Spatial resolution of images Representation of images with interactively adjustable number of points (dip6ex02.01). Quantization of images Representation of images with interactively adjustable number of quantization levels (dip6ex02.02). Context-dependent brightness perception Interactive demonstration of the context-dependent brightness perception of the human visual system (dip6ex02.03).

Contrast resolution of the human visual system Interactive experiment to determine the contrast resolution of the human visual system (dip6ex02.04). Gamma value Interactive adjustment of the gamma value for image display (dip6ex02.05). Partitioning into periodic patterns Interactive demonstration of the partitioning of an image into periodic patterns, i. e., the basis functions of the Fourier

Contrast resolution with a logarithmic imaging sensor Compute the relative brightness resolution Δg’/g’ caused by digitalization (Δg’ = 1) of an image sensor with a logarithmic response of the form g’ =  +  log g and a contrast range of six decades for 8 and 10 bit resolution. The minimum gray value g is mapped to g’

Commutativity and associativity of convolution Show by applying the convolution masks a) and d) from Exercise 4.2 to a step edge . . . 0 0 0 0 0 1 1 1 1 1 . . . that convolution is commutative and associative. Convolution masks with even number of coefficients Also for filters with an even number of coefficients

Inverse convolution Does an inverse operator exist for the following convolution operators? a) 1/6[1 4 1] b) 1/4[1 2 1] c) 1/3[1 1 1] Are these inverse operators again a convolution operator? (see Section 4.4.2) If yes, do they have a special structure?

Change of statistics of 1-D signals by convolution Compute the auto covariance vector of an uncorrelated time series with constant variance σ2 for all elements that have been convolved with the filters from Exercise 4.2. Analyze the results, especially for the variance of the convolved time series.

Recursive relaxation filters Interactive demonstration of recursive relaxation filters (dip6ex04.02). Recursive resonance filters Interactive demonstration of recursive resonance filters (dip6ex04.03). Pyramids Interactive demonstration of Gaussian und Laplacian pyramids (dip6ex05.01).

Physical systems and recursive filters Physical systems can be regarded as implementations of recursive filters. Compute the point spread function (impulse response) and transfer function of the following physical systems: 1. A cascaded electric low pass filter consisting of two stages each with a resistor R and a capacity C. 2. A spring pendulum with a mass m, a

Band pass filter Design a band pass filter with the following properties: 1. The pass-through wave number should be k = 0.5. 2. The bandwidth of the pass-through range should be adjustable. The filter should be implemented both as a recursive and a non-recursive filter. (Hint: Take the filter [-1 0 2 0 1]/4 as a starting point

Pyramid with finer scale resolution One problem of conventional pyramids is that the size decreasing in every direction by a fixed factor of two. Some applications call for a finer scale resolution. How could you generate a pyramid where the size in both directions decreases not by a factor of two but by a factor