Afdeling Toegepaste Wiskunde/ Division of Applied Mathematics Representation and description(11.3: Regional descriptors) SLIDE 1/12

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1 Representation and description(11.3: Regional descriptors) SLIDE 1/ Regional descriptors Common practice to combine boundary and regional descriptors Some simple descriptors Area: Numberofpixelsinregion Perimeter: Length of boundary Compactness: Perimeter 2 /Area Meanandmediangraylevels Minandmaxgraylevelvalues Numberofpixelswithvaluesaboveorbelowmean Topological Descriptors Topology: Study of properties of a figure that are unaffected by any deformation Eulernumber: E=C H Number of connected components: C Numberofholes: H

2 Representation and description(11.3: Regional descriptors) SLIDE 2/12

3 Representation and description(11.3: Regional descriptors) SLIDE 3/12

4 Representation and description(11.3: Regional descriptors) SLIDE 4/12 Polygonal networks: Euler formula... V Q+F = C H = E V: Numberofvertices Q: Numberofedges F: Numberoffaces = 1 3 = 2

5 Representation and description(11.3: Regional descriptors) SLIDE 5/12 Example 11.9 E=C H 1552=

6 Representation and description(11.3: Regional descriptors) SLIDE 6/ Texture (1) Statistical approaches(2) Structural approaches(3) Spectral approaches Statistical approaches When p(z i ), i=0,...,l 1 represents a histogram of gray-levels, the nth momentofz aboutthemeanis L 1 µ n (z)= (z i m) n p(z i ) wheremisthemeanvalueofz... Relative smoothness... Thethirdmoment... m= i=0 L 1 i=0 R(z)=1 µ 3 (z)= z i p(z i ) 1 1+σ 2 (z) L 1 (z i m) 3 p(z i ) i=0

7 Representation and description(11.3: Regional descriptors) SLIDE 7/12 Thefourthmoment... µ 4 (z)=... measure of histogram s flatness Measure of uniformity... L 1 (z i m) 4 p(z i ) i=0 U(z)= L 1 i=0 p 2 (z i )... ismaximumforanimageinwhichallgreylevelsareequal Average entropy measure... e(z)= L 1 i=0 p(z i )log 2 p(z i )... measureofvariabilityandis0foraconstantimage Measures of texture computed using only histograms suffer from the limitation that they carry no information regarding the relative position of pixels with respect to each other Gray-level co-occurrence matrices: READ

8 Representation and description(11.3: Regional descriptors) SLIDE 8/12 Example 11.10: Texture measures based on histograms

9 Representation and description(11.3: Regional descriptors) SLIDE 9/12 Structural approaches A simple texture primitive can be used to form more complex texture patterns by means of some rules that limit the number of possible arrangements of the primitive(s) Spectral approaches Three features of Fourier spectrum that is useful for texture description... (1) Prominent peaks principal direction of texture patterns (2) Location of peaks fundamental spatial period (3) Elimination of periodic components non-periodic image elements statistical descriptors

10 Representation and description(11.3: Regional descriptors) SLIDE 10/12 Spectrum is symmetric about origin only half of frequency plane needs to be considered every periodic pattern associated with only one peak Consider spectrum in polar coordinates S(r, θ) Foreachdirectionθ,consider1-dimensionalS θ (r) Foreachfrequencyr,consider1-dimensionalS r (θ) More global description obtained by summation... π S(r)= S θ (r) S(θ)= θ=0 R 0 r=1 S r (θ)... wherer 0 istheradiusofacirclecenteredattheorigin Descriptors of these functions themselves can be computed in order to characterize their behavior quantitatively, for example... (1) location of the highest value (2) mean and variance (3) distance between mean and highest value

11 Representation and description(11.3: Regional descriptors) SLIDE 11/12 Example 11.12: Spectral texture

12 Representation and description(11.3: Regional descriptors) SLIDE 12/12 Example in 2nd edition: Spectral texture