Calibration and Validation of an Experimental Setup for the Measurement of the Cylindrical Body Shapes and Curvatures of the Objects and Subjects through the Techniques of Rasterstereography

The intent of study is to establish a criterion for the experimental setup of rasterstereography, one that is more efficient, simple, accurate and precise to examine and analyse the curvature of the object or the subject. Firstly, the setup is needed to be calibrated and for this purpose we considered a reference plane, eleven cylinders of different diameter ranging from 30-119mm were used for calibration of curvature maps of cylinders and cylindrical objects through the regression line. Further this model was tested on subjects and for that we reckoned cylindrical body parts of boys and a total of 30 college students were involved as subjects in this process. The body parts to be measured had curvature like cylinders of different diameters ranging from 42-120mm. The distortion of raster grid was observed, quantified and recorded with the help of different tools and results were established. The regression line was obtained between the measured (x) and computed (y). The standard error of the cylindrical object was 0.04 and that of cylindrical body parts of subjects was 0.0407. This technique was validated through the coefficient of correlation for objects and subjects which was found to be 0.99982 and 0.999141 respectively. Accuracy and Precision were also calculated for this model, which were 99.60% accurate and 99.49% precise. Curvature maps were found more than 99%. This technique is inexpensive, reliable, reproducible and may be installed easily in hospitals to examine appraise body shape, composition and deformities of young men.

[10] developed a new method for biomechanical analysis of skeletal geometry using functional rasterstereographic images. Guarnieri, and Guarnieri [11]   The mean curvature is given by: (1) and the Gaussian curvature by: Instead of the principal curvatures themselves, these quantities can be used equally well for an invariant shape analysis.

Statement of the Problem
Researchers used this technique in some fields, but most of them applied in clinical sides. Specially this technique was used just to analyse the back shape, scoliosis, orthodontics and surface shapes of other body parts. It is surprising that after more than thirty years the benefits of rasterstereography are very far from the reach of humanity. This factor could be minimized by the new setup of rasterstereography.

Setup
Objects of various sizes were placed on reference surface. First of all, objects were aligned with the help of reference surface and spirit level. A raster grid placed on overhead projector and it was 1500mm away from object. A traveling telescope and camera vertically aligned in the same line, which were 1500mm from the object and 100mm from the Overhead Projector.
Experimental setup of Rasterstereography shown in

Method
A raster grid was projected on the object or Subject which was placed and aligned on reference plane. The periodic spacing on the reference surface (flat surface) is S and X is the periodic spacing on the curved surface(measured) and the distortions of the curved Object or Subject recorded with the help of traveling telescope and camera simultaneously and it is d (for the calculation of radius of curvature). A software was used for the calculation of radius of curvature.

Calculations
After measurements of periodic spacing of the plane surface "s" and periodic spacing of curved surface "d" for cylinders and Cylindrical body parts of the subjects, horizontal curvature (k 1 ), and vertical curvature (k 2 ), and radius of curvature (y) were calculated.
Radius of curvature 'y' is given by: Where is the curvature which is given by:

Calibration and Validation of an Experimental Setup for the Measurement of the Cylindrical Body Shapes and Curvatures of the Objects and
Subjects through the Techniques of Rasterstereography

Calibration and Validation of an Experimental Setup for the Measurement of the Cylindrical Body Shapes and Curvatures of the Objects and Subjects through the Techniques of Rasterstereography
andVertical curvature for the body part of different subjects (k 2 ) as shown in Fig. 5 and Table 2.
Graph between the Actual and Theoretical Radii for the cylindrical body parts of subjects which shows the results were more than 99 % correct that shown in Figs. 6-7.

Regression Line
A line was fitted between the measured (x) and computed radii (Y) of curvature of various objects and subjects (Tables 3-4 and Figs. 8-9)

Accuracy and Precision for Cylinderical Subjects
Accuracy and Precision of measurement of vertical curvature were calculated by taking five points on the surface of cylindrical body parts of the subjects as shown in Tables 5-7 and Figs. 10-11.
The reference value 'R' in the data is found to be as R=35.7398mm, which is close to actualvalue x = 35.81, x =35.5409, D=0.1821, D R =0.1434.

Statistical Analysis
For statistical analysis coefficient of correlation 'r' was calculated by: x y y where where y b x a   (11) where n x x   (12) and n y y

CONCLUSION
The technique was calibrated through the regression line for objects and subjects and validated through the coefficient of correlation and standard error and it was found that it is inexpensive, reliable, reproducible, efficient, effective and accurate. The rasterstereography setup may be installed easily in hospitals to examine the body deformities of the children.
Follow up at regular intervals till the end of their growth periods shall ensure. This technique may also find application in sports performance analysis as well as developing identification systems.

ACKNOWLEDGEMENT
Authors are thankful to MS Sajiha and Mr. Junaid Anwer, who helped in photography for this technique.