LAB 4: Operations on binary images Histograms and color tables

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1 LAB 4: Operations on binary images Histograms an olor tables Computer Vision Laboratory Linköping University, Sween Preparations an start of the lab system You will fin a ouple of home exerises (marke with a pointing han) to be answere before the session. Log in an open a terminal winow from the bakgroun of the sreen. Then give the following ommans in the terminal winow: moule a prog/matlab/8. matlab & Then give the following ommans in the MATLAB winow: apath( /site/eu/bb/mips/7. ); mips; Histograms an gray sale transformations From a histogram, we get information about the gray sale istribution in the image. Compute the histograms (see Operation winow Statistis) of the images li an blo56, where one is light an the other is ark. QUESTION : How are the lighting onitions reflete in the histograms?

2 QUESTION : Compute the histogram of the image baboon. How is the relatively low ontrast in the image reflete in the histogram? You will now make a graysale transformation on baboon so that the ontrast inreases. Clik on baboon to make it ative. Then write the following oe in the MATLAB winow, but replae A an B with numbers. As a suggestion, you an letf = 5 g = an f = g = 55. % Copy the image baboon to the MATLAB matrix f: f = getative; g = A * f-b; % Copy the MATLAB matrix g to the image monkey: newimage (g, monkey, ); QUESTION 3: How o you replae A an B? QUESTION 4: Look at the histogram of g, the transforme image. How oes this histogram relate to the previous histogram off? Binary operators. Non-onnetivity preserving expansion an ontration QUESTION 5: The operations ilation (expansion) an erosion (ontration) an be use to smooth the outline of binary images. Desribe the priniples of ilation an erosion!

3 QUESTION 6: Sketh the struturing elements for (4), (8) an otagonal metri! Whih struturing element allows for the most uniform ilation an erosion? Suppose that the operations are repeate several times. QUESTION 7: How an we fill in raks an holes in the objet? How an we remove spurs an unwante branhes along the outline of the objet? QUESTION 8: Loa the image nuf4b an threshol it by using the operation threshol. How o you use the histogram to fin out an appropriate threshol for the image? Note that the objet shoul be white (ontain ones) after thresholing, beause the system regars white pixels (ones) as objets! Remember: white=objet an blak=bakgroun for binary images. 3

4 QUESTION 9: The threshole image that you get from nuf4b has alreay a smooth outline, right? However, the threshole images that you will get from nufa an nuf5 have some problems with the outline. Make experiments to fin out a ombination of ilations (expan) an erosions (ontrat) in (4) an (8) metris to improve the outline of these images. nufa has an unwante branh: The roof of nuf5 is not onnete to its boy :. Connetivity preserving shrinking Unlimite use of the previously esribe operations for erosion may have a evastating impat on small objets in the image. These an easily be ut off or ompletely isappear. An appropriate ation may then be to prevent pixel wie lines to isappear. This is provie by onnetivity preserving shrinking. In MIPS, you an reate your own onnetivity preserving shrinking operations. With the help of the logop4 operation, you an selet whih struturing elements to be applie in four phases on your binary images. Before you an use logop4 you must first reate the struturing elements. Use the menu Struturing elements. Then the struturing elements an be alle from logop4. Do you think that it is a iffiult to use logop4? Then onsult the help funtion Operation help for logop4 - or the teaher. QUESTION : Give the struturing elements for onnetivity preserving shrinking (to point)! 4

5 Implement onnetivity preserving shrinking (to point) in MIPS aoring to your preparations. Try a few iterations on a familiar image. Compare this operation with erosion (ontrat). QUESTION : Whih operator removes noise best? Whih operator gives the smoothest outline? Whih operator may ivie one objet into two?.3 Kernels QUESTION : If you apply the previous operation for several iterations, only one point, the kernel, will be left. Consult the help funtion Operation help for logop4 for a suitable parameter for the number of iterations. Whih value o you hoose? QUESTION 3: There exist some objets that will not be shrunk to a point. Try to fin suh an objet in the image nufa. What is the speial property of suh an objet?.4 Skeletons If we want to shrink the objet, but still keep the overall shape of it, we an perform thinning an en up with a skeleton. thin is suh an operation. Make both 4- an 8-onnetive skeletons. QUESTION 4: What is the ifferene between a 4- an an 8-onnetive skeleton? 5

6 QUESTION 5: Is it possible to reonstrut the objet from its skeleton? QUESTION 6: Give the struturing elements for thinning, onnetivity preserving shrinking (to skeleton)! QUESTION 7: Implement onnetivity preserving shrinking (to skeleton) in MIPS with logop4. Try your operator on a familiar image. Make sure that your operator works satisfatorily by zooming in the skeleton image. Does your skeleton look similar to a skeleton obtaine by thin? QUESTION 8: Note that skeletons have istrating spurs. Delete the spurs with a ouple of iterations of onnetivity preserving shrinking (to point). This operation is alle pruning. Whih parameters o you hoose? QUESTION 9: Atually, it is not neessary to use all the 6 struturing elements for this operation. Whih struturing elements an be remove? 6

7 .5 Appliation: Ejiri s algorithm for iruit boar heking As a simple appliation of the so far omplete operations, we will now implement automate inspetion of iruit boars. We want to etet too narrow istanes between the onnetors an to fin too thin onnetors. It is also goo to etet soler garbage. See the hart with Ejiri s algorithm in the leture power point presentation. Implement Ejiri s algorithm for the images kretskort an/or kretskort. The onnetors in kretskort are speifie to be at least five pixels wie an the onnetors in kretskort are speifie to be at least three pixels wie. Write a MATLAB program that first etet too thin onnetors an then too narrow istanes between onnetors. Loa kretskort into A an then write: k = getimg( A ); That omman will take the image loate in A an loa it into the MAT- LAB matrixk. k has values between an 55. Create a file name minalgoritm.m with the following ontent an hek that it works. At first, it threshols the image to a binary image kbin with values between an. Then it ilates the objet step times. The images are shown. Be sure not to use the first figures (figure() to figure(5)) beause they are oupie by MIPS. kbin = threshol(k, 8, > ); figure(3) olormap(gray) images(kbin, [ ]) axis image; axis off; title( original iruit boar ) step = 4; kexp = expan(kbin, 8, step); figure(3) olormap(gray) images(kexp, [ ]) axis image; axis off; title( ilate iruit boar ) Can you see that the iruit boar has been ilate? 7

8 Now moify minalgoritm.m so that it performs the two funtions of Ejiri s algorithm. Exept for the funtions in minalgorithm.m, you will nee ontrat, invert, an.*. If you nee, onsult the MATLABhelp funtion. What types of errors o the iruit boar images ontain? Are there any ases that are wrongly marke as errors? In suh a ase, where an why? 8

9 3 Segmentation an labeling Thresholing segments the image into objets an bakgroun. The proess to ientify iniviual objets an to give them names is alle labeling. The labeling algorithm use in MIPS is the run-trak (RT) algorithm. When the algorithm is finishe, all objets are marke with unique labels, an we will be able to see how many objets there are in the image. 3. The RT algorithm See the figure below. San the image from top to bottom. Note if there are neighboring pixels with ifferent labels. ) a a a b ) a a a b a a b 3) a a a a b a a b b b 4) a a a a b a a b b b N) a a a b a a a b b b a a a b b b b ) Right san. If : Set new label. Sprea labels to the east. 9

10 ) Sprea labels to the south. 3) Left san: Sprea labels to the west. 4) Similar to san. N) Preliminary result. The final result is reeive after a new labeling onsiering neighbor pixels with ifferent labels. 3. Segmentation in pratie Make an image whih ontains a number of objets (5-). You an, for example, threshol the image baboon an apply some ilation (expan) an erosion (ontrat). Then apply the labeling operation. You may nee to hange the olor table to see well. QUESTION : Whih label values o the objets in your image reeive? Look for min an max values! QUESTION : Whih label value is given to the bakgroun? QUESTION : In whih orer brings labeling out the labels to the various objets an is it in agreement with the example? QUESTION 3: Then, how will the objets in the example be labele if the MIPS labeling was applie?

11 4 Measurements in images 4. Appliation: Fingerprint measures QUESTION 4: Give the struturing elements for 4-onnetive etetion of ramifiations! QUESTION 5: Give the struturing elements for 4-onnetive etetion of en points! Fingerprints an be use for ientifiation of riminals in fingerprint registers. It an also be use for ientity verifiation instea of oes an ars. The fingerprint image must normally be preproesse before it an be threshole to a binary image. This has alreay been performe on the image fingerbinary. Loa the image an reate two images, the first with markings at the ramifiations an the seon with markings at the en points. Use the operations thin an logop. QUESTION 6: Di you fin all ramifiations an en points? Now you will ount the number ramifiations an en points automatially by the following ation. First loa the image into MATLAB by: a=getative; Then alulate the number of ones in the image by: sum(sum(a)) QUESTION 7: Give the number of ramifiations an en points!

12 5 Distane measures in binary images 5. Distane maps A istane map of the objet shows the shortest istane from eah pixel in the objet to the outline of the objet. See the hart below with the original objet to the left an the resulte istane map in (4) -metris to the right Create some istane maps with the help of the operation istmap by applying it on a few binary images. When you are stuying the istane maps, you an use the olor table slump, RGB33 or istane to see well. QUESTION 8: Can you see the istane map an oes it make sene? QUESTION 9: It is also possible to make a istane map of the bakgroun instea of the objet. How o you hange the parameters to istmap then?

13 5. Appliation: Solving a labyrinth QUESTION 3: Here we will apply the solution to the shortest path problem on labyrinths. Dissolve at least one of the labyrinths on the next pages. Di you manage to solve a labyrinth? Loa one of the labyrinths an threshol it. Use the funtions ista an istroute to fin the shortest path through the labyrinth. QUESTION 3: Di you fin the same path when you solve the labyrinth manually? Compare the labyrinths on the next pages with the labyrinths in the omputer. There is a slight ifferene in the form of two blak spots. QUESTION 3: Why was it neessary to a these blak spots? 3

14 6 Labyrinth images Labyrint 4

15 Labyrint 5