Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 1

RE-SEQUENCING A HISTORICAL PALM LEAF MANUSCRIPTRE-SEQUENCING A HISTORICAL PALM LEAF MANUSCRIPTWITH BOUNDARY-BASED SHAPE DESCRIPTORSWITH BOUNDARY-BASED SHAPE DESCRIPTORS

Devrim AkcaDevrim Akca, , Armin GruenArmin GruenInstitute of Geodesy and Photogrammetry, ETH - Zurich, Switzerland

http://www.photogrammetry.ethz.ch

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 2

IntroductionIntroduction In the collection of Museum Riethberg-Zurich is a palm leaf manuscript from India,consisting 66 folios, inscribed on both sides.

100 erotic poems and more pictures were inscribed by 8th century AD Sanskrit poet Amaru.

The manuscript was prepared about 200 years ago.

Folios 1-18 were paginated. However the sequence of the rest is unknown.

The stack was damaged by a mouse biting pieces off (5-10 % from left side).

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 3

The GoalThe Goal

The geometry of the leaf perimeter, as left over after eating, should bear useful informationto find the original sequence.

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 4

METHODOLOGYMETHODOLOGY Image Acquisition Rectification of the Images Boundary Tracing Fourier Descriptors Spatial Boundary Intersection Evaluation of the Shape Data using Tree-search

RESULTS AND CONCLUSIONRESULTS AND CONCLUSION

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 5

Image AcquisitionImage Acquisition

Sony DSC-F505 Cybershot1600 x 1200 pixelfocal length : 7.1 mm

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 6

Rectification of the ImagesRectification of the Images

X

Z

omegax

z

y

Y

Projection center of the camera

Projective transformationBi-linear resampling

Imaging geometry

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 7

Cropping the images

2D leaf coordinate systems according to holes

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 8

Boundary TracingBoundary Tracing

Inner boundary tracing(8-connectivity mode)

Save as ASCII file

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 9

Fourier DescriptorsFourier Descriptors

(x0,y0), (x1,y1),,(xN-1,yN-1)

x0 , y0

x1 , y1

x

y

( ) ( ) ( )kyjkxk +=s k = 0,1, ,N-1})k(s{)u(a NF=

})u(a{)k(s~ 1M= F M < N

Original boundary708 elements

Inv.Fourier Trf. using250 coefficients

Inv.Fourier Trf. using150 coefficients

Inv.Fourier Trf. using75 coefficients

Inv.Fourier Trf. using25 coefficients

Inv.Fourier Trf. using10 coefficients

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 10

Original boundary (1532 elements) 250 Fourier coefficients

F , F-1

dMax

area

Additional shape features

66x661,650,65

65,10,1

65,01,0

fourier

0...............

...0

...0

=

dd

dddd

D

( ) ( )( ) ( )

=

jiji

j1i1j0i0

ij ...uaua

uaua

areaarea

dMaxdMaxv

=

area

dMax0...00

0...00...............

00...1000...01

WW

P

ijTijij vPvd = i , j = {0,1,,65} i != j

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 11

Spatial Boundary IntersectionSpatial Boundary Intersection

Intersected_areaIntersection_distances

n

ddist =

2

int_areadistijij areadist int_int_ Wint_Wint_dI +=

66661,650,65

65,10,1

65,01,0

0...dIdI............

dI...0dIdI...dI0

x

=Dintersection

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 12

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 13

Evaluation of the Shape Data using Tree-SearchEvaluation of the Shape Data using Tree-Search

YES

NO

START

YESNO

Go to starting leaf (18th )

Find most similar leaf on matrix D

Go to new leaf

Has thesequence been finished? END

Has it been usedbefore?

The partial problems:

Which leaves might be ancestor orsuccessor for a pointed leaf in thesequence?

The global problem:

How can this information be usedefficiently to generate the full sequence?

Dfourier and Dintersection

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 14

UNITS LABELSL18

L21 L19

L19 L22 L20 L37 L21 L22 L64

18th leaf

19th leaf

20th leaf

21th leaf

th leaf

Tree-Search

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 15

The Proposed SequenceThe Proposed Sequence

Orthographic view of theproposed sequence

Texture mapped model ofthe palm leaf manuscript

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 16

ConclusionConclusion

The missing sequence of the historical palm leaf manuscript was found by using shapedescriptors.

Akca, Gruen, CIPA 2003 - Antalya Re-sequencing a Historical Palm Leaf Manuscript with Boundary-based Shape Descriptors 17

THANK YOU FOR YOUR ATTENTION!THANK YOU FOR YOUR ATTENTION!