Page 1
Supplemental Material III
(intermediate results of applying our method to facade images)
Below we show the intermediate results of some representative facade images, including edge detection, penaltyfunctions in two directions (green lines), initial splitting lines (red lines), iteration of grouping and rectification.For grouped elements, we use the average pixel color to display them.
1
Page 2
Example #01
(a) (b)
Figure 1: Input image and detected edges
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: horizontal.
1
Page 3
(a) grouping (b) rectification
Figure 3: Level 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
2
Page 4
(a) horizontal (b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 7: Level 2, group 2, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 8: Level 2, group 3, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 9: Level 2, group 3, iteration of grouping and rectification.
3
Page 5
(a) input image (b) output partition
Figure 10: final result
4
Page 6
Example #02
(a) (b)
Figure 1: Input image and detected edges
1
Page 7
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: horizontal.
2
Page 8
(a) grouping (b) rectification
Figure 3: Level 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
3
Page 9
(a) horizontal (b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 7: Level 2, group 2, iteration of grouping and rectification.
4
Page 10
(a) horizontal (b) vertical
Figure 8: Level 2, group 3, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
Figure 9: Level 2, group 3, iteration of grouping and rectification.
5
Page 11
(a) input image (b) output partition
Figure 10: final result
6
Page 12
Example #03
(a) (b)
Figure 1: Input image and detected edges
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 3: Level 1, iteration of grouping and rectification.
1
Page 13
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: horizontal.
(a) grouping (b) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
(a) input image (b) output partition
Figure 6: final result
2
Page 14
Example #04
(a) (b)
Figure 1: Input image and detected edges
1
Page 15
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: horizontal.
2
Page 16
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 3: Level 1, iteration of grouping and rectification.
3
Page 17
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
(e) grouping (f) rectification
Figure 7: Level 2, group 2, iteration of grouping and rectification.
4
Page 18
(a) input image (b) output partition
Figure 8: final result
5
Page 19
Example #05
(a) (b)
Figure 1: Input image and detected edges
1
Page 20
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: horizontal.
2
Page 21
(a) grouping (b) rectification
Figure 3: Level 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
3
Page 22
(a) horizontal (b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
Figure 7: Level 2, group 2, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 8: Level 2, group 3, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
Figure 9: Level 2, group 3, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 10: Level 2, group 3, penalty function. Determined splitting direction: vertical.
4
Page 23
(a) grouping (b) rectification
Figure 11: Level 2, group 3, iteration of grouping and rectification.
(a) input image (b) output partition
Figure 12: final result
5
Page 24
Example #06
(a) (b)
Figure 1: Input image and detected edges
1
Page 25
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: horizontal.
2
Page 26
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 3: Level 1, iteration of grouping and rectification.
3
Page 27
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 7: Level 2, group 2, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 8: Level 2, group 3, penalty function. Determined splitting direction: vertical.
4
Page 28
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 9: Level 2, group 3, iteration of grouping and rectification.
(a) input image (b) output partition
Figure 10: final result
5
Page 29
Example #07
(a) (b)
Figure 1: Input image and detected edges
1
Page 30
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: horizontal.
2
Page 31
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 3: Level 1, iteration of grouping and rectification.
3
Page 32
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: horizontal.
(a) grouping (b) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 7: Level 2, group 2, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 8: Level 2, group 3, penalty function. Determined splitting direction: vertical.
4
Page 33
(a) grouping (b) rectification
(c) grouping (d) rectification
(e) grouping (f) rectification
Figure 9: Level 2, group 3, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 10: Level 2, group 4, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 11: Level 2, group 4, iteration of grouping and rectification.
5
Page 34
(a) input image (b) output partition
Figure 12: final result
6
Page 35
Example #08
(a) (b)
Figure 1: Input image and detected edges
1
Page 36
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: horizontal.
2
Page 37
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 3: Level 1, iteration of grouping and rectification.
3
Page 38
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
(e) grouping (f) rectification
Figure 7: Level 2, group 2, iteration of grouping and rectification.
4
Page 39
(a) input image (b) output partition
Figure 8: final result
5
Page 40
Example #09
(a) (b)
Figure 1: Input image and detected edges
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: horizontal.
1
Page 41
(a) grouping (b) rectification
Figure 3: Level 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: vertical.
2
Page 42
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 7: Level 2, group 2, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 8: Level 2, group 3, penalty function. Determined splitting direction: vertical.
(a) grouping (b) rectification
(c) grouping (d) rectification
Figure 9: Level 2, group 3, iteration of grouping and rectification.
3
Page 43
(a) input image (b) output partition
Figure 10: final result
4
Page 44
Example #10
(a) (b)
Figure 1: Input image and detected edges
(a) horizontal (b) vertical
Figure 2: Level 1, penalty function. Determined splitting direction: vertical.
1
Page 45
(a) grouping (b) rectification
(c) grouping (d) rectification
(e) grouping (f) rectification
Figure 3: Level 1, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 4: Level 2, group 1, penalty function. Determined splitting direction: horizontal.
2
Page 46
(a) grouping (b) rectification
Figure 5: Level 2, group 1, iteration of grouping and rectification.
(a) horizon-tal
(b) vertical
Figure 6: Level 2, group 2, penalty function. Determined splitting direction: horizontal.
3
Page 47
(a) grouping (b) rectifica-tion
Figure 7: Level 2, group 2, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 8: Level 2, group 3, penalty function. Determined splitting direction: horizontal.
4
Page 48
(a) grouping (b) rectification
Figure 9: Level 2, group 3, iteration of grouping and rectification.
(a) horizontal (b) vertical
Figure 10: Level 2, group 4, penalty function. Determined splitting direction: horizontal.
5
Page 49
(a) grouping (b) rectification
Figure 11: Level 2, group 4, iteration of grouping and rectification.
(a) input image (b) output partition
Figure 12: final result
6