When reviewing these results, several points should be noted. First, this study utilized a two-dimensional analysis algorithm. A limitation of the study was that exactly four calibration points were required to define the scaling from screen coordinates to actual coordinates. The use of more than four points would likely result in less variability. Second, all coordinates and calculated errors were normalized to dimensions of the image. Although there were many possibilities for the choice of dimension (e.g., horizontal, vertical or diagonal image size; maximum horizontal, vertical, or diagonal coordinate; average of horizontal and vertical image size or maximum coordinate; etc.), the dimensions used to normalize were assumed to best represent the image size. It is clear from these data that a systematic error caused by lens distortion occurred when using the underwater video system. Lens distortion errors were less than 1% from the center of the image up to radial distances equivalent to 25% of the horizontal image length (normalized R equal to 0.5). Errors were less than 5% for normalized R up to 1, an area covering most of the image. There seemed to be some degree of random noise. This was evident in the scatter pattern seen in the graphs in figure 5. This error can most likely be attributed to the process of digitizing. There are factors which limit the ability to correctly digitize the location of a point, such as: if the point is more than one pixel in either or both dimensions, irregularly shaped points, a blurred image, shadows, etc. Because of these factors, positioning the cursor when digitizing was often a subjective decision. Four trials were analyzed in this study. Although all the data were normalized, there were slight differences among the four trials (fig. 5 and table 2). These can most likely be attributed to the uncertainty in determining the grid size, which was estimated from the fraction of a grid unit from the outermost visible grid lines to the edge of the images.Two types of regressions were fit to the data: linear and binomial. The interpretation of the coefficients of the linear regression can provide insight into the data. A1, the slope of the error-distance relation represents the sensitivity of the error to the distance from the origin. Thus, it is a measure of the lens distortion. A0 the intercept of the linear relation can be interpreted as the error at a distance of zero. If the relation being modeled were truly linear, this would be related to the random error not accounted for by lens distortion. However, in this case, it is not certain if the error-distance relation was linear. The RC values gave an indication of how good the fit was. The binomial curve fit seemed to more correctly represent the data. The interpretation of these coefficients, however, is not as straightforward. Conclusions This study has taken a look at one of the sources of error in video-based motion analysis using an underwater video system. It was demonstrated that errors from lens distortion could be as high as 5%. By avoiding the outermost regions of the lens, the errors can be kept to less than .5%.
© Copyright 1993 All rights reserved.