Bobkov A.V. - Image registration in the real time applications, страница 13

I1+(I2 – I1)/4),[I1+(I2 – I1)/4) ... I2 – (I2 – I1)/4)] and (I2 – (I2 – I1)/4) ... 255) appropriately.1.6.If G1+G3<2G2 , then distribution is unimodal, and all pixels in the areamust be marked as containing no edges1.7.In the other case, if G1+G3>=2G2 , the distribution is multimodal:491.7.1.If G1>G3, then G1 is the main mode. All pixels in the area withbrightness greater than It must be marked as edge contour pixels1.8.1.If G1<G3, then G3 is the main mode. All pixels in the area withbrightness less than It must be marked as edge contour pixelsThere are number of methods that provide higher accuracy in threshold andnumber of computationed modes, for example – by approximation of thedistribution by orthogonal polynoms. But these methods are more computationallyintensive.

The algorithm placed above provides better trade-off betweenperformance, accuracy and reliability.2.2.3. Statistical method characteristicsStatistical methods, like differential methods, provide the contour widthgreater than one pixel, and require additional operations for contour thinning.These operations require knowing the brightness gradient value in the contourpixels found. So the same differential methods will be used, but the number ofpixels to be processed is reduced in 5-20 times.Statistical methods are more reliable to noise in comparison to differentialmethods.

But there are kinds of noise that make statistical methods work lessreliably.Statistical methods do not misplace the contour pixels from its originallocation. This is important feature for several applications.To select the best edge detector, the characteristics of statistical and gradientmethods must be compared to examine the quality and correctness of the furtherdetection of more complex contour elements.2.3. Contour thinningUsing the edge detector the pixels with non-zero brightness derivative arefound (Fig.2.3). Often there are too many such pixels and only part of them definethe elements of contour. Other pixels found are texture elements, small details,noise and pixels near the real contours (since the object edges are often blurred onthe real images), and they must be eliminated.The pixels to be deleted can be classified into three groups:1.

Pixels with a relatively small value of the gradient magnitude. This can bea texture elements and non-significant details.2. Pixels with any gradient magnitude near the pixels with a greater gradientmagnitude. Such pixels appear due to edge blurring.3. Separate pixels with a large gradient magnitude. They appear due to highfrequency noise.50a)b)c)Fig.2.3.

Edge extraction and thresholdinga) Source image (model fragment of agricultural landscape)b) Edges produced by the Sobel filterc) Edges produced by thresholding51The pixels of the first group can be found by comparison with a localthreshold: pixels with gradient magnitude lower than threshold must be deleted.Such operation is called binarization, or thresholding.The processing of second group pixels is more complex for the followingreason. The local maximums of the gradient magnitude are placed near another andform a contour line. The pixels on this line must remain while the pixels out of linemust be deleted. One way to do it is to suppress non-maximum values in thegradient direction and highlight the pixels in perpendicular direction.

Suchoperation is known as non-maximum suppression.The processing of third group pixels is computationally extensive operation.One of the ways to implement it is to use emboss and dilate filters. However, sucha filter can damage other edge pixels. Another solution is to process these pixels onthe contour line detection stage.

Since these pixels do not belong to a contour line,their presence does not affect the line detection process.2.3.1. ThresholdingThe task of thresholding is to eliminate pixels with a small value ofbrightness gradient magnitude and to separate contour pixels from texture elementsand noise.The simplest method is to select a constant threshold value L and toeliminate pixels with a gradient magnitude |G|<L. The main problem in thethreshold level calculation is that the threshold must be different for differentimages and even for the different areas of the same image.To avoid this difficulty it is possible to use the adaptive thresholdcalculation.

In this case the threshold value is calculated for local image areas sizeof from 8x8 to 16x16. Threshold of each area depends on average pixel brightnessI0 in this area. Then the threshold value is:L = k * I0 ,where k=1,2..1,8 is a constant binarization coefficient.The change of k value will not cause significant changes of extractedcontour quality (as opposed to the threshold value L itself), and the value of k=1,5is acceptable for a most of images.Another modification of this method is calculating the threshold value Lseparately for different gradient orientations. This prevents removing importantdetails near the brighter objects.

This method is more computationally extensive (alocal direction histogram must be found), but allows an increase in the thresholdvalue without loss of information and hence it reduces the amount of false edges.The results of both methods are approximately the same. Since the firstmethod is simpler and thus more reliable, it looks more preferable.Experiments on Fig.2.4 and 2.5 have showed that smooth changing of localthreshold level causes smooth changing in number of contour points found andnumber of line segments detected. This allows using the local threshold level as atuning parameter for selecting proper line amount.

This property will be used inexperiments in the further chapters.52Fig.2.4. Results of the experimental determination of dependence of edgepixel amount from the threshold coefficientFig.2.5. Results of the experimental determination of dependence ofextracted line amount on the threshold coefficient532.3.2. Global and local thresholding comparisonA global threshold level is not easy to determine, and manual tuning is oftenrequired. A local threshold level is not so critical: the same values of thresholdlevel can be used for wide range of images.To compare the properties of local and global thresholding, a series ofexperiments was performed.First we have tested the thresholding behaviour in the case of brightnesschanges.

Two images – bright and dark – were used for test (Fig.2.6). When globalthreshold of level 10 was applied to pictures of different brightness, the firstpicture has been processed properly whereas in the second picture a number ofedges are corrupted. However, local thresholding of the same level (120%) allowsthe correct processing of both pictures.Then the sensitivity to the level value was tested. We take the bright imagefrom Fig.2.6,a and apply global and local thresholding of different levels (Fig.2.7).Results of global thresholding can change dramatically when a level changes byonly one point. However, local thresholding results have no such dramatic changeseven when the level changes significantly.

The local thresholding appears is muchless sensitive to value level variations.In common case the adaptive threshold technique is far from optimal, but itprovides an acceptable quality along with high performance. Some other methodsdiscussed in [Davies 1990] can produce better results but require much moreextensive computations, which is unacceptable for real time tasks.54a)b)c)d)e)f)Fig.2.6.

Global and local thresholding for the image of different brightnessa) and b) – original imagesc) and d) – global threshold of 10 is applied to pictures of different brightness.Picture a) processed properly but picture b) edges are corrupted.e) and f) – local threshold of 120% is applied. Both pictures are processedcorrectly.Global threshold level is uneasy to determine, and manual tuning is often required.55a)b)c)d)Fig.2.7. Global and local thresholding during level changinga) Global tresholding of T=3 is appliedb) Global tresholding of T=4 is applied; many pixels has been removed.c) Local tresholding of L=120% is appliedd) Local tresholding of L=150% is applied; most of pixels are remain.Small changes in global threshold level causes a slightly different results –in the case a) a lot of noise points remains whereas in the case b) they are mostlyeliminated. But even significant changes of local threshold value in the cases c)and d) produce similar results.562.3.3.

Non-maximum suppressionThe thresholding method described above is effective for suppression ofnoise and texture elements, but it cannot significantly reduce an edge width. Forthe best case the contour width must be a single pixel to exactly determine theparameters of a line passing through the contour. The wider a contour the lower theaccuracy of line parameter computation and the more false lines will be found. Sothe reduction of contour width is a very important task.On the other hand, a wide curved contour can be easily approximated by linesegments, so a thinned contour must be near-to-linear.The non-maximum suppression algorithm can be described as follows.

Foreach pixel that potentially contains an edge (i.e. where the gradient magnitude isnon-zero) the neighbouring pixels in the gradient direction are examined. If theirgradient magnitude is greater than the current pixel, the current pixel is marked asa pixel to be removed (Fig.2.8). After all pixels are processed, marked pixels areremoved. This procedure will affect only edge width, and simply searches a localmaximum in a cross-section that is perpendicular to edge direction.Such a procedure is extremely fast because it requires about 3 or 4 logicoperations per edge pixel. Results it application is shown on Fig.2.9.In several cases it is required to implement additional operations to restoreand enclose the contour.