2012.09.25 - Local and non-metric similarities between images - why, how and what for ?

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2012.09.25 - Local and non-metric similarities between images - why, how and what for ?

  1. 1. Local and Non-Metric Similarities Between Images - Why, How and What for ? Frédéric Morain-Nicolier CReSTIC - URCA - Troyes 2012.09.25 1
  2. 2. Outlines• Local similarities• Non metric similarities• Conclusion : • Local non-metric similarities ? • solutions • open problems 2
  3. 3. Local Similarities 3
  4. 4. Local Similarities, Why ? 4
  5. 5. 3D Acquisition ?[Troyes Library - Early Rennaissance Collection - Bibliothèque Bleue] 5
  6. 6. 3D Acquisition[Thanks to Le2I - Le Creusot Team] 6
  7. 7. 3D Acquisition : Economical Solution 7
  8. 8. 3D Acquisition : An Example ANALYSIS AND CONSERVATION OF ANCIENT WOODEN STAMPS ANALYSIS AND CONSERVATION OF ANCIENT WOODEN STAMPS 115 7 Range image (‘Pisces’ stamp) computed from projec- 6 3D View of acquired points of ‘Pisces’ stamp: point tion of point cloud cloud acquired with Minolta scanner Else t5Mzk*s (M.m and the neigh- a stamp, the printing zones are high elevation ones; 7 Range image (‘Pisces’ stamp) computed bourhood is in a low zone) 6 3D View of acquired points of ‘Pisces’range imagespoint the high grey-level pixels in the stamp: have to tion of point cloud End if be binarized as black (pixel50). The non-printing If pixel.t Then pixel50 cloud acquired with Minolta scanner zones must therefore be binarized as white (pixel51). Else pixel51Stamp 3D model Range Image A modified Niblack’s algorithm is used to binarize End if Else t5Mzk*s (M.m an range images.11,12 The main task is to adapt the End Do a stamp, the printing zones are high elevation ones; threshold over the image. The threshold is deter- bourhood is in a low zone The local threshold computing can be summarized the high grey-level pixels from the local meanimageslocal standard mined in the range and the have to End if by equation (1) deviation, computed on a restricted neighbourhood t~max(M,m)zk à s (1) be binarized as blackeach pixel. for (pixel50). The non-printing If pixel.t Then pixel50 By modifying the k parameter, it is possible to zones must therefore be binarized as white (pixel51). Define: Else pixel51 simulate the inking and printing process for various m the local mean computed on a [w6w] 8 A modified Niblack’s algorithm is used to binarize neighbourhood End if conditions (ink quantity, paper quality or humidity, 11,12 ink fluidity, exerted pressure etc.). Figure 8 shows the
  9. 9. 3D Acquisition ➙ Virtual PrintingRVATION OF ANCIENT WOODEN STAMPS 115 local threshold 7 Range image (‘Pisces’ stamp) computed from projec- point tion of point cloud Else t5Mzk*s (M.m and the neigh- ones; bourhood is in a low zone)ave to End if inting If pixel.t Then pixel50el51). Else pixel51narize End ifpt the End Do deter- The local threshold computing can be summarizedndard by equation (1)rhood t~max(M,m)zk à s (1) By modifying the k parameter, it is possible to simulate the inking and printing process for variousw6w] conditions (ink quantity, paper quality or humidity, ink fluidity, exerted pressure etc.). Figure 8 shows themplete same range image as that used in Fig. 7, binarized for k50.1–0.8. Note the ‘inking’ variations produced byd on a the k value modification. 3.3 Comparison between virtual and real stamping In order to test the proposed method, the results of 9 virtual printing were compared with real ones. For
  10. 10. 3D : Virtual vs. Real Fidelity ? Virtual Resolution ! Real 10
  11. 11. A Local Comparison is needed ! 11
  12. 12. A Local Comparison is Needed ! 12
  13. 13. A Local Comparison is Needed ! small diffs scattered diffsbig localised diffs 13
  14. 14. A Local Comparison is Needed ! 14
  15. 15. Local Similarities, How ? 15
  16. 16. Local Dissimilarity Map (LDM) Φ( , ) Which measure ? Which size ?e 7.4 – Comparaison de deux groupes de lettres. L’image de la CDL indique clai CDL indique clalisations des dissimilarités. La comparaison est également quantifiée. quantifiée. LDMon de deux groupes de lettres. L’image de la CDL indique clairement n de deux L’image de la CDL indique clairementmilarités. La comparaison est également16quantifiée.milarités. également quantifiée.
  17. 17. Local Dissimilarity Map Which measure between small images ?• MSE - PSNR?➡ pixel to pixel diffs A dA,B (p) = |A(p) B(p)| |A(p) B(p)|➡ low information and hard to interpret B 17
  18. 18. Local Dissimilarity Map Which measure between small images ? DH(A, B) = max (h(A, B), h(B, A)) ✓ ◆• Binary image = set of h(A, B) = max min d(a, b) pixels (foreground) a2A b2B h(B, A)➡ Hausdorff distance DH(A, B) [Huttenlocher 1993] DH(A, Tv A) = kvk➡ numerous variations, A including partial HD ieme B hK (A, B) = Ka2A d(a, B) 18
  19. 19. Local Dissimilarity MapWhich size for the sliding window ? ➡ adaptative ➡ must encompass the «diffs» but no more A B (a) (a) (b) (b) (c ➡ increase until the Figure 7.2 – Illustration de la notion de dissimilarité locale. Les Les imag Figure 7.2 – Illustration de la notion de dissimilarité locale. image A measure equals itsdissimilaires. Les Les fenêtrescentrepetite et AetetABetcar carc), petites.perme dissimilaires. fenêtres de taille de taille petitemoyenne (en (en ne permetten la dissimilarité locale au centre des des images la dissimilarité locale au images moyenne B trop c), ne trop petites. theoretical max ⇒ stopping criterion Nous pouvons donner uneune idée générale. les pixels situés dans la Nous pouvons donner idée générale. Si Si les pixels situés dans partiennent à des des traits grossiers,fenêtre doitdoit avoir une taille su⇥ partiennent à traits grossiers, la la fenêtre avoir une taille su⇥san écarts résultant de la comparaison de ces ces traits. les traits sont fins, écarts résultant de la comparaison de traits. Si Si les traits sont fi fenêtre soitsoit trop grande. Dans le cas contraire, des écarts qui sont plu fenêtre trop grande. Dans le cas contraire, des écarts qui ne ne sont 19
  20. 20. rmax = max r|DHW (p,r) (A, B) = r . (7.27) r>0 Local Dissimilarity Map En pratique ce théorème indique que tant que la distance de Hausdor locale est égale au rayon de la fenêtre, la mesure optimale n’est pas atteinte.In the Hausdorff distancedissimilarités locales 7.1.4.4 Définition de la carte des case : La carte des dissimilarités locales est définie maintenant aisément. Elle regroupe l’ensemble des mesures de dissimilarités locales réalisés pour di érentes positions. L’algorithme général lorsque la distance locale est basée sur la distance de Hausdor est le suivant : Algorithme 7.1 Algorithme itératif de calcul de la carte des dissimilarités locales (CDL) entre deux images binaires A et B. W (p, n) désigne la fenêtre carrée centrée au pixel p et de rayon n. Pour chaque pixel p, faire 1. n ⇤ 1 2. tant que DHW (p,n) (A, B) = n et n ⇥ DH(A, B), faire n⇤n+1 3. CDLA,B (p) = DHW (p,n 1) (A, B) =n 1 84 20
  21. 21. Local Dissimilarity MapWith the Hausdorff distance : fast computation CDLA,B (p) = |A(p) B(p)| max (d(p, A), d(p, B))Distance transform (or function) based TDA (p) = d(p, A)(distance to the nearest foreground pixel : very fast with a chamfer distance)⇒ linear expression (binary images) : CDLA,B = A.TDB + B.TDA [Baudrier PhD - Pattern Recognition 2008] 21
  22. 22. Local Dissimilarity Map : Toy Examples CDLa,b Figure 7.3 – Comportement de la CDL avec des motifs simp comparer. d est la CDL entre a et b, e est la CDL entre b et c e CDL de le niveau b,c gris est foncé, plus grande est la valeur locale de la FigureFigure 7.3 – Comportement de la CDL avec des simples ; a,b,c sont lessont les images à 7.3 – Comportement de la CDL avec des motifs motifs simples ; a,b,c images à comparer. d est la d est la CDL et b, e est b, e est la CDL entreet fet cCDL la CDL entre Plus c. Plus comparer. CDL entre a entre a et la CDL entre b et c b la et f entre a et c. a et le niveau de gris est foncé, plus grande est la valeur locale de la mesure.mesure. le niveau de gris est foncé, plus grande est la valeur locale de la Cet algorithme est coûteux en temps de calcul car itératif. En Figure 7.3 – Comportement de la CDL avec des motifs simples ; a,b,c sont le est en O(m4 ) pour deux images composées deet f⇥ m pixels. No comparer. d est la CDL entre a et b, e est la CDL entre b et c m la CDL entre A quantified and localized information le niveau de gris est distance de grandeEn elaet, la complexité de mesure. la foncé, plus Hausdor est utilisée dans de mesure locale de dis locale la la calcul Cet algorithme est coûteuxcoûteux en temps de calcul car itératif.valeur et, la complexité de calcul en temps de calcul car itératif. est7.3 – Comportement de algorithme est des motifs simples ; a,b,c sont les imagese à Cet la CDL avec très rapide. En. d est laest en entreen et b, 4 ) est la deux images composées de m ⇥ m pixels.c. Plus avons montré que lorsque 4 ) pour deux images composées de m ⇥ m pixels. Nous avons montré que lorsque CDL O(m a O(m e pour CDL entre b et c et f la CDL entre a et Nous est de gris est distancedistance deest estvaleur locale Théorème mesure locale dedes dissimilaritéscalcul peut être la foncé,la de grande Hausdor est dansde la mesure. plus Hausdor la utilisée utilisée dans la locale La dissimilarité, le calcul peut être entre deux la mesure 7.8. de carte dissimilarité, le locales 22
  23. 23. Local Dissimilarity Map : Toy Examples ➡ structural informations 23
  24. 24. 3.7. G´n´ralisation aux images en niveaux de gris e e 85 Local Dissimilarity Map : Toy Examples➡How to save time during holidays ? 24
  25. 25. Local Similarities, What for ? 25
  26. 26. Ancients PrintingsÉ. Baudrier et al. al. / Pattern Recognition 41 (2008) 1461 – 1478 É. Baudrier et / Pattern Recognition 41 (2008) 1461 – 1478 et 1471 1471É. É. Baudrier al. al.Pattern Recognition 41 41 (2008) 1461 – 1478 Baudrier et / / Pattern Recognition (2008) 1461 – 1478 14711471 É. Baudrier et al. al. / Pattern Recognition 41 (2008) 1461 – 1478 É. Baudrier et / Pattern Recognition 41 (2008) 1461 – 1478 1471 1471 É. É. Baudrier al. al.Pattern Recognition 41 41 (2008) 1461 – 1478 Baudrier et et / / Pattern Recognition (2008) 1461 – 1478 14711471 20 20 1616 20 20 20 20 1616 16 1416 18 18 20 20 18 1416 16 14 14 14 18 18 1816 14 12 14 16 18 18 16 16 14 12 12 16 16 14 14 16 16 14 1412 12 12 12 10 12 12 10 14 14 14 14 10 10 10 12 12 12 10 10 10 8 8 12 12 10 10 12 12 10810 8 88 8 10 10 10 10 8 668 8 8 8 6 66 6 8 8 6 6 8 8 64 6 6 44 4 6 6 6 26 6 6 44 4 4 4 4 4 224 4 4 2 2 4 4 2 2 22
  27. 27. Ancients Printings É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 1471 É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 1471 É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 16 20 16 20 16 18 20 1614 18 20 14 16 18 16 14 12 18 14 12 14 16 14 12 16 12 1010 12 14 12 14 10 10 12 10 12 88 10 810 10 8 88 66 68 86 É. Baudrier et al. 46 /4Pattern Recognition 41 (2008) 1461 – 1478 66 44 É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 6 1471 24 42 44 22 É. Baudrier et al. 0 Pattern Recognition 41 (2008) 1461 – 1478 02/ 22 00 É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 2 1471 20 0 16 0 16 00 20 16 20 18 16 18 18 14 20 18 14 1616 18 1614 16 16 18 18 12 18 14 16 12 16 1416 16 1412 14 14 16 12 14 16 16 14 10 14 12 10 14 1214 12 14 12 10 12 14 14 12 12 10 10 10 8 8 12 10 12 10 12 12 10 10 88 88 12 10 6 10 6 8 10 8810 88 666 810 10 6 44 6 88 66 66 4 44 4 68 8 22 4 66 44 44 2 2 46 6 2 02 20 00 2 4 24 2 24 4 2 00 00 0 2 2 02 2 0 0 1818 0 0 0 16 16 0 18 18 Fig. 8. Medieval impressions and their LDMaps. Here are four medieval impressions. Imp. 1, Imp. 2 and Imp. 3 illustrate the same scene with a di 1616 and their LDMaps. Here are four medieval impressions. Imp. 1, Imp. 2 and Imp. 3 illustrate the same scene with a Fig. 8. Medieval impressions16 16 16 16 kind 8. Medieval impressions Imp. their LDMaps. Here aare four medieval 14 Comparaison d’illustrations 12 14 14 Figure 20 – 14 Imp. their LDMaps. Here aare four 16 anciennes.Imp. 1, Imp. 22 and Imp. 3illustrate the same16 scene with a Fig. of grass and helmets in and 3. Imp. 4 illustrates distinct scene. impressions. Imp. 1, images a, b3et c représentent la a di 7.9 14 and 3. Imp. 4 illustrates distinct medieval impressions. Les Imp. and Imp. illustrate the same with m scene kind 8. Medieval impressions Fig. of grass and helmets in 14in Imp. 3. Imp. 4 illustrates a distinct 16 scene. 20 16 kindFigure 18CDL Imp.(f) CDL d’illustrations anciennes. Les images a, b et cde scènes dissimila of grass and 7.9 –12 Comparaison ; (g) CDLscene. (h) CDL . La comparaison représentent la m 14 14 kind of grass and helmets 20 12 12 20 18 14 scène. (e)18 10 helmets12 ; 3. Imp. 4 illustrates a distinct14 in 12 scene. ; 10 14 18 14 12 12 a,b 10 a,c a,d 10 16 c,d 12 10 10 scène. (e)methods are (f) CDLa,c ; (g)réparties; sur CDLc,d .the measure result is h).image comparaison produit 14 16 CDLa,b ; importantes ones12a,d (h) whether La comparaison de scènes dissimila 8 10 8 8 16 comparisondes valeurscompared with the CDLobtained 8 toute l’image (en g et an La (case of the LD 16 10 12 14 14 12 10 comparison methods86are compared with the ones 10obtained 6 whether LSDMap) or aresultvalue (case of(case ofof the L comparisonThe five classification methods réparties sur toute l’image (en result is h).image comparaison 14 ones obtained6 methods are compared with the are the follo- 8 10 whether the measure realet is an image 10 HD and LD 12 the the measure an (case the its 88 produit 10 valeurs importantes manually. des 12 and 10 faible measure g 12 scènes methods66 produit with the ones 8obtained 4 and the LSDMap) or a real value ou très8the HD and i 12 manually. The10 five 64classification des valeurs importanteswhetherLSDMap) or a resultvalue(case of 8(case of is itsL comparison similaires classificationmethods are the follo-4 La the en the In the first case,(en is an (case of method the the nombrereal e) image the HD and the classification localisées 6 are compared methods are the follo- 8 10 6 wing ones: The five manually. 4 and ations). a 44 scènes similaires produit methods are the follo-2 2 ations). Inin Sectioncase, In theclassificationmethod is is manually. The wing ones: wing ones: 6 8 five42classification des valeurs importantes enthe LSDMap) or a real valueou très6localisées 8 2 4 6 6 and 88 faible nombre (en e) (case of the HD and 6 described the first case, the classification 4 an empirica ations). 66 first 6.2. the second case, method a 2 6 20 4 2 wing ones: 44 based on the LDMap, • our method 02 4 4 0 0 describedforthe first case,In the second case, an empirica ations). Inin each class C In and C Section 6.2. the classification method is described Section 6.2. sim the second is computed from 44 tribution case, an empiri 0 0 2 In and Cdissim 2 0 2 dissim 0 • ourthe so-calledbased on the LDMap, • our method Local the LDMap, method22 based on Simple Difference Map (LSDMap) us- 0 22 2 describedfor eachthe modes of the dissim isis computed fr in each class Csim and C empirical distribution Section 6.2. sim the second case, an empiri tribution set. different C Medieval impressions and their LDMaps. Here are four medieval on the LDMap, Imp. 2 and Imp. 30illustrate the same 0 learning a As class tribution 0 computed fro • and are four illustrateLocal SimpleImp. theasimple difference locallythe same0 scene set. eachthe modes of the empiricalcomputed f ourImp. the medievalthe Simple with 1, Imp.Map (LSDMap) us- • the the • so-callededieval impressions and their LDMaps.2Here ing so-called based impressions. Imp. 1, different (LSDMap) us- impressions. method00 Localmap, but Difference 2Map Imp. 316 distance same sceneDifference and 0illustrate scene with tribution with As the easy of the dissim 16 distribution learning for a different Csim and C empirical distributi class is 16ure andimpressions. Imp. Imp.Imp.d’illustrations anciennes.(F, G)imagesdifferencelocally learning ladefined, anmodesand efficient classification mef medieval impressions. Imp. 1, Imp. 2 and Imp.33 illustrate the same scene with a different b 16 c représentent grass 7.9 – Comparaisonillustrates 4 20medieval helmets Imp. 3. 3. 1, 4 illustrates a a distinctscene. in Imp. scene. with 20Local Simple Difference Map a, quite well 20 Les simple ∩ W − Get W |,us- learning set.mêmeanmodesand efficient classification m • ing instead ofcthe HD: but with la = |F difference locally 20 ons anciennes. Les images a, bdistance map, H SD W the même (LSDMap)ass and helmets in t scene. scene. Imp. the ing the distance map, but with the simple so-called distinct the et 18 représentent 18 18 14 14 ∩ quite well defined, an easy method. empirical distributi quite maximum likelihood and the the 18 18 18 As the easy of efficient 14 is 18 well defined, 14 classification 16 e. (e) CDLa,b ; (f) CDLa,c ;insteadglobal the map,SD W (F, G)La=comparaisonW |, scènes16 well defined, an easymethod. (g) CDL16 HD: H but with . G) |F difference W de • instead of ; (h) CDL (F, simple W − G 12 |, 18 16 ingthe of theHD,HD: H SD Wc,dthe = |F ∩∩ W − G 12locally the distance16 a,d 16 ∩ ∩ 16 16dissimilaires quite maximum likelihood and efficient 14 16 is 14 maximum likelihood method. is the the 16 16 12 classification 12La,d ; methods are c,d . La comparaison14HD, H SD W (F, G) =measure result1014 an image (case of the LDMap (h) CDL compared withinsteadglobal HD: 14de scènes dissimilaires 16 arisondes valeurs importantes theones the sur whether the |F ∩ W g 14 W |, La comparaison likelihood method. 14 14duitmethods are comparedmeasuretherépartiesimage touteof the LDMap − Get12h). imageis 12 maximum deson • of 14 • the global HD, PHD,14 obtained 12 12 l’image 27 result10 an (en ∩is 14 14 the 12 of the LDMap 10 12 10 12rties sur toute l’image (enresult isobtained comparaison de obtained whether the with the g et 10 La (case ones h). an whether the measure 12is 8 (case 12 12 6.3.2. Results 10 8
  28. 28. Ancients Printings • LDM classification • similar • dissimilar ➡ SVM Bonne classification (en %) CDL DPP DH PHD MHD pour Csim 98 90 60 83 77 pour Cdissim 97 92 75 81 83Table 7.1 – Performances en classification d’images similaires issues de la base d’impressionsanciennes. CDL = carte des dissimilarités locales, DPP : di érence pixel à pixel, DH : distancede Hausdor , PHD : distance de Hausdor partielle, MHD : distance de Hausdor modifiée(voir 7.2.1.4). [Baudrier PhD] 28
  29. 29. Tumor Evolution t1 t2 t3 (a) (b) (c) ? ? Fig. 2. Segmented MRI.7.12 – Un exemple de la segmentation d’une tumeur. Seule une coupe d’u représentée, à trois dates di érentes. values in (f) do not reflect et al. 2007] in this case. As [Nicolier the similarity a short conclusion, the LDMap is a useful tool for non- 29
  30. 30. (S1) Coupes de la segmentation 1 A. Segmentation Method R ESULTS III. using SVM with RBF kernel. (j) Tumor Evolution A. MRI images are acquired on a 1.5T GE (General Segmentation Method Electric Co.) machine using an axial1.5T IR (Inversion on a 3D Slices 18 to 23 (a-f) of the Local Distance Volu MRI images are acquired Fig. 5. GE (General Recuperation) machine using an axialan axial FSE (Fast Electric Co.) T1-weighted sequence, 3D IR (Inversion Spin Echo) T2-weighted, ansequence, anPD-weighted 3) and 2 (fig 4). The distances are absolute volumes 1 (fig se- Recuperation) T1-weighted axial FSE axial FSE (Fast quence and T2-weighted, an axial FSE examination, we distance histogram (logarithmic scale in g Spin Echo) an axial FLAIR. eq. one PD-weighted se- For (3). (j) is the (a) (b) (c) have 24and an axial FLAIR.signals with a voxel size quence slices of the four colormap of images (a-f). For one examination, we of 0.47 ⇥slices ⇥ 5.5 mm3. signals with a and all size 0.47 of the four All the slices voxel the (a) (b) (c) have 24 examinations are⇥ 5.5 mm3. All SPM software. all the of 0.47 ⇥ 0.47 registrated using the slices and examinations are registrated using SPM software. using We use the first examination for training SVM RBF kernelthe first examination for training SVM using We use [10]. The training set was obtained from one (a) slice(b) using mouse to(c) (c) RBF by choose ten pixels into the tumour kernel [10]. The training set was obtained from one (d) (e) (f) (a) and (b) outside. We perform theten pixels into the tumour sliceten using mouse to choose first segmentation of this by (c) (c) volume by usingWe perform the first segmentation of this Fig. 4. Segmentation of the de (e) volume (slices from(f) to 23, a-f) and (b) outside. the SVM model obtained. So, we build using SVM with RBF kernel. second segmentation 18 (d) Coupes (S2) la 2 (c) t1 (a) ten (c)hundred points into the tumour automatically about one model obtained. So, we build Fig. 4. Segmentation of the second volume (slices from 18 to 23, a-f) volume by using the SVMhis case. As and outside from all one hundred slices. into retraining a using SVM with RBF kernel. automatically about the tumoral points We the tumour second SVM fromuse it fortumoral slices. Wesegmentation (a) (b) ol for non-his case. As and outside and all the perform a second retraining a for improve the first it for perform this last SVM model, As a true distance is used to compute the LDV, the ). It is non- for thus ol case. As (d) second SVM and use result. With a second segmentation (e) (f)his we perform the segmentationWith given scalar are true physical distance in mm. The given ). It is non- thus (d) for improve the first result. of others examinations. At Fig. 3. Segmentation of the first volume (slices from (f) to 23, a-f) this last SVM model, (e) 18 As a true distance is used to compute the LDV, the ol for using SVM with RBF kernel. eachperform the segmentation of others examinations. At given scalar are true physical there are mm. more low we segmentation of examination, we use this 2 steps distances histogram indicates distance inmuch The given ). It is thus (d) Coupesprocess for improve of examination, we use this 2 steps distances than (b) distances. This a coherent fact as non- Fig. 3. Segmentation of thede (e) segmentation(f) to 23, Fig 2 contains an example (S1) each la segmentation the 1 first volume (slices from 18 result. a-f) (a) distances histogram indicates there are much more low high (c) using SVM with RBF kernel. zero LDV values aredistances. in theaintersection of as non- Fig. 3. Segmentation of thede la obtained segmentation. All the nine slices of two the for (slices from result. a-f) process segmentation18 distances high obtained This coherent fact the two (S1) Coupesof first volumeimprove the 1 to 23, Fig 2 contains an example volumes. than intersection is locally filled with increasing segmented volumes are given All the and slices of two zero LDVThe are obtained in the intersection of the two using SVM with RBF kernel. the obtained segmentation. in figs 3 nine 4. of values (d) (e) E (General values, starting from zero locally filledmaximum local segmented volumesDetails are given in figs 3 and 4. volumes. The intersection is up to the with increasing E (Inversion B. Implementation distance starting from volumes. to the maximum 7. Us Fig. (General l FSE (Fast Fig. 6. a new mageJ is 15.56mm. This represent the higher straight distance values, between the zero the The maximum tumor hasvo A three-dimensional view of up LDV between re local distance E (Inversion (General B. The computation DetailsLDV is done with Implementation of the distance between the volumes. The maximum has progresse distance leighted se- FSE (FastR (Inversion 2. plugin computation2GHz opteron, donecomparison mageJ between the two volumes. the higher straight directed dista The [6]. With a of the LDV is the with a new of the is 15.56mm. This represent (d) (e) (f) distance tweighted we 2 ination, se- l voxel (Fast FSE (a) (b) ⇥ 512 ⇥ 9 volumes is done in 39 seconds. plugin [6]. (c) The proposed Local Distance Volume can be used to two 512 With a 2GHz opteron, the comparison of the between the two volumes. and 4). (b) is (j) ination, size we (a) (VDM) - coupes duprecisely the variations between two volumes. S track more volume des dissimilarités can be used to locales entreweighted these- and all size two (b) ⇥ (c) C. Results 512 ⇥ 9 volumes is done in 39 seconds. 512 The proposed Local Distance Volume voxel we ination, Fig. 5. Slices 18 to 23 (a-f) of the The Hausdorff Distance in a window (eq. (3)) is defined as track more precisely the variations between two2 volumes. ds C.The LDV is computed between Figure 1 and – Exemple de volume des dissimilarités (j) is the distance histogram (l volumes 7.13 2. The the maximum of two directed distance. In(3)) is Les deux locales. are. and all size (a) (b) (c) volumes 1 (fig 3) and (fig 4). The voxel the SVM using Results The Hausdorff Distance in a window (eq. the present case eq. (3). defined as are. and all one results LDVpresented in betweenS2)the z-resolution is L’histogramme indique la useful information.(a-f). (A, B) are is computed fig 5. As sont 1 and 2. The the maximum of two directed distance.of imagespresent case(e comparées. the directed distances carry répartition des distances clearly seen (by high negative distances). colormap hW d from the Local Dissimilary Volume The volumes In the SVM using are. tumour slightly greather than the xfigy 5. As the (with a ratio of carry the information on voxels sont expriméesW (A, B) results are presented in resolutions z-resolution is the directedniveaux de gris, present in vol. 1h ennot in Les distances, traduites par des distances carry useful information. and mm. (j) the d from one SVMof this using (d) 11.7), the obtained distance depends only(with a ratiothe vol. 2. SymmetricallyonW (B, A) carry in vol. 1 and not on (e) (f) information h voxels Volume the information in slightly greather than the x y resolutions lightly on of carry the (a-f) of the Local Distance present betweenationtumour the Fig. 5. Slices 18 to 23 z-axis information. distance dependsobtained distance is voxels present indistances andabsolute accordinginformation B) Only when the only lightly vol. 2. (fig 4). The vol. hWare not carry the to hW (A, on 2 (B, A) in vol. 1. So o, from this d we build one (d) Coupesgreathersegmentation the z-information has beenon the(fig 3) and 2 Symmetricallytumor has regressed and h (B, A) Fig. 4. Segmentation of the11.7), the obtained from(f) to 23, a-f) (S2) de la 2 volumes 1 the ofationtumour the tumour using SVM with RBF kernel. (e) than 11.7mm, 18 second volume (slices Fig. 4. Segmentation of the de (e) volume (slices froma18 to 23, a-f) IV. CONCLUSION z-axis information. Only when the obtained distance (j) is the distance histogram the 2 and notinin vol. 1. the hW (A, B) taken indicates where (logarithmic scale gray) and So W eq. (3). is voxels present in vol. ation build o, weof this (d) Coupesinto account. Fig 6 is (f) z-information has been taken images (a-f). where the tumor has regressedillustrated(B, fig. (S2) second segmentation 2 la than 11.7mm, the greather colormap of three-dimensional representation where the tumor has progressed. This is and hW in A) indicates retraining a the tumour using SVM with RBF kernel. o, we build of the LDV. Fig is 18 to 23, a-f) Fig. 4. Segmentation of theinto account. (slices6from a three-dimensional representation second volume (a) (b) (c) 97 7 and fig. 8. The has progressed. This central occlusion is where the tumor augmentation of the is illustrated in fig.egmentation retraining a VM tumour the model, using SVM with RBF kernel. the LDV. of As a true distance is used to compute the LDV, the A distance measure between volumes has 30 7 and fig. 8. The augmentation of the central occlusion is
  31. 31. Binary Pattern Localization x y P I(x,y) I(x,y)P CDLP,I(x,y) I 31
  32. 32. Binary Pattern Localization Local dissimilarities aggregation : XX MDGI,P = CDLI,P (k, l) k l with CDLI,P = I.TDP + P.TDI ) DI,P = TD2 P +I TD2 I P sum of two oriented measuresChamfer score [Borgefors, 1988]: how much I looks like à P? 32
  33. 33. Binary Pattern Localization : Example Fig. 2.Chamfer score MDG In (c), image response by Borgefors chamfer matcher. – In (d), image obtained with symmetric LDM-matcher. – A good match with the reference pattern is reported by low values (with dark gray levels).ce pattern, the ideal location in (a) 33
  34. 34. Binary Pattern Localization : Example I [Morain-Nicolier et al. 2009] 34
  35. 35. (%+* "#$ Brain Internal Structures Segmentation ! (,-*(,* ! ! !! ! ! ! /01!! ! !! "#$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"%$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"&$! "#$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"%$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"&$! "#$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"%$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"&$! "#$! !"%$! !"&$ ! ()*+,!-./!"0$!12!3*405!#+0(5!066,0+05%,!"#$!%7+7508!"%$!09(08!"&$!:0)(;;08! "#$! "#$! !"%$! !"%$! !"&$ !"&$ ! ! ()*+,!-./!"0$!12!3*405!#+0(5!066,0+05%,!"#$!%7+7508!"%$!09(08!"&$!:0)(;;08! ()*+,!-./!"0$!12!3*405!#+0(5!066,0+05%,!"#$!%7+7508!"%$!09(08!"&$!:0)(;;08! 35
  36. 36. Brain Internal Structures Segmentation caudate putamen putamen thalamus"#$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"%$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"&$! 36
  37. 37. Brain Internal Structures Segmentation ! "#. !! !!!!!! Deformation ?!!! Atlas %/! "#$! Test Volume %+ ! ! %&! !"($! "#. !! )*+ %/! !%+ 37 !"#$! !!!
  38. 38. Brain Internal Structures SegmentationOptimal transformation : regularization T ⇤ = argminT 2 {Esim (B, A T ) + Ereg (T )} similarity measureClassic solution : 1 2 Esim (B, A T ) = kB A Tk 2Displacement field : (A T B)(p) u(p) = 2 rB(p) (A T B)2 (p) + krB(p)k 38

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