1. Identify the Artist of a Mystery Painting
Unknown Zhang Daqian
(1899-1993)
J.M.W. Turner
(1775-1851)
Ivan Aivazovsky
(1817-1900)
Objective: There is one mystery painting whose artist is unknown as the first picture shows below. Given three works
of three different artists, this project is to identify which artist is most probably responsible to the unknown painting.
Strategy: A painter has own style and habits which are latent in pixel values of a painting. Therefore by extracting and
comparing the information behind pixel values, the possible artist can be found. Treat the pixel value as elevation, and
that make sense when judging the pixel values, where the lighter the pixel, the higher the elevation. Viewing the
“elevation” changes with contours of these four paintings in 3D vision (as shown below), it seems that Aivazovsky’s
painting has the most similar trend to that of the unknown painting. And the evidences from next four aspects just
verified this hypothesis.

2. Tonal Deviation Unknown Zhang Variance from Unknown Turner Variance from Unknown Aivazovsky Variance from Unknown
Low 90.60% 84.90% -5.70% 88.30% -2.30% 88% -2.600%
Medium 9.20% 14.20% 5.00% 10.50% 1.30% 11.20% 2.000%
High 0.20% 0.90% 0.70% 0.50% 0.30% 0.80% 0.600%
Criteria 1. Tonal Deviation (Deviation of “Elevation”)
Conception:
The deviation of
elevation (pixel value)
indicates the variance of
painting tones. The
higher the elevation
deviation to adjacent
pixels, the rougher the
surface is, or for the
painting the tones are
more dispersed. Method
is shown as left. Then
comparisons and
differences of this
perspective are list in the
table below.
Step 1.
Create "smoother"
surface:
<Focal Statistics>
- MEAN
Step 2.
Calculate the
Standard
Deviation (STD):
<Focal Statistics>
- STD
Step 3.
Reclassify to High, Medium, Low levels of elevation deviation <Reclassify>
Original “Elevation” Smoothed Elevation Elevation STD
Unknown Zhang Turner Aivazovsky
Example: “Unknown”
Reclassified
Elevation STD
Legend
Vaule Level
1 = Low
2 = Medium
3 = High

3. Tonal Change Rate Unknown Zhang Variance from Unknown Turner Variance from Unknown Aivazovsky Variance from Unknown
Low 1.70% 2.30% 0.60% 2.10% 0.40% 2.20% 0.50%
Medium 15.25% 16.70% 1.45% 16.60% 1.35% 15.60% 0.35%
High 83.10% 81% -2.10% 80.20% -2.90% 82.20% -0.90%
Criteria 2. Tonal Change Rate (Change Rate of Slope)
Conception:
Use slope tool to create
the surface’s slope and
the slope’s slope, which
describes the change rate
of the slope values. Form
a painting view, it can be
understood as the tonal
change rate. Method is
shown as left. Then
comparisons and
differences of this
perspective are list in the
table below.
Original “Elevation”
Step 1.
Calculate the
slope Of the
surface
<Surface> - Slope
Step 2.
Calculate the
slope Of the
slope
<Surface> - Slope
Slope Slope’s Slope
Example: “Unknown”
Step 3.
Reclassify the change rate of slope to High, Medium, Low levels <Reclassify>
Unknown Zhang Turner Aivazovsky
Legend
Value Level
1 = Low
2 = Medium
3 = High
Reclassified
Slope’s Slope

4. Brushstroke Veer Unknown Zhang Variance from Unknown Turner Variance from Unknown Aivazovsky Variance from Unknown
Low 7.60% 14.90% 7.30% 17.00% 9.40% 12.90% 5.30%
Medium 20.70% 23.40% 2.70% 23.70% 3.00% 24.00% 3.30%
High 71.70% 61.70% -10.00% 58.40% -13.30% 63.10% -8.60%
Criteria 3. Brushstroke Veer (Range of Aspect)
Step 3. Reclassify the aspect range to High, Medium, Low levels <Reclassify>
Step 1. Get the Aspect of the surface
<Surface> - Aspect
Step 2. Calculate the focal range of the aspect
<Focal Statistics> - Range
Unknown Zhang Turner Aivazovsky
Conception:
Use the Aspect and Focal
Statistics tool to look
the paintings’ aspect and
its range. The range of
aspect can viewed as the
brushstroke veer range at
the details of these
paintings. Method is
shown as left. Then
comparisons and
differences of this
perspective are list in the
table below.
Example: “Unknown”
Legend
Value Level
1 = Low
2 = Medium
3 = High
Flat (-1)
North (0-22.5)
Northeast (22.5-67.5)
East (67.5-112.5)
Southeast (112.5-157.5)
South (157.5-202.5)
Southwest (202.5-247.5)
West (247.5-292.5)
Northwest (292.5-337.5)
North (337.5-360)
Aspect Aspect Range
High:r360.409
Low: 4.98773
Original “Elevation” Aspect Aspect Range
Reclassified
Aspect Range

5. Illumination Variety Unknown Zhang Variance from Unknown Turner Variance from Unknown Aivazovsky Variance from Unknown
Low 13.70% 14.50% 0.80% 18.90% 5.20% 14.70% 1.00%
Medium 32.00% 27.50% -4.50% 27.70% -4.30% 28.00% -4.00%
High 54.30% 58.00% 3.70% 52.40% -1.90% 57.40% 3.10%
Criteria 4. Illumination Variance (Hillshade Variety)
Reclassified
Hillshade Variety
Step 1. Create Hillshade of the “elevation ”
<Surface> - Hillshade
Step 2. Calculate the variety of focal hillshade]
<Focal Statistcs> - VarietyConception:
The hillshde of a surface
reflects the illumination
distribution. The variety of
hillshade can reveal
paintings the style of
illumination processing.
Method is shown as left.
Then comparisons and
differences of this
perspective are list in the
table below.
Unknown
Zhang
Turner
Aivazovsky
Step 3. Reclassify the hillshade variety to High, Medium, Low levels <Reclassify>
Original “Elevation” Hillshade Hillshade Variety
Legend
Value Level
1 = Low
2 = Medium
3 = High
Example: “Unknown”
Hillshade
High: 254
Low: 0
High: 9
Low: 1
Hillshade Variety

6. Paintings
Zhang Daqian J.M.W. Turner Ivan Aivazovsky
Total Difference from the Unknown 44.55% 45.65% 32.25%
Summary
Considering all the four aspects, the total differences of the unknown painting to three with known artists are list in the table below. The total difference
is calculated as the absolute sum of all the differences in the three level of the four criteria. The result shows that the painting of Ivan Aivazovsky has the
Ivan Aivazovsky.least difference to the unknown one. Therefore, it is most possible that the mystery artist of the unknown painting is
Shown below are 3-D vision of the four aspects of the two most like paintings
Unknown Ivan Aivazovsky
Hillshade Variety
Aspect Range
Slope Change Rate
Elevation Deviation