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Traditional Best-Fit Algorithms. Algorithms that fit a curve to a set of points have existed for hundreds of years. Although traditional best-fit algorithms usually deal with a functional approximation for a given set of data, they can be extended to computer vision. If the pixels along an edge are considered data points, it is possible to find a curve that approximates them. Examples of traditional curve-fitting algorithms are least mean squares, linear interpolation, and splining. For brevity, we will deal only with fitting lines to the data.
There are two basic types of world representation: object centered and view centered. In an object-centered technique, a physical model of the real world is created in the computer, and that model is compared with the current image. Objectcentered representation requires a transform from object space to feature space or from feature space to object space in order for the comparisons to be made. View-centered representations are direct records of the expected feature set. They are more efficient than object-centered representations because the measured data can be compared directly with the model without any additional transforms.
The major difference between filtering and morphological operations is that filtering changes the image based on frequency characteristics, and morphological operations change the object on the basis of shape characteristics. Because morphological operations are based on shape, they are useful if there is a good deal of a priori knowledge about the expected shape of the object. The morphological approach has the additional advantage of mathematical rigor. Instead of each image being expressed as the result of a convolution filter as with the frequency case, morphological operations are built from primitive operations and allow the user to express imaging processing as a kind of algebra.