A HIERARCHICAL RULE-BASED METHOD FOR IMAGE SEGMENTATION USING MAXIMUM GRADIENT PROFILES. A.C.F.Colchester 1 R. T. Ritchings 2 N.D.

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1 2 A HERARCHCAL RULE-BASED METHOD FOR MAGE SEGMENTATON USNG MAXMUM GRADENT PROFLES A.C.F.Colchester R. T. Rtchngs 2 N.D.Kodkara 2 Department of Neurology, Guy's Hosptal, London Brdge SEl Department of Computaton, UMST, PO Box 88,Manchester M60 9RT QD For each pxel n an mage we determned the local drecton of greatest grey level change and lnked pxels n ths drecton to form maxmum gradent profles (MGP). Adjacent MGP's were lnked sde-by-sde to form edge sectons. These edge sectons corresponded very closely to those from a Canny operator. For the present applcaton, whch was concerned wth detecton and charactersaton of blood vessels on angograms, subsequent groupng was restrcted to ant-symmetrc edge sectons whch formed a rdge wth hgh grey values n the centre. The rdges corresponded closely wth blood vessels shown n the mage. The wdth of each rdge and the locus of ts centrelne were derved from antsymmetrc MGP pars and corresponded very well wth expert judgement of vessel wdth and centre lne locaton. Advantages of the MGP groupng method ncluded explct representaton of the profles of grey values normal to edges; ease of mplementaton of hgher-order groupng stages whch were natural extensons of lower level processes; and herarchcal data structure representng mage features at all scales, allowng mproved nteracton of bottom-up and top-down processng. ntroducton Our prevous work on knowledge based nterpretaton of angographc mages ' 2 ' 3 has underlned the need to establsh a herarchcal data structure whch represents the mage at multple scales and whch allows smplfed control of the nteracton between mage-drven and knowledge-drven processes. The method has been developed as a potental alternatve to the current multresoluton technques whch use mage blurrng of dfferent degrees n the analyss of features at multple scales 4. We have developed the method n the context of the analyss of blood vessel mages but t s not restrcted to angograms and, as wll be seen, very few of the processng steps use domanspecfc knowledge. We consder an mage as a 3-D grey level landscape wth topologcal features-* and we treat an edge as a "hllsde" or steep regon on ths 3-D surface. The most fundamental component of the edge s the profle of grey level change along lnes of maxmum gradent. Adjacent lnes of maxmum gradent on an edge wll have smlar profles and tend to be approxmately parallel. The drectons of these maxmum gradent profles (MGP's) are normal to the drecton of the edge. Our method of extractng mage structure s based on MGP's, s easy to mplement, and has a number of mportant propertes. 2 AVC 988 do:0.5244/c.2.33

2 Fgure Regon of nterest before dgtsaton Method Conventonal angographc mages showng the carotd arteres and ther branches n the neck were analysed. They had already been photographcally subtracted.e. radographc flm obtaned before njecton of contrast medum had been subtracted from a flm taken mmedately after njecton. Regons of nterest on the angograms were dgtsed to 28x28x6 bt resoluton. Examples are shown n Fgs and 8. The mages were transferred to an Apollo DN 3000 workstaton n the Department of Computaton at UMST where the system was mplemented. A par of 3 x 3 Sobel operators was used to establsh the local drecton and magntude of maxmum gradent for every pxel. A threshold for these gradents was derved automatcally as follows. The mage was dvded nto nonoverlappng 0x0 pxel squares and the Sobel operator magntudes (regardless of drecton) were examned wthn every square. The square wth the mnmum standard devaton of Sobel magntudes('s') was used for calculatng the threshold whch was then appled globally. All pxels whose Sobel output was greater than 3s were retaned. The neghbours of each of these pxels were examned, and any whose Sobel gradent magntude was greater than 2s were also retaned. Other pxels were gnored. Subsequent processng steps nvolved successvely groupng elements to form larger elements, larger elements nto stll larger elements, and so on. Pxels wth a local gradent above the threshold were lnked along the path of maxmum gradent to form MGP's provded that the track of an MGP dd not change drecton by more than 45 n total. MGP's were termnated f there were no gradents above threshold or f a further lnk would nvolve a change of drecton of more than 45. The overall drecton (n x & y) of the MGP was obtaned from a least squares straght lne ft to the (x,y) value of the MGP. At 22

3 the ends of each MGP neghbourng MGP's wth the nearest end ponts were examned, and f the MGP's were approxmately co-lnear they were lnked end to end to form a composte MGP. The pont(s) of steepest slope of the MGP were found. MGP's whose steepest slope ponts were near neghbours were compared, and where these MGP's had smlar drecton and maxmum gradent they were grouped to form a sde by sde set of MGP's or "hllsde" regon wth a normal gven by the mean of the MGP drectons. Edge sectons were formed from the ponts of steepest slope on adjacent MGP's by means of a rule set whch (a) attempted to mantan the edge secton drecton perpendcular to the MGP's and (b) mnmsed small devatons n the drecton of the edge secton (smlar to a 5-pont smoothng). Where approprate the rule set chose between competng steepest-slope ponts on a sngle MGP or nterpolated new ponts. The edge sectons thus derved were compared wth edge sectons derved from Canny and from Marr- Hldreth operators. The scale parameter of these was set at pxels after some expermentaton. Processng usng the edge sectons derved from the MGP groupng method was contnued by lnkng near-neghbour ant-symmetrc edge sectons to form rdges or valleys. f these were long n extent they corresponded to lne features n the mage. n the present applcaton, where the objectve was to detect blood vessels on good qualty angographc mages on whch blood vessels appeared as rdyes on the 3-D surface, edges wthout antsymmetrc partners formng a rdge were suppressed. Along the length of rdges the wdth of the rdge and the locus of ts centre-lne or symmetrc axs were derved from the edge ponts of antsymmetrc MGP pars. The majorty of the code was n the form of condtonal rules programmed n Lsp; the Sobel operator was programmed n Pascal. Fgure 2A Ango : Perspectve vew of Maxmum-Gradent Profles shown as f supermposed on the 3-D grey level surface Results Two e x a m ples of the dgtsed regon of nterest are shown n Fgures and 8. Fgs 2 to 5 show stages of processng of Angogram, Fgs 9 to 2 stages of Angogram 2. Perspectve vews of the extracted MGP's, shown as f supermposed on the 3-D grey level surface of the mages, are shown n Fgures 2 and 9. Fg 2B s an enlarged vew of a regon just above the centre of Fg 2A. When the edge ponts are dsplayed the method can be seen to functon as a very effectve low level edge detector (Fgures 3 and 0). Wth further processng to extend edge sectons and remove those sectons wthout an ant-symmetrc partner formng a rdge, a relable blood vessel boundary map was generated (Fgures 4 and ). The detected vessel centre lnes, whch corresponded very well wth an expert's judgement of centre lne poston, are shown n Fgures 5 and 2. 23

4 Fgure 2B Ango : Enlarged vew of Maxmum Gradent Profles from regon near centre of Fgure 2A 24

5 Edge sectons detected by the MGP groupng method (Fgs. 3 and 0) were compared wth the Canny (Fgs 6 and 3)and Marr-Hldreth (Fgs 7 and 4) operators. The Marr- Hldreth method suffers from major dstorton at sharp corners. The MGP groupng method performs comparably to the Canny (compare Fgs 3 wth 6 and 0 wth 3). Dscusson Conventonal mage pre-processng typcally nvolves the convoluton of smple kernels wth mage grey data and then thresholdng to generate edge sectons. These then ' ' : : '. '. ; j. "! = : ':_ :. :.' ": : : ;. : : : : : : : : : ': '. : : ' U [ ^,. «: :. :.. ' : : : : : : : ^ '/ ; : =.". :"' j; : :.! : : ' : '.' :.. «' : : : '!!!! ' ' ' : ' ' Fgure 4 Ango : Blood vessel boundary map derved from MGP groupng method. "«', '" ", '».. «. * L J.! f '- ' s.!! ;! 'j!!,'l 'l ', J, v'!. '. " L. *! '.. T". '. ll '... t : «" " H ^^ A B A * «* * Fgure 5 Ango : Blood vessel centrelnes derved from MGP groupng method Fgure 3 Ango : steepest-slope ponts on the Maxmum Gradent Profles 25

6 ^, M," «/... A, ; ::' v '... '! V :: - :,/ fcj: W J N H H r V,.W4 ) J ; n Fgure 6 Ango : Canny operator output wth wdth = pxels Fgure 7 Ango : Marr-Hldreth operator output wth wdth = pxels Fgure 8 Ango 2: Regon of nterest before dgtsaton 26

7 j \ :.. "-' ; l' : j! : ':...: :'', "j. ' : ' t. :' l" _ l. :_ t j j!.!... t j : : _ : \! t :...*: : :' :" ^: : :': : ) ' ] *! : t! Fgure 9 Ango 2: Perspectve vew of Maxmum-Gradent Profles shown as f supermposed on the 3-D grey level surface Fgure Ango 2: Blood vessel boundary map derved from MGP groupng method -*'. ~ ' : -, -,, ~\ ff V"' - L '. L ; ] ' «lb kj,, \* J ] "n ' :., , '<. r «j Fgure 0 Ango 2: Steepest-slope ponts of the Maxmum Gradent Profles Fgure 2 Ango 2: Blood vessel centre lnes derved from MGP groupng method 27

8 r\ \ \ \ '. '.,, : r -!«-. Fgure 3 Ango 2: Canny operator output wth wdth = pxels Fgure 4 Ango 2: Marr-Hldreth operator output wth wdth = pxels have to be subjected to a dfferent type of processng^ for lnkng, s ke e ton sa t on, etc. Our approach also requres the same type of geometrc lnkng processes to group and extend edge sectons nto larger edge sectons, larger edge sectons nto objects etc., but these same processes are also used at lower levels to generate edge sectons. The dstncton between preprocessng and subsequent analyss s thereby blurred. Smlarly, the same basc data structures whch are used for hgh-level, more abstract representatons of objects can be used throughout the processng routne. n these ways, feedback to refne earler processng results can be controlled n a more unform manner and less re-processng of mage grey-level data s requred. Wth our method, each stage of processng groups smaller elements nto larger features. n that the same basc groupng rules are appled at each stage, and the number of features progressvely decreases, our method s a type of pyramdal algorthm^'^ wth rapd convergence. However, unlke Rosenfeld's algorthms, the scale of the elements beng lnked at each stage s not predetermned, but s set by local data. As wth other pyramdal algorthms, scale ncreases as one ascends from the lowest level to the hghest n our data structure, but the level of a feature n the herarchy specfes the number of generatons of subfeatures below t, rather than absolute sze. The dfferent approaches used n the MGP groupng method and conventonal edge detectors have made t dffcult to decde whch stages of the MGP groupng method to nclude n a comparson wth more conventonal operators. Objectve comparson was also made dffcult because of user nput to the processng. To obtan optmum results from the Canny and Marr Hldreth operators requred several experments wth dfferent scale parameters usng expert knowledge to assess the results before the optmum settng for ths partcular applcaton was establshed. Our prelmnary evaluaton of the MGP groupng 28

9 method ndcates that when appled to angographc subtracton mages t performs smlarly to the Canny operator n the detecton of edge fragments. A sgnfcant advantage of the MGP groupng method arose n the mplementaton of later stages of processng. The lnkng of ant-symmetrc edge sectons and dervaton of the centre-lne and wdth of rdges were all natural extensons of the earler groupng stages and very successful n operaton. The mages so far examned have relatvely strong features and we have yet to evaluate the MGP groupng method n very nosy mages. Future extensons of the MGP groupng method should help to ensure good performance n nosy mages. Frstly, small peaks or rdges due to nose, on a larger "hllsde" representng the edge of a vessel, wll be categorsed as subparts of the larger edge and wll not prevent detecton and charactersaton of the larger structure. Secondly, f local lnks are not establshed at any level of the pyramd at any locaton, then groupng wll be attempted over a wder area. Ths s the stuaton whch wll often arse n nosy mages. Processng tme wll be ncreased, but where strong local structure s found, ths tme penalty wll be avoded. n many types of mage, the shape of the grey-level profles normal to edges carres mportant nformaton 9 whch s potentally useful both durng mage-drven segmentaton and durng mage nterpretaton usng doman specfc knowledge. Ths s partcularly true n quanttatve angography, where many of the calculatons about vessel wdth, cross-sectonal area, crosssectonal shape and other parameters are derved from the profle of grey level values along a track perpendcular to the long axs of the vessel^. Tradtonally the constructon of these transverse densty profles has requred several ntal steps: vessel recognton (usually wth extensve user nteracton); edge localsatonj centre-lne localsaton; calculaton of the normal to the centre-lne; and selecton of nearest pxels for grey level samplng. The MGP groupng method descrbed here provdes a much more effcent processng sequence. There are stll many aspects of the MGP groupng method to be explored and evaluated. The prelmnary results descrbed here have been suffcently encouragng to justfy further nvestgaton and our work n ths area s contnung. Future extensons wll nclude the detecton and classfcaton of other topologcal features such as valleys and grey-level maxma and mnma at dfferent scales (hll tops and valley bottoms). n ths way the whole mage wll be represented wthout usng domanspecfc knowledge as a herarchcal tree structure whch codes the relatonshp between features at multple scales. References. Rtchngs RT and Colchester ACF. (986) Detecton of abnormaltes on carotd angograms usng syntactc technques. Pattern Recognton Letters Rtchngs RT, Colchester ACF and Wang H - Q. (986) Knowledge based analyss of carotd arterograms. mage and Vson Computng 3^ ~ 3. Wang H-Q, Rtchngs RT and Colchester ACF. (987) An mage understandng system for carotd angograms. mage and Vson Computng ~ 4. Pzer SM, Olver WR, and Bloomberg S H. (9 8 7) Herarchcal shape descrpton va the mult-resoluton symmetrc axs transforms. Pattern Analyss & Machne ntellgence PAM

10 5. Koendernk JJ (988) mage structure. n Vergever MA and Todd-Pokropek A (eds) Mathematcs and Computer Scence n Medcal magng, Berln: Sprnger, Shra Y (973) A context senstve lne-fnder. Artfcal ntellgence^: Baugher S and Rosenfeld A (986) Boundary localsaton n an mage pyramd. Pattern Recognton J^9: Rosenfeld A (987) Pyramd algorthms for effcent vson, TR 866, Center for Automaton Research, Unv. Maryland, College Park, June 987. Slegh AC (985) The extracton of boundares usng local measures drven by rules. BPRA 3rd nternatonal Conference, St. Andrew's, Scotland. Colchester ACF (985) The effect of changng Pa CO? on cerebral artery calbre estmated by a new technque of dynamc quanttatve dgtal angography. PhD Thess, Unversty of London. 220