Image Measurements

Figure 2. Step edge and its equation where θ is the line angle and u(x) is the step function, i.e. u(x)=1 if x >0 and u(x)=0 otherwise. A discretized image is obtained from a camera after the lenses have possibly blurred the scene and each sensor have added its own sensor noise. Consider the sensor noise to be additive White Gaussian and the blur to be described by a Gaussian convolution with the scene values. Then, the final discretized image is obtained by sampling the resulting convolution of the blur with added white noise. Thus, we can write the observed image due to the step edge scene as I1(x,y)