Surface Topography of Surface Topography of Cuneiform TabletsCuneiform Tablets

Monica Barbu* and Robert H. Johnston, Monica Barbu* and Robert H. Johnston, and Jonathan S. Arneyand Jonathan S. Arney

Chester F. Carlson Center for Chester F. Carlson Center for Imaging ScienceImaging Science

Rochester Institute of TechnologyRochester Institute of Technology

OverviewOverview

• BackgroundBackground

• TheoryTheory

• AccomplishmentsAccomplishments

• SummarySummary

Cuneiform TabletCuneiform Tablet

• First form of writing.First form of writing.

• 5cm.length 4cm.wide 5cm.length 4cm.wide 1cm.high.1cm.high.

• Evolved from pictographs.Evolved from pictographs.

• Used as documents about Used as documents about property, inventory and property, inventory and taxes.taxes.

• Consist of wedge marks Consist of wedge marks and cylinder seal and cylinder seal impressions.impressions.

The Challenges of Photographing The Challenges of Photographing Cuneiform Tablets Cuneiform Tablets

• Transfer 3-dimensional characteristics to a 2-Transfer 3-dimensional characteristics to a 2-dimensional plane.dimensional plane.

• In the past:In the past:– Artists hired to draw the features - time consuming Artists hired to draw the features - time consuming

and subjective.and subjective.

– Nearfield microscopy - expensive.Nearfield microscopy - expensive.

• Proposed technique:Proposed technique:– Surface TopographySurface Topography - simple equipment and - simple equipment and

inexpensive.inexpensive.

Surface TopographySurface Topography

Surface TopographySurface Topography

• Calculating the topography of an object from Calculating the topography of an object from digital images is a distinct way of extracting digital images is a distinct way of extracting contour measurements.contour measurements.– Described as variation in height across a horizontal Described as variation in height across a horizontal

dimension.dimension.

– Results in the quantitative relationship between surface Results in the quantitative relationship between surface angle and the observed irradiance in the camera.angle and the observed irradiance in the camera.

Surface TopographySurface Topography

• Provides relationship between topography and irradiance.– The surface of the object is a Lambertian reflector.

Schematic representation between Schematic representation between topographic height, h and the surface angle, topographic height, h and the surface angle,

Surface TopographySurface Topography

I1(x) = IoR sin [01 + (x)]

I2(x) = IoR sin [02 + (x)]

Characteristics of the two images in one dimension is:Characteristics of the two images in one dimension is:

Capturing images with novel Capturing images with novel devicedevice

• One light source attached to a graded arc.One light source attached to a graded arc.

• The arc has the ability to be positioned at The arc has the ability to be positioned at any degree from the base.any degree from the base.

• The arc is attached to a ring which is free to The arc is attached to a ring which is free to move 360º around the object.move 360º around the object.

• The object is stable in the center of this The object is stable in the center of this ring.ring.

Capturing the Images

Flat FieldingFlat Fielding

• Calibrate the camera, in order to use the Calibrate the camera, in order to use the digital camera as a primary instrument for digital camera as a primary instrument for measuring light.measuring light.

• Flat fielding the images.Flat fielding the images.– Removes the side to side variation in brightness Removes the side to side variation in brightness

which is caused by non-uniform illumination.which is caused by non-uniform illumination.– The result consists only the random variations The result consists only the random variations

caused by the surface of the object.caused by the surface of the object.

Surface Topography of the SphereSurface Topography of the Sphere

ResultsResults

• Matrix of alpha valuesMatrix of alpha values• Scaled to 256 gray Scaled to 256 gray

levels.levels.• 1-dimensional array 1-dimensional array

across the center of the across the center of the sphere extracted for sphere extracted for analysis.analysis.

Trace of Tan(alpha) Values Calculated Across the Trace of Tan(alpha) Values Calculated Across the Row of Pixel Values in the “Scan” LineRow of Pixel Values in the “Scan” Line

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30

Position (mm)

Tan(alpha)

meas alpha

calc alpha

Topographic Height Across the “Scan” LineTopographic Height Across the “Scan” Line

-1

0

1

2

3

4

5

6

7

0 5 10 15 20 25

Position in Millimeters

Height in Millimiters

6.44mm

Surface Topography of Cuneiform TabletSurface Topography of Cuneiform Tablet

Before After

Topographic Height Across the “Scan” Topographic Height Across the “Scan” Line from the Cylinder Seal ImpressionLine from the Cylinder Seal Impression

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Position (mm)

Height (mm)

Unfolded TabletUnfolded Tablet

ConclusionConclusion

• Cuneiform Tablets are remains of historic cultural Cuneiform Tablets are remains of historic cultural values.values.

• Surface topography would be beneficial in Surface topography would be beneficial in characterizing the evolution of these artifacts.characterizing the evolution of these artifacts.

• Make these documents more accessible.Make these documents more accessible.• Offer a clue to the specific tools used to make the Offer a clue to the specific tools used to make the

impressions.impressions.