Making the substitutionx= y;b=a, we have the Fouriertransform of the line image given by a certain angle band may thus be obtained by applying a bandpass lter in an angle band perpendicu
Trang 1Analysis of Oriente d Patterns
Many images are composed of piecewise linear objects Linear or orientedobjects possess directional coherence that can be quantied and examined toassess the underlying pattern An area that is closely related to directional im-age processing is texture identication and segmentation For example, given
an image of a human face, a method for texture segmentation would attempt
to separate the region consisting of hair from the region with skin, as well asother regions such as the eyes that have a texture that is dierent from that
of either the skin or hair In texture segmentation, a common approach foridentifying the diering regions is via nding the dominant orientation of thedierent texture elements, and then segmenting the image using this informa-tion The subject matter of this chapter is more focused, and concerned withissues of whether there is coherent structure in regions such as the hair or skin
To put it simply, the question is whether the hair is combed or not, and if it isnot, the degree of disorder is of interest, which we shall attempt to quantify.Directional analysis is useful in the eective identication, segmentation, andcharacterization of oriented (or weakly ordered) texture 432]
8.1 Oriented Patterns in Images
In most cases of natural materials, strength is derived from highly coherent,oriented bers an example of such structure is found in ligaments 35, 36].Normal, healthy ligaments are composed of bundles of collagen brils thatare coherently oriented along the long axis of the ligament seeFigure 1.8 (a)
Injured and healing ligaments, on the other hand, contain scabs of scar terial that are not aligned Thus, the determination of the relative disorder
ma-of collagen brils could provide a direct indicator ma-of the health, strength, andfunctional integrity (or lack thereof) of a ligament 35, 36, 37, 531] similarpatterns exist in other biological tissues such as bones, muscle bers, andblood vessels in ligaments as well 414, 415, 532, 533, 534, 535, 536, 537, 538,
539, 540, 541, 542, 543]
Examples of oriented patterns in biomedical images include the following:Fibers in muscles and ligaments seeFigure 8.22
Trang 2Fibroglandular tissue, ligaments, and ducts in the breast see Figures7.2and8.66.
Vascular networks in ligaments, lungs, and the heart seeFigures 9.20
and8.27
Bronchial trees in the lungs seeFigure 7.1
Several more examples are presented in the sections to follow
In man-made materials such as paper and textiles, strength usually reliesupon the individual bers uniformly knotting together Thus, the strength
of the material is directly related to the organization of the individual brilstrands 544, 545, 546, 547, 548, 549]
Oriented patterns have been found to bear signicant information in severalother applications of imaging and image processing In geophysics, the accu-rate interpretation of seismic soundings or \stacks" is dependent upon theelimination of selected linear segments from the stacks, primarily the \groundroll" or low-frequency component of a seismic sounding 550, 551, 552] Tho-rarinsson et al 553] used directional analysis to discover linear anomalies inmagnetic maps that represent tectonic features
In robotics and computer vision, the detection of the objects in the vicinityand the determination of their orientation relative to the robot are important
in order for the machine to function in a nonstandard environment 554, 555,556] By using visual cues in images, such as the dominant orientation of ascene, robots may be enabled to identify basic directions such as up and down.Information related to orientation has been used in remote sensing to ana-lyze satellite maps for the detection of anomalies in map data 557, 558, 559,
560, 561, 562] Underlying structures of the earth are commonly identied bydirectional patterns in satellite images for example, ancient river beds 557].Identifying directional patterns in remotely sensed images helps geologists tounderstand the underlying processes in the earth that are in action 553, 562].Because man-made structures also tend to have strong linear segments, di-rectional features can help in the identication of buildings, roads, and urbanfeatures 561]
Images commonly have sharp edges that make them nonstationary Edgesrender image coding and compression techniques such as LP coding andDPCM (see Chapter 11)less ecient By dividing the frequency space into di-rectional bands that contain the directional image components in each band,and then coding the bands separately, higher rates of compression may beobtained 563, 564, 565, 566, 567, 568, 569] In this manner, directional l-tering can be useful in other applications of image processing, such as datacompression
Trang 38.2 Measures of Directional Distribution
Mardia 570] pointed out that the statistical measures that are commonly usedfor the analysis of data points in rectangular coordinate systems may lead toimproper results if applied to circular or directional data Because we do notusually consider directional components in images to be directed elements (orvectors), there should be no need to dierentiate between components thatare at angles and 180o therefore, we could limit our analysis to thesemicircular space of 0o180o] or ;90o90o]
8.2.1 The rose diagram
The rose diagram is a graphical representation of directional data sponding to each angular interval or bin, a sector (a petal of the rose) isplotted with its apex at the origin In common practice, the radius of thesector is made proportional to the area of the image components directed inthe corresponding angle band
Corre-The area of each sector in a rose diagram as above varies in proportion
to the square of the directional data In order to make the areas of thesectors directly proportional to the orientation data, the square roots of thedata elements could be related to the radii of the sectors Linear histogramsconserve areas and are comparatively simple to construct