Spatial filtering operations are widely used in image processing to enhance the source image's appearance or to accentuate edges between dissimilar areas (segments) within an image. This chapter reviews noise models, then derives the filter kernels used to remove spatially distributed noise and to detect edges between image segments.
The output (response) of an electronic imaging system is proportional to the incident light quanta, as opposed to the negative exponent behavior of the photochemical material on films. Although noise is inherent in both forms of image capture, thermal noise and the random fluctuation of photon numbers during sensing affect only photoelectronic sensors. Thermal noise [nth(x, y)] may be reliably modeled as a Gaussian process with uniform distribution (white noise), while the random variation in photon numbers is signal-dependent and therefore more difficult to model. One approach is to interpret the photon noise [nph(x, y)] as the mean electron emission rate at any location (x, y) on the image surface (sensor plane). The noisy output generated by the sensor may then be expressed as
where e0(x, y) is the ideal (noise-free) image signal, nth(x, y) is a Gaussian variable (typically with zero mean and unity standard deviation), and b is typically taken as 1/2 or 1/3.