Segmentation with constant background
All segmentation methods are faced with the problem of systematic errors. Assume that an image contains objects with different, but constant brightness. The background has a constant brightness h. For the following computations it is sufficient to use two objects with brightness g1 and g2. The objects have a width l > 5 and are convolved by a rectangular point spread function with 5 pixel width during the image acquisition process. The image signal contains an additive zero mean white noise with a variance σ2.
Three segmentation approaches are available:
P Pixel-based segmentation with a constant global threshold at the brightness level t, G Edge-based segmentation on the base of first-order derivative filters. The edge position is given by the maximum value of the magnitude of the gradient. L Edge-based segmentation on the base of second-order derivative filters. The edge position is given by zero crossings of the Laplacian operator. Answer the following questions for the three segmentation methods:
- Which brightness difference is required in order to distinguish the objects from the background in a statistically significant way? The difference between thresholds and signal levels should be at least three times the standard deviation σ of the noise.
- Is it possible that one of the methods causes a systematic error in the size of the object? If yes, compute the systematic error and compare it for the different methods.