January 2021

Linear and cubic interpolation A cosine signal is sampled either four or eight times per wavelength. Which signal form is generated when a continuous signal is reconstructed from these sampled signals by either linear or cubic interpolation? Box filters and binomial filters Interactive demonstration of smoothing with box filters and binomial filters (dip6ex11.01)

Multistep smoothing with box filters and binomial filters Interactive demonstration of multistep smoothing with box filters and binomial filters (dip6ex11.02) Box filter Box filter were discussed in detail in Section 11.3. Answer the following questions: 1. Why are box filters bad smoothing filters? List all reasons! 2. Do the bad features improve if you apply

Filter design A filter should be designed with a small mask and optimal smoothing properties. Use a mask with 3 coefficients: [α, β, γ]. The filter should have the following properties: a) Preservation of the mean value b) No shift of gray value structures c) Structures with the largest possible wave number should vanish Questions and

Noise suppression by smoothing 1. Prove that it is not possible to improve the signal-to-noise ratio for a arbitrary single wave number with a linear smoothing filter H. (Hint: write the image G as a sum of the signal part S and the noise part N.) 2. Assume white noise (equally distributed over all wave numbers), but a spectrum of the signal that

Transfer function of the 1-D box filter Prove Equation (11.12) for the transfer function of the 1-D box filter. (Hint: there are at least to ways to do this. One is to write the transfer function that it can be seen as a geometric sequence (1+q + +. ..+) with the sum  (− 1)/(q − 1). The other solution is based on the

Edge and line detection Interactive demonstration of edge and line detection with several edge detectors based on first-order and second-order derivative filters (dip6ex12.01) Edge and line detection on pyramids Interactive demonstration of edge and line detection with several first-order and second-order derivative filters at different scales on pyramids (dip6ex12.02)

Design of second-order difference filter Use all necessary properties for a second-order difference filter to show that there can be only one such filter with three coefficients ([α βγ]). If a filter has five coefficients, one free parameter remains. What are the coefficients of this filter and what is its transfer function if you apply

Accelerated morion With accelerated motion, the continuity equation of the optical flow can be extended as follows: (f + at)∇g + gt = 0 Formulate the over determined linear equation system for the optical flow f and the acceleration a (4 parameters in 2-D images) with an approach similar to that in Section 14.3.2. Show

Second-order differential method The second-order differential method determines optical flow without further averaging from Eq. (14.74). At which gray value structures it is possible to determine optical flow from Eq. (14.74) without ambiguity? Does this cover all types of second-order gray value structures at which it is principally possible to determine the complete optical flow

Statistical parameters for texture analysis Interactive demonstration of statistical parameters for texture analysis (dip6ex15.01) Local orientation for texture analysis Interactive demonstration of texture analysis using the structure tensor for orientation analysis (dip6ex15.02) Texture analysis with pyramids Interactive demonstration of texture analysis with a multiscale approach on pyramids (dip6ex15.03)