Centroid Usage and Explanation
For eBx and eGx
By Chuck Rasbach
Summary
The Centroid function in eGx™ (formerly known as Gage-X) and eBx™ (formerly known as Basic-X) software utilizes a series of filters that can be applied before or after the identification of the object within the region of interest (ROI) that is being analyzed. These filters allow the image to modified so that the extracted data closely approximates the required values. Surface texture and lighting factors demand some method of data reduction for the correct object to be identified. Once correctly identified, the boundaries of the object must be calculated. This calculation can be accomplished with simple pixel counting or most sophisticated edge detection techniques. The Centroid functions returns a variety of calculations such as Area, Location, Perimeter, and Min/Max Radius.
The Centroid function allows the measurement of an object that has an undefined size and shape (form). The Centroid function is limited to field of view (FOV) measurements since the entire object must be analyzed in total. The perimeter of the object is determined and used for calculations of size and the center of mass is calculated for location.
Primarily, the Centroid function needs to separate the region of interest foreground or background before an object is analyzed. The region of interest potentially contains the intensity values of every pixel. A threshold value could be established and every intensity value could be separated into either the foreground or background. The determination of the threshold value is set manually by the operator or automatically. The Centroid function utilizes a proprietary algorithm to set the threshold automatically. Many different Gaussian curves can be extrapolated from the intensity values that contain different amplitude, mean, and variance. The proprietary algorithm utilizes histogram techniques that calculate a threshold per region of interest.
Potentially, with a highly texture surface, the determination of a threshold could be difficult. The establishment of a threshold that correctly allows the separation of the object from the region of interest is often problematic on a highly textured surface. The Centroid function provides a filter that averages out the intensity values of adjacent areas in the region of interest. This filter groups the intensity values of adjacent pixels and allows for pixel grouping. This is performed previous to the determination of the threshold, which allows for the correct segmentation of the object.
Segmentation of the object must be performed after it has been separated from the region of interest. Segmentation of an object can be performed by many methods. Some common techniques include allowing the image to be converted to binary and extracted, grey scale analyzes to be performed on the boundaries, and pattern matching based upon a vector gradient field. The Centroid Function utilizes a proprietary algorithm that works similar to the "edge trace" function that is standard in eGx and eBx.
Once the largest object is identified in the region of interest, other filters are available which effect the final calculation. Multiple objects may be obtained from the region of interest. A filter is provided that allows the user to input the percentage of the total region of interest that the multiple objects must exceed before consideration on the calculations. If multiple objects do appear within a larger object, the area could be "filled" by the use of another filter.
The resultant calculations returned by the Centroid function are:
- Area: The calculated area of the found object(s)
- X Location: The calculated x location of the center of the object(s)
- Y Location: The calculated y location of the center of the object(s)
- Z Location: The calculated z location of the center of the object(s)
- Perimeter: The calculated perimeter of the object(s)
- Max/min radius: The maximum/minimum distance from the calculated center to the edge of the object.
Notes: The area calculation as performed by the Centroid function is based upon the segmentation of the entire object. This will yield different results than the extrapolation of the area from a "best-fit" diameter using other types of edge detection tools. The later calculation is based upon the assumption that the object is perfect in shape as determined by best-fitting individual data points (of potentially unequal spacing) around the circumference of the circle. The Centroid function segments the object to determine to area based upon its current form.