January 2021

Interactive viewing and inspection of all image sequences and volumetric images used throughout this textbook (dip6ex01.01). Inter disiplinary nature of image processing 1. Which other sciences contribute methods that are used in digital image processing? 2. Which areas of science and technology use digital image processing techniques?

Figure 1.13 contains a systematic summary of the hierarchy of image processing operations from illumination to the analysis of objects extracted from the images taken. Investigate, which of the operations in this diagram are required for the following tasks. 1. Measurement of the size distribution of color pigments (Section 1.2.1, Fig. 1.1c) 2. Detection of

Comparison of computer vision and biological vision In Section 1.7 we discuss the components of a digital image processing system. Try to identify the corresponding components of a biological vision system. Is there a one-to-one correspondence or do you see fundamental differences? Are there biological components that are not yet realized in computer vision systems

Amounts of data in digital image processing In digital image processing significantly larger amounts of data are required to be processed as this is normally the case with the analysis of time series. In order to get a feeling of the amount of data, estimate the amount of data that is to be processed in

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.