Rotation and Scale Variant Texture Features

Local Orientation

As local orientation has already been discussed in detail in Chapter 13, we now only discuss some examples to illustrate the signifi cance of local orientation for texture analysis. As this book contains only gray scale images, we only show coherence images of the local orientation.

Figure 15.4 shows the coherence measure for local orientation as de- fi ned in Section 13.3. This measure is one for an ideally oriented texture where the gray values change only in one direction, and zero for a dis- tributed gray value structure. The coherency measure is close to one in the areas of the piece of shirt cloth with horizontal stripes (Fig. 15.4a) and in the dense parts of the dog fur (Fig. 15.4b). The orientation analy- sis of the curtain (Fig. 15.1a) results in an interesting coherency pattern (Fig. 15.4c). The coherency is high along the individual threads, but not at the corners where two threads cross each other, or in most of the ar- eas in between. The coherency of the local orientation of the woodchip paper image (Fig. 15.1d) does not result in a uniform coherence image as this texture shows no predominant local orientation.

 

Local Wave Number

In Section 13.4 we discussed in detail the computation of the local wave number from a quadrature fi lter pair by means of either a Hilbert fi lter (Section 13.4.2) or quadrature fi lters (Section 13.4.5). In this section we apply these techniques to compute the characteristic scale of a texture using a directiopyramidal decomposition as a directional bandpass fi lter followed by Hilbert fi ltering.

The piece of shirt cloth in Fig. 15.5a shows distinct horizontal stripes in certain parts. This image is fi rst bandpass fi ltered using the levels one and two of the vertical component of a directiopyramidal decomposition of the image (Fig. 15.5b). Figure 15.5c shows the estimate of the local wave number (component in vertical direction). All areas are masked out in which the amplitude of the corresponding structure (Fig. 15.5d) is not signifi cantly higher than the noise level. In all areas with the horizontal stripes, a local wave number was computed. The histogram in Fig. 15.5e shows that the peak local wave number is about 0.133. This structure is sampled about 7.5 times per wavelength. Note the long tail of the distribution towards short wave numbers. Thus a secondary larger-scale structure is contained in the texture. This is indeed given by the small diagonal stripes.

Figure 15.6 shows the same analysis for a textured wood surface. This time the texture is more random. Nevertheless, it is possible to determine the local wave number. It is important, though, to mask out

15.3 Rotation and Scale Variant Texture Features                            421

 

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Figure 15.5: Determination of the characteristic scale of a texture by computa- tion of the local wave number: a original texture, b directional bandpass using the levels one and two of the vertical component of a directiopyramidal decomposi- tion, c estimate of the local wave number (all structures below a certain threshold are masked to black), d amplitude of the local wave number, and e histogram of the local wave number distribution (units: number of periods per pixel).

 

the areas in which no signifi cant amplitudes of the bandpass fi ltered image are present. If the masking is not performed, the estimate of the local wave number will be signifi cantly distorted. With the masking a quite narrow distribution of the local wave number is found with a peak at a wave number of 0.085.

422                                                                                                                15 Texture

 

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Figure 15.6: Same as Fig. 15.5 applied to a textured wood surface.

 

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