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)

Features for texture analysis Which features are suitable for texture analysis? Try to list the features in a systematic way starting from the simplest possible feature such a the mean gray value and continuing to more and more complex textures. Briefly explain your approach! Structure tensor for texture analysis Which types of texture can be

Invariant texture features Show which of the listed texture features is invariant under a change of the scale, rotation, and a change of the brightness of the image: 1. Variance operator: (G − BG) 2 2. Local gray value histogram computed in a certain neighborhood 3. Local histogram of the first-order derivative in x direction 4. Magnitude of the gray value

Simple segmentation methods Interactive demonstration of simple segmentation methods (dip6ex16.01). Hough transform Interactive demonstration of the Hough transform (dip6ex16.02) Inhomogeneous and anisotropic diffusion Interactive demonstration of smoothing using inhomogeneous and anisotropic diffusion (dip6ex17.01)

Segmentation with constant background All segmentation methods are faced with the problem of systematic errors. Assume that an image contains objects with different, but constant brightness. The background has a constant brightness h. For the following computations it is sufficient to use two objects with brightness g1 and g2. The objects have a width l