Bobkov A.V. - Image registration in the real time applications, страница 14

An example of a method that has such an operation is thewell-known Canny filter [Canny, 1986]. These operations are not significant forcontour line detection, because modern line detection algorithms (e.g. Houghtransformation) do not require the contour to be enclosed.Fig.2.8. Scheme of edges thinning by non-maximum suppression (darkersquares mean pixels with greater gradient magnitude; crosses mark pixels to beremoved).57a)b)c)Fig.2.9.

Example of edge thinninga) Source imageb) Gradient magnitudec) Results of gradient non-maximum suppression582.3.4. Use the thresholding and edge thinning at the same timeThe use of edge thinning procedure can cause the amplification of noise andthe extraction of small detail contours, which cannot be approximated by long linesor by wide arcs and hence, is useless. These items are hard to eliminate bythresholding (Fig.2.10, a).

On the other hand, if the thresholding is implementedbefore edge thinning, it can cause the contour damaging in such a way that edgethinning will work incorrectly (Fig.2.10, b).The root of problem is each of these procedures destroys informationneeded by the other. To avoid this problem, both procedures must be implementedindependently.

The pixels, which must remain after each of procedures, are markedseparately. The destination image will have only those pixels that collect bothmarks.Such an approach allows solving the problem completely and requires ainsignificant amount of additional operations.2.4. Comparison of statistical and differential methodsStatistical methods are free from many drawbacks of differential methods.They provide thinner and properly place contours and allow finding lines andangles more reliably and accurately. The statistical filter works better on images ofaverage and high quality (Fig.2.11).On the other side, when the image spectrum contains high-frequencycomponents – noise, small detail and texture, the processing quality of statisticalfilters is reduced significantly (Fig.2.13).Differential methods use the thresholding procedure to suppress highfrequency elements.

The thresholding in statistical method has a lesser effect: sincethe edges are much thinner, it is harder to obtain enough statistical data to computethreshold correctly (Fig.2.14). Lower values of threshold do not allow eliminatinghigh-frequency details, and higher values cause important detail elimination.Another possible solution is to use high-frequency pre-filtration, e.g. Gaussor median filter.

Even in this case the problem of the accurate selection of filterparameters still remains (Fig.2.15). Experiment shows that small changes in filterparameters (10% for STD in Gauss filter) causes significant changes in theextracted contour quality. That is why it is impossible to take the filter parametersas a constant.Traditional methods of optimal filter development cannot be used in thiswork because the filter parameters must be found and optimised in real time.In such a way, the statistical detectors look more promising in comparison toclassical differential filters, but the problem of selecting the high-frequencysuppression parameters is still has no good solution.59a)b)c)Fig.2.10.

Different variants of edge thinninga) Results of thresholding after the thinning. There is no enough statistics fordynamic level computation, and some contours are corruptedb) Results of thinning applied after thresholding. Amount of noise andinsignificant details are reduced, however, some contours are lost.c) Final variant–thinning and thresholding implemented at the same time60Statistical method with the localarea size of 4х4х8Statistical method with the localarea size of 2х2х8Fig.2.11.

Statistical methods comparison. Reduction of actual frame sizeallows producing better edges, however it requires more computations.61Amount of elements foundDifferential method:Edge pixels: 8140(10%)Lines:295Corners:374Source imageStatistical method:Edge pixels: 9392(11%)Lines:362Corners:521Differential methodLines and corners foundStatistical methodLines and corners foundFig.2.12. Comparison of statistical and gradient edge detectorStatistical methods allow extracting more contour pixels and producing lessfalse elements for a high quality images.62Amount of elements foundDifferential method:Edge pixels: 11137(13%)Lines: 331Corners: 291 (not shown)Source imageStatistical method:Edge pixels: 18635(23%)Lines: 540Corners: 1199 (not shown)Differential methodLines foundStatistical methodLines foundFig.2.13.

Comparison of statistical and gradient edge detectorIf the image contains a high-frequency noise, statistical method does notsuppress tiny details. As a result, a larger amount of false lines is found.63Statistical methods after Gaussfilter applied, STD is 0,5Lines foundStatistical methods after medianfilter appliedLines foundFig.2.14. Statistical method with pre-processingA pre-processing with Gauss filter with a small σ or with median filter cancorrect the previous situation, but the common results are worst than the gradientmethod can achieve.64Thresholding with k=80 is usedLines foundThresholding is not usedLines foundFig.2.15.

Statistical filter with thresholding of level L=80A larger threshold level cause the elimination of edge points, because theedges are thin and contain small number of pixels. A lesser threshold level cannotproduce the desired effect.2.5. ConclusionThis chapter examines the most popular methods of edge extraction andlabelling. There are gradient methods, second derivative methods and statisticalmethods.Statistical methods have received particular attention in the recent past sincethey looked very promising due to such properties as higher accuracy and noise65stability. Nevertheless, the behaviour of statistical methods has not beeninvestigated systematically. There is a whole set of unsolved problems, e.g.

relatedwith pre-filtration parameter selection. Furthermore, there are number of specialcases where the edge detection quality will be significantly lower than classicalmethods can provide.Brightness second derivative methods are also widely used now. One ofmost popular schemes is the Marr-Hildred filter. Taking into account of secondderivative allows analysing the edge position more thoroughly. Furthermore, itbecomes possible to determine edge formation – single step, line, corner, edgecrossing, T-formation etc. However, second derivative by itself is more sensitive tonoise in comparison to the first derivative, and cannot provide information aboutedge direction and exact position. So the second derivative methods usually useboth first and second derivatives of brightness in order to reduce noise effects andthereby increase edge detection accuracy.

Unfortunately, the amount ofcomputations required is raised as well, and makes this approach computationallyexpensive.Gradient methods are known to be the first methods of edge detection. Theyare deeply investigated and widely used in practical applications. They are thefastest and most universal, and allow processing of a wide class images.

One ofmost popular schemes that uses brightness gradient is a Canny’s filter. It is oftenused as an etalon for the different edge detection method comparison.The main disadvantages of the gradient methods are limitation on accuracyand noise sensitivity, which cannot be catered for without a significant amount ofcomputation. A gradient filter with a small mask size cannot determine accurately,regardless of noise, neither position nor orientation of the edge. The use of a largermask causes an insignificant increasing in accuracy, but to realise this smallincrease many more computations a required in proportion to the number of maskelements.To exactly localise an edge pixel, gradient methods use either thresholdingor non-maximum suppression.

Thresholding requires the threshold value to beproperly calculated – it is complex task by itself. Non-maximum suppressionresults depend on proper determination of edge orientation, but the orientationaccuracy is low and depends on noise for the masks of practically acceptable size.However, the method of edge labelling, proposed in this work, uses both adaptivethresholding and non-maximum suppression. This allows reducing the maindisadvantages of gradient filters while keeping the amount of computation at a lowlevel.

So the method proposed in this work has potentially higher stability withrespect to noise and higher performance, and can be successfully used for imageprocessing in real time.In such a way, this research proposes a new gradient-based edge detector.The proposed method combines well-known techniques in an optimal way, whichallows provision of a good ratio of performance, accuracy and stability to noise.The method in certain circumstances has the potential to better characteristics thanother methods provide, so it can be used as a first stage in the image registrationprocess.66Chapter 3.

Line and corner detectionIn this chapter the methods of contour element detection will be reviewedand analysed. These elements are lines, line segments, corners, curves, arcs etc.The use of contour elements instead of image pixels leads to a significantsimplification of the further task of image registration and recognition, but requiresspecial detection methods. These methods must provide enough performance,accuracy and reliability.3.1. Contour representationA contour can be represented in several forms.