Locating landmarks using templates [Elektronische Ressource] / von Jan Kalina

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• Publié par: universitat_duisburg-essen
• Publié le: 01 janvier 2006
• Nombre de lectures: 31
• Langue: English
• Poids de l'ouvrage: 1 Mo

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Locating Landmarks Using Templates
Dissertation
zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften
(Dr. rer. nat.)
dem Fachbereich Mathematik der Universit at Duisburg-Essen vorgelegt
im August 2006
von
Jan Kalina, geb. in Prag (Tschechische Republik)
Tag der mundlic hen Prufung: 12. Januar 2007
Gutachter: Prof. Dr. P.L. Davies (Universit at Duisburg-Essen)
Prof. Dr. Daniel Pena~ (Universidad Carlos III de Madrid)Contents
1 Introduction. Motivation. 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Existing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Templates 13
2.1 Measures of Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Weighted Correlation Coe cien t . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Construction of Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Weighted Correlation With Radial Weights . . . . . . . . . . . . . . . . . . . . . 19
2.5 Locating the Mouth Using Templates . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Optimization of Templates 31
3.1 Formulation of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Analytical Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Approximative Search Without Constraints . . . . . . . . . . . . . . . . . . . . . 42
3.4e Search Withts . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Two-Stage Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.6 Results in Another Database of Images . . . . . . . . . . . . . . . . . . . . . . . . 62
3.7 Preliminary Transformations of the Data . . . . . . . . . . . . . . . . . . . . . . . 67
3.8 Robustness of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.9 Optimizing the Weights for the Eyes . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.10 Optimization of the Template Itself . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4 Locating Landmarks in Faces|Other Results 87
4.1 Locating the Eyes Using the Information about the Mouth . . . . . . . . . . . . 87
4.2 Mouth and Eyes Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3 Locating the Nose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4 Final Remarks. Future Research. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Bibliography 97
iii CONTENTSList of Figures
1.1 An example of an image: the photo of dr. Stefan B ohringer. . . . . . . . . . . . . 1
1.2 Some landmarks of the face. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 An image with the face rotated by +45 degrees. . . . . . . . . . . . . . . . . . . . 3
2.1 Mouth templates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Some of the eye templates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Left: radial weights. Right: the same image in the log scale. . . . . . . . . . . . . 19
2.5 A mouth and a nonmouth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Left: mouth against the mouth template. Right: nonmouth against the same
template. Least squares regression (red) and arithmetic mean (blue). . . . . . . . 22
2.7 Left: mouth against the mouth template. Right: nonmouth against the same
template. Weighted regression (red) and weighted mean (blue) with radial weights. 22
2.8 Left: the mouth of the person from Figure 1.1. Right: residuals of the linear
regression of that mouth against the bearded template from Figure 2.2. . . . . . 25
2.9 The rst eigenmouth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1 The mouth area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Weights for the bearded mouth template. Solution of the analytical search with
di eren t values of the upper boundc. Left: c = 0:005: Right: c = 0:02: . . . . . . 38
3.3 Sorted values of the solution of the linear problem. . . . . . . . . . . . . . . . . . 38
3.4 Left: solution of the approximative search without constraints. Right: the same
image in the log scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5 Largest weights from Figure 3.4 and their positions in the template. . . . . . . . 43
3.6 The worst case with radial weights over the whole database of 124 images. Mouth
(left) and nonmouth (right) from the same image. . . . . . . . . . . . . . . . . . 44
3.7 Weighted regression and weighted mean with radial weights. Left: mouth against
the template. Right: nonmouth against the template. . . . . . . . . . . . . . . . 47
3.8 Weighted regression and weighted mean with the weights from Figure 3.4. Left:
mouth against the template. Right: nonmouth against the template. . . . . . . . 47
3.9 Solution of the constrained approximative search with c = 0:02. . . . . . . . . . . 50
3.10 of the approe search with di eren t values of the upper
boundc. Left: c = 0:01: Right: c = 0:005: . . . . . . . . . . . . . . . . . . . . . . 50
3.11 Approximative search withc = 0:005 modifying 8 pixels (left) and 16 pixels (right)
at the same time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
iiiiv LIST OF FIGURES
3.12 Results of the two-stage search with di eren t initial weights. In each row: initial
weights (left), result of analytical (middle) and two-stage search (right) for optimal
weights with the bearded template. . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.13 Results of the two-stage search minimizing the di erence between the mouth and
nonmouth. In each row: initial weights (left), result of analytical (middle) and
two-stage search (right) for optimal weights with the bearded template. . . . . . 55
3.14 Left: result of the two-stage search with the mouth teplate of Figure 2.8 (left)
and radial initial weights. Right: result of the modi ed two-stage search with
the bearded template starting with radial weights; the approximative search was
used modifying the weights in 8 pixels at the same time. . . . . . . . . . . . . . . 60
3.15 Weights obtained by the approximative search over the new database of images
starting with radial weights. Unconstrained (left) and constrained search with
c = 0:005 (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.16 Optimal weights in new images. Results with radial initial weights. Left: analyt-
ical search. Right: approximative search applied after the analytical search. . . . 63
3.17 Optimal weights in new images. Results with equal initial weights. Left: analyt-
ical search. Right: approximative search applied after the analytical search. . . . 64
3.18 The best weights obtained for all 212 images. Starting with equal weights, the
analytical and then the constrained approximative search with c = 0:005 have
been applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.19 The bearded mouth template after the transformation (3.11). . . . . . . . . . . . 68
3.20 Figure 1.1 after the transformation (3.11). . . . . . . . . . . . . . . . . . . . . . . 68
3.21 Optimal weights for images transformed by (3.11). Starting with equal weights,
the analytical (left) and then the approximative (right) search has been applied. 69
3.22 A mouth with a plaster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.23 The mouth from Figure 2.5 modi ed by" = 0:1 is used to examine the robustness
of the methods to nonsymmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.24 Study of robustness to of the mouth. Grey values in a half of the
mouth area increased by 0.10 (left) and 0.15 (right). . . . . . . . . . . . . . . . . 74
3.25 Above: a template for the right eye. Below: di eren t initial weights (left), result
of the analytical (middle) and two-stage search (right). . . . . . . . . . . . . . . . 80
3.26 Above: a template for the left eye. Below: di eren t initial weights (left), result
of the analytical (middle) and two-stage search (right). . . . . . . . . . . . . . . . 81
3.27 Weights obtained as a result of the approximative search with c = 0:30 for the
template from Figure 3.25 and radial initial weights. . . . . . . . . . . . . . . . . 82
3.28 Optimal template obtained with optimal weights (top right corner of Figure 3.12)
and bearded initial template. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.29 Optimal template obtained with di eren t weights and bearded initial template.
Left: initial weights. Middle: optimal template. Right: optimal weights for the
optimal template. Results of the two-stage search with the upper boundc = 0:005: 86
4.1 Left: the eyes are searched for in the horizontal strip based on the known position
of the mouth (Chapter 4.1). Right: the eyes are searched for based on a suspicious
mouth (Chapter 4.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2 Mouth and eyes in a picture rotated by 10 degrees. . . . . . . . . . . . . . . . . 90
4.3 Search for the nostrils. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93List of Tables
2.1 Sums of squares in the example of Chapter