision surface: A mesh can be going with rules on the best way to subdivide it into a better work. By applying these standards, recursively, boundlessly commonly, one winds up with a surface with a higher level of smoothness than the first work. The level of smoothness relies upon the subdivision rules. The portrayal comprises of a unique work and the standards. It is appropriate to speak to smooth (or piecewise smooth) surfaces with complex geometries and topology. The disadvantage is that focuses on the surfaces are not given unequivocally [12].

1. Parametric surface: A parametric surface is the assortment of focuses (x, y, z) that can be composed as

x = f1(u, v), y = f2(u, v), z = f3(u, v)

where, (u, v) are the parameters of the surface. A trifling parametrisation is x = u, y = v, z = f(u, v) which is an unequivocal capacity surface. By picking different parametrisations progressively complex surfaces can be spoken to. The parametric methodology can be utilized when fitting a parametric B-spline, however other parametric choices are additionally conceivable. Parametric surfaces have various great properties however in fitting issues it very well may be elusive a reasonable parametrisation. They are utilized, in shifting structures, by the majority of the cutting edge CAD/CAM frameworks [13].

1. Curved patches: Compared to the level triangular mesh we get a progressively broad portrayal on the off chance that we permit bended patches with at least three sides. Most well known are the quadrilaterals which are utilized in tensor item surfaces and bended triangles, e.g., triangular Bezier patches. By joining requirements when sewing the extraordinary fixes together it is conceivable to speak to smooth surfaces of discretionary topology [14].

3. PROPOSED SURFACE FITTING ALGORITHM

This proposed work mainly utilized to determine the initial displacement which is based on the distance weight concept utilized in digital image processing shown in figure 2. M-SFA utilizes the integrated interpolation algorithm based on gray level. This integration includes bilinear along with nearest neighbor interpolation algorithm. Initially the pixel weight is calculated by moving template through entire surface of region of interest (ROI). Measure the subpixel value, based on this value the proposed algorithm M-SFA accuracy is verified through simulation.

Figure 2: Proposed work block diagram

To determine the initial displacement value, M-SFA measures the integrated interpolation outputs by finding the gray level value of the neighboring pixel 2 x 2 in both horizontal as well as vertical direction (ie 4 neighbor pixels) near to the interpolation point. Based on the gray level variance weighting coefficient constructed. At last, the final interpolation value is obtained based on the cumulative weight of two values from integrated interpolation method. The M-SFA finds the improved initial displacement accuracy of the subpixel by considering the gray level distribution of the neighbor pixels along with the distance between the neighboring and interpolation points.

4. performance Analysis

In demand to confirm the execution of M-SFA, the precision is tried by utilizing the computer simulated spot test. An alphanumeric spot picture is chosen as the reference casing, with the predetermined hypothetical dislodging field assumed. M-SFA and E-SFA are utilized for investigating the exploratory outcomes over the reproduced spot field which remade as the figuring mount. The dislodgment of the spot in the picture can be unequivocally constrained by utilizing the algebraic strategy to recreate speckle picture of the unchanging and changing hypothetical distortion field. The counterfeit dot picture size in Figure 2 is 256×256 pixels, and the concentration of the dot is Gaussian. The dot size is 4 pixels, and the quantity of dots is 200. The size of figuring window in SFA and M-SFA is 41×41.

4.1. Test with uniform deformation

The effectiveness of M-SFA and E-SFA is tried by utilizing the unchanging distortion field spot picture of Figure 3 (b). The dislocation of the spot field in Figure 3 (b) is appeared by

Relating counts are performed utilizing M-SFA and E-SFA individually. Figure 3 shows the parallel displacement field acquired by M-SFA and E-SFA.

It is initiate from Figure 3 that the disarticulations in M-SFA and E-SFA are stratified, and the stratification esteems are predictable with the realistic dislodgment work, demonstrating that mutually M-SFA and E-SFA can compute the unchanging dislocation field. The dislocation limit in the u-field cloud guide of M-SFA is flatter than that of E-SFA, and the dislocation limit of E-SFA is sporadically rugged, demonstrating that M-SFA is additional exact than E-SFA on count of unchanging dislocation field.

In Figure 5, the sidelong dislocation determined by M-SFA is nearer to the hypothetical worth, and the computation aftereffect of E-SFA has a specific nonconformity from the hypothetical worth, showing that the count exactness and security of M-SFA are improved than E-SFA. In Figure 5, the general fault of M-SFA in regular distortion field is around 0.9%, which is 50% lesser than E-SFA.

4.2. Test with non-uniform deformation

The advert image of non-uniform deformation is recreated numerically by M-SFA and E-SFA which is appeared in Figure 3 (c). The dislocation of the speckle field in Figure 3 (c) is appeared by

M-SFA and E-SFA are utilized, separately, to compute non uniform distortion fields and the territory examined is x=32∼44 pixel and y=1∼125 pixel. Figure 5 displays the sidelong dislocation field determined by M-SFA and E-SFA.

In the u-field nephogram, the dislocation limit of M-SFA is evener than that of E-SFA, which shows that M-SFA is improved than E-SFA in managing changing dislocation field. Particularly on account of large displacement, estimation of M-SFA is nearer to the hypothetical worth, while the benefit of E-SFA is lower, the primary explanation being that the underlying estimation of displacement choose by M-SFA is progressively exact.

(a)

(b)

(c)

Figure 3: (a) Reference image. (b) Uniform deformation field. (c) Nonuniform deformation field.

(a)

(b)

Figure 4: Uniform deformation (a) M-SFA. (b) E-SFA.

The information on the y= 40 pixel interface are chosen for fault examination. The abscissa facilitates in Figure 5 characterize to the pixel directions of x, and the ordinate organizes speak to the estimation of u.

(a)

(b)

Figure 5: Non-uniform deformation (a) M-SFA. (b) E-SFA.

From the figure 4 and 5 unmistakably the incline of distortion is huge, the determined consequence of E-SFA diverges from the hypothetical worth significantly, and M-SFA is nearer to the hypothetical worth, showing that the spatial determination and displacement determination of M-SFA are advanced than that of E-SFA and M-SFA is progressively appropriate for dissecting in the locale of the huge angle of dislocation.

The measured results are shown in Table 1. Displacement of the theoretical value is compared with the E-SFA and M-SFA started from 0.1 pixels to 10 pixels, displacement and error is measured. Results shows that measured displacement value is much closer to the theoretical value and the measured error of E-SFA is approximately 2.5 times that of M-SFA

Table 1: Measurement of Displacement and Error using E-SFA and M-SFA

4. Conclusion

This work brings the modified surface fitting algorithm based on distance weight idea. Digital speckle simulation utilized for verifying the accuracy of M-SFA.  M-SFA can be easily implemented in real time application due to the less computational complexity and high accuracy. Due to the high stability, M-SFA finds highly suitable in both uniform and nonuniform displacement fields. The final result in E-SFA is comparatively lower in measuring the continuous deformation in the region with more displacement. Measured error is also two and half times more than the M-SFA. Simulation results shows that the M-SFA has higher spatial resolution than the E-SFA. By comparing M-SFA and SFA with the actual theoretical value, results show M-SFA overcomes the E-SFA in terms of accuracy.

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