January 2021

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

Regularized motion analysis Interactive demonstration of several techniques for regularized motion analysis (dip6ex17.02) Iterative inverse filtering Interactive demonstration of iterative inverse filtering; generation of test images with motion blur and defocusing (dip6ex17.03). Elementary morphological operators Interactive demonstration of elementary morphological operators, such as erosion, dilation, opening, and closing (dip6ex18.01)

Commutativity of morphological operators Check if morphological erosion and dilation operators are commutative and prove your conclusion! (Hint: If one of the operators is not commutative, present a counter example.) Hit-miss operator Interactive demonstration of the hit-miss operator (dip6ex18.02) Morphological boundary detection Interactive demonstration of morphological boundary detection (dip6ex18.03)

Morphological operations with gray-scale images Interactive demonstration of morphological operators with gray-scale images (dip6ex18.04) Opening and closing Opening and closing are two of the most important morphological operators. 1. What happens if you apply an opening or a closing with the same structure element several times? 2. What is the structure element for an opening

The Pr¨ufer code  : T → W defined by equations (1.3) and (1.4) is a bisection. Figure 1.6 shows some trees and their Pr¨ufer codes for n = 6 (one for each isomorphism class, see Exercise 4.1.6). Let G be a connected multi graph having exactly 2k vertices of odd degree (k 0). Then the edge set

Give a formula for the degree of a vertex of L(G) (using the degrees in G). In which cases is L() an SRG? Let G be a connected graph. Find a necessary and sufficient condition for L(G) to be Eulerian. Conclude that the line graph of an Eulerian graph is likewise Eulerian, and show that

Determine the minimal number of edges a graph G with six vertices must have if [G] is the complete graph . If G is Eulerian, then L(G) is Hamiltonian. Does the converse hold? Every chessboard of size m × n (where m ≤ n) admits a knight’s cycle, with the following three exceptions: (a) m and