The document discusses various methods for measuring and quantifying shape, including traditional morphometrics like elliptical Fourier descriptors, landmarks, and pseudo-landmarks. It also introduces chain coding as a method to encode contour shape and persistent homology for analyzing branching topologies in plants. The document uses violins and their shapes as a case study example to demonstrate some of these shape quantification techniques.

1. Morphometrics and
persistent homology:
From violins and leaves to
the branching topologies of
plants
Dan Chitwood
Independent Researcher
June 9, 2017

2. There are many ways to measure shape:

3. There are many ways to measure shape:
Pseudo-landmarks
Chitwood & Sinha, 2016

4. There are many ways to measure shape:
Elliptical Fourier Descriptors
Chitwood & Sinha, 2016

5. There are many ways to measure shape:
Homologous landmarks
Chitwood & Sinha, 2016

6. An introduction to
traditional morphometrics:
Elliptical Fourier Descriptors
and violin shape
Persistent Homology
and the branching
topologies of plants

7. How to put
a number on shape?
An example, using violins

13. Photos from auction:
>9,000 instruments
>400 violin makers
>400 years of history
Chitwood (2014) Imitation, genetic lineages, and time
influenced the morphological evolution of the violin. PLOS ONE

16. How to measure shape:

17. Shape = { xn, yn }
How to measure shape:
Coordinates, landmarks, pseudo-landmarks

18. How to measure shape:
Chain code

19. How to measure shape:
Chain code

20. How to measure shape:
Chain code

21. How to measure shape:
Chain code
0
1
2
3
4
5
6
7

22. How to measure shape:
Chain code
0
1
2
3
4
5
6
7

23. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0

24. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0

25. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0

26. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7

27. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0

28. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6

29. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0

30. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6

31. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6

32. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6

33. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6

34. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6

35. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6

36. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6

37. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4

38. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6

39. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6

40. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6

41. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6

42. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6

43. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0

44. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0

45. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6

46. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6

47. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6

48. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7

49. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6

50. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6

51. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5

52. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6

53. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6

54. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4

55. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6

56. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4

57. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4

58. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6

59. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4

60. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4

61. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4

62. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4

63. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4

64. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4

65. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3

66. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4

67. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3

68. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3

69. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3

70. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2

71. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2

72. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2

73. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2

74. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0

75. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2

76. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2

77. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2

78. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0

79. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0

80. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2

81. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2

82. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2

83. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2

84. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2

85. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3

86. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2

87. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2

88. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2

89. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2

90. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2

91. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2 2

92. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2 2 0

93. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2 2 0
2

94. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2 2 0
2 0

95. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2 2 0
2 0 1

96. How to measure shape:
Chain code
0
1
2
3
4
5
6
7
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2 2 0
2 0 1 0

97. How to measure shape:
Chain code
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2 2 0
2 0 1 0
Shape =
{ }
Chain code is lossless:
perfect reconstruction
from compressed data

98. How to measure shape:
Chain code + Fourier = Elliptical Fourier Descriptors
Graphic: Christine Daniloff

99. How to measure shape:
Chain code + Fourier = Elliptical Fourier Descriptors
Graphic: Christine Daniloff Graphic: Cardiff University
Graphic: Workshop Mizzotti

100. How to measure shape:
Chain code + Fourier = Elliptical Fourier Descriptors
Kuhl and Giardina Computer Graphics & Image Processing (1982)

101. How to measure shape:
Chain code + Fourier = Elliptical Fourier Descriptors
Kuhl and Giardina Computer Graphics & Image Processing (1982)

102. How to measure shape:
Chain code + Fourier = Elliptical Fourier Descriptors
0 0 0 7 0 6 0 6 6 6
6 6 6 6 4 6 6 6 6 6
0 0 6 6 6 7 6 6 5 6
6 4 6 4 4 6 4 4 4 4
4 4 3 4 3 3 3 2 2 2
2 0 2 2 2 0 0 2 2 2
2 2 3 2 2 2 2 2 2 0
2 0 1 0
Shape =
{ }

103. How to measure shape:
Chain code + Fourier = Elliptical Fourier Descriptors
a1, a2, a3 … an
b1, b2, b3 … bn
c1, c2, c3 … cn
d1, d2, d3 … dn
Shape =
{ }
Harmonic coefficients:

104. -1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
z4941_1
# harmonics
2
4
8
16
32
64
How to measure shape:
Chain code + Fourier = Elliptical Fourier Descriptors

105. Deviations along the outline
Points sampled along the outline
Deviation(in%ofthecentroidsize)
30 60 90 120
0.050.100.150.200.25
# harmonics
2
4
8
16
32
64
How to measure shape:
Chain code + Fourier = Elliptical Fourier Descriptors

106. The morphological evolution of violins:
The effects of time, space, & people on violin shape

107. The morphological evolution of violins:
The effects of time, space, & people on violin shape

109. The morphological evolution of violins:
Why does shape correlate with time? Violin makers?

110. The New York Times

111. The morphological evolution of violins:
Does violin shape have a “genetic” basis?

113. House Gagliano:
Giuseppe (Joseph)
Gennaro (Januarius)
Nicoló
Ferdinando
**
*
*

114. *
House Testore:
Carlo Giuseppe
Carlo Antonio
*

115. House Degani:
Giulio
Eugenio
**

116. House Guarneri:
Giuseppe (del Gesú)
Giuseppe (filius Andrea)
Pietro (of Venice)
Pietro (of Mantua)
Andrea
*
*
*
*
*

117. But the Stradivarius shape doesn’t necessarily
produce a “superior” instrument.
Is shape just a viral meme?
Fritz et al. PNAS (2012, 2014)

118. Sometimes shapes are functional,
but can still vary in non-functional ways
Nia et al., Royal Society Proc A (2015)

119. Sometimes shapes are functional,
but can still vary in non-functional ways
Nia et al., Royal Society Proc A (2015)

121. Sometimes shapes are functional,
but can still vary in non-functional ways
Darren Li
Tommy Yu

122. f-hole shapes are like signatures,
characteristic of their makers
Darren Li
Tommy Yu

123. Darren Li
Tommy Yu
Violin body harmonics f hole landmarks
Evolution of f-hole and body outline shapes differ

124. An introduction to
traditional morphometrics:
Elliptical Fourier Descriptors
and violin shape
Persistent Homology
and the branching
topologies of plants

125. These slides made by:
Mao Li
Donald Danforth Plant Science Center
Chitwood Lab & Topp Lab
Persistent homology: a
tool to universally
measure
plant morphologies across
organs and scales

126. These slides made by:
Mao Li
Donald Danforth Plant Science Center
Chitwood Lab & Topp Lab
Persistent homology: a
tool to universally
measure
plant morphologies across
organs and scales

127. These slides made by:
Mao Li
Donald Danforth Plant Science Center
Chitwood Lab & Topp Lab
Persistent homology: a
tool to universally
measure
plant morphologies across
organs and scales

128. These slides made by:
Mao Li
Donald Danforth Plant Science Center
Chitwood Lab & Topp Lab
Persistent homology: a
tool to universally
measure
plant morphologies across
organs and scales

129. Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?

130. r
Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?

131. r
Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?

132. r
Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?

133. Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?
It depends on scale!

134. r
Persistent Homology, HOW?
Persistence Barcode

135. r
Persistent Homology, HOW?
Persistence Barcode

136. r
Persistent Homology, HOW?
Persistence Barcode

137. r
Persistent Homology, HOW?
Persistence Barcode

138. r
Persistent Homology, HOW?
Persistence Barcode

139. r
Persistent Homology, HOW?
Persistence Barcode
#connectedcomponents
r

140. r
Persistent Homology, HOW?
Persistence Barcode
#connectedcomponents
r
Now, apply!

141. tomato introgression lines
Eshed et al. , Genetic, 1999
Chitwood et al., The Plant Cell 2013
(domesticated, cv. M82) (wild)
IL4_3
• Significant difference is caused by the gene in the small region
• The difference is usually subtle

143. 16 annulus (rings) density estimator
A tool: Local and smooth side view
Blind to size, position, and orientation

144. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

145. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

146. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

147. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

148. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

149. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

150. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

151. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

152. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

153. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

154. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

156. Coarse approximation
Elliptical Fourier Transform
http://haitham.ece.illinois.edu
First harmonics 5 harmonics 10 harmonics 20 harmonics

157. Euler characteristics = # connected component - # loops
level

158. Euler characteristics = # connected component - # loops
level

159. Leaf Serrations QTL
level

163. Root Architecture QTL

164. Persistent homology detects concerted changes in shoot and root architecture
median values plots

165. Persistent Homology
• robust to noise
• invariant with respect to orientation
• capable of application across diverse scales
• compatible with diverse functions to quantify
disparate plant morphologies, architectures, and
textures
• Appropriate for the branching structures of plants

166. Persistent homology: a tool to universally
measure plant morphologies across organs
and scales
Mao Li, Margaret H Frank, Viktoriya Coneva,
Washington Mio, Christopher N Topp, Daniel H
Chitwood
bioRxiv 104141 doi: https://doi.org/10.1101/104141

168. Joe Wan
Twitter: @i_am_joe_wan

169. 2,392
9,619
4,765
34,637
2,885
17,859
865
5,733
3,301
866
84,859
5,814
2,422
176,017 leaves!
Demarcating a
leaf morphospace

170. 2,392
9,619
4,765
34,637
2,885
17,859
865
5,733
3,301
866
84,859
5,814
2,422
176,017 leaves!
Demarcating a
leaf morphospace

171. Discriminating
leaves:
Across
flowering
plant
families

172. Discriminating
leaves:
Across
sites
around
the world

173. Zoë Migicovsky
Morphometrics reveals complex and heritable
apple leaf shapes
bioRxiv Pre-print
https://doi.org/10.1101/139303

174. Chris Topp, Keith Duncan, Ni Jiang, Mao Li
A universal theory of plant morphology:
Persistent homology and plant topology

175. A universal theory of plant morphology:
Persistent homology and plant topology
Chris Topp, Keith Duncan, Ni Jiang, Mao Li

176. Chris Topp, Keith Duncan, Ni Jiang, Mao Li
A universal theory of plant morphology:
Persistent homology and plant topology

177. Chris Topp, Keith Duncan, Ni Jiang, Mao Li
A universal theory of plant morphology:
Persistent homology and plant topology

178. A universal theory of plant morphology:
Persistent homology and plant topology
Mander et al. (2013) Proc Biol Sci 280(1770):20131905
Mander et al. (2017) Royal Soc Open Sci 4:160443

179. A universal theory of plant morphology:
Persistent homology and plant topology
Mao Li, Keith Duncan, Chris Topp, Dan Chitwood (2017) Am J Bot
Persistent homology and the branching topologies of plants

180. Acknowledgments
FSU
Mio Lab
Donald Danforth Plant Science Center
Topp Lab
Donald Danforth Plant
Science Center
Chitwood Lab

181. “Transect” and Leafsnap data
Transect data
Dana Royer, Wesleyan University
Daniel Peppe, Baylor University
Peter Wilf, Penn State
Huff PM, Wilf P, Azumah EJ. 2003. Digital future
for paleoclimate estimation from fossil leaves?
Preliminary results. Palaios 18: 266-274.
Royer DL, Wilf P, Janesko DA, Kowalski EA, Dilcher
DL. 2005. Correlations of climate and plant ecology
to leaf size and shape: potential proxies for the
fossil record. American Journal of Botany 92: 1141-
1151.
Peppe DJ, Royer DL, Cariglino B, Oliver SY,
Newman S, Leight E, Enikolopov G, Fernandez-
Burgos M, Herrera F, Adams JM, Correa E, Currano
ED, Erickson JM, Hinojosa LF, Iglesias A, Jaramillo
CA, Johnson KR, Jordan GJ, Kraft N, Lovelock EC,
Lusk CH, Niinemets U, Penuelas J, Rapson G, Wing
SL, Wright IJ. 2011. Sensitivity of leaf size and
shape to climate: global patterns and paleoclimatic
applications. New Phytologist, 190: 724-739.
Leafsnap: A Computer Vision System for Automatic
Plant Species Identification
Neeraj Kumar, Peter N. Belhumeur, Arijit Biswas,
David W. Jacobs, W. John Kress, Ida C. Lopez, João V.
B. Soares
Proceedings of the 12th European Conference on
Computer Vision (ECCV), October 2012

182. The leaf morphospace group
Analysis
Mao Li, Danforth Center
Isolation
Rebekah Mohn, Miami University
Potato
Shelley Jansky, USDA, Wisconsin-Madison
Diego Fajardo, National Center to Genome Resources
Pepper
Allen van Deynze, UC Davis
Theresa Hill, UC Davis
Tomato
Viktoriya Coneva, Danforth Center
Margaret Frank, Danforth Center
Chris Topp, Danforth Center
Grape
Allison Miller, Saint Louis University
Jason Londo, USDA/ARS, Geneva, NY
Laura Klein, Saint Louis University
Passiflora
Wagner Otoni, Universidade Federal de Vicosa
Arabidopsis
Ruthie Angelovici, University of Missouri, Columbia
Batushansky Albert, University of Missouri, Columbia
Clement Bagaza, University of Missouri, Columbia
Edmond Riffer, University of Missouri, Columbia
Braden Zink, University of Missouri, Columbia
Brassica
J. Chris Pires, University of Missouri, Columbia
Hong An, University of Missouri, Columbia
Sarah Gebken, University of Missouri, Columbia
Cotton
Vasu Kuraparthy, North Carolina State University
Viburnum
Erika Edwards, Brown University
Elizabeth Spriggs, Yale University
Michael Donoghue, Yale University
Sam Schmerler, American Museum of Natural History
Grasses
Lynn Clark, Iowa State
Timothy Gallaher, Iowa State
Phillip Klahs, Iowa State

183. Thanks!