Probability & Statistics

Images are inherently random (unpredictable) for many reasons. If we image the same object many times with the same imaging system, we will get unpredictably different images each time because of the noise that arises from electronic circuitry or detection of radiation, but in fact the objects and the imaging systems also vary unpredictably. Information derived from images is therefore random as well. If we estimate a tumor volume or compute a linear discriminant function, for example, the result will be unpredictable because the randomness in the object, noise and imaging system. A full understanding of the properties of images and of the conclusions drawn from them thus demand accurate probability models and rigorous statistical tests, and image-quality assessment is virtually synonymous with statistical analysis of images.

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