Presentation given at the University of Tokyo and The Japanese Society of Mathematical Biology in Fukuoka during September, 2016. The presentation begins with a discussion of the application of landmark and Elliptical Fourier Descriptor methods to grapevine and Passiflora leaf data and ends with the use of persistent homology to morphometric questions.
New and old ways of looking at shape: morphometric analysis of leaves
1. New and old ways of
looking at shape:
morphometric analysis
of leaves
Dan Chitwood
Donald Danforth Plant Science Center
September 3, 2016
2. Chitwood & Sinha, 2016
Leaf shape varies by
evolution, genetics, development and
by present climates & ancient climates
3. Leaf shape varies by
evolution, genetics, development and
by present climates & ancient climates
Chitwood & Sinha, 2016
4. Paleomap, scotese.com
Leaf shape varies by
evolution, genetics, development and
by present climates & ancient climates
Chitwood & Sinha, 2016
5. There are many ways to measure shape:
Pseudo-landmarks
Chitwood & Sinha, 2016
6. There are many ways to measure shape:
Elliptical Fourier Descriptors
Chitwood & Sinha, 2016
7. There are many ways to measure shape:
Homologous landmarks
Chitwood & Sinha, 2016
8. There are many ways to measure shape:
All methods are comprehensive,
but they’re not equivalent
Landmarks Elliptical Fourier Descriptors
Chitwood & Sinha, 2016
47. 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
48. r
• Persistence: track the evolution of features across scales
• 0-homology: connected components
• 1-homology: loops (holes)
Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
49. Sublevel Set Filtration:
Blue Red
Superlevel Set Filtration:
Red Blue
A Persistent Homology Primer
How to get a nest sequence of shapes
51. 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
52.
53. 16 annulus (rings) density estimator
A tool: Local and smooth side view
Blind to size, position, and orientation
54. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent
55. CV1
• Our approach integrates very different morphological characteristics
into a single descriptor.
Leaf Shape QTL
Statistical techniques: Multidimensional scaling (MDS, reduce dimension)
Canonical variate analysis (CVA, feature that most distinguish groups)
68. 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