Determination of the Resolution of a Dinosaur Footprint

Project Team:

Project Goals:

Using a scanning laser profiler (SLM) determine the resolution of a dinosaur footprint that has been casted in mud.

Scope:

This project is a collaboration work started by the efforts of Prof. Stephen M. Gatesy of Brown University during his exploits in the Arctic in recovering the dinosaur footprint along with other artifacts. WPI’s surface metrology lab has agreed to measure the skin imprint found on the cast for Professor Gatesy of Brown University and to do an analysis to determine the resolution of the footprint.

Rationale:

This project poses an interesting problem in surface metrology of being able to determine the scales at which the complexities of two surfaces are different. In the past we have differentiated surfaces by the relative areas. This is the first time we have attempted to differentiate surfaces by their complexities.

Determination of the scale at which the dinosaur’s passing has changed the complexity of the mud, and the succeeding stone allows us to determine the resolution with which we can learn about the texture of the dinosaur’s skin and the movements during walking.

Measurement:

The dinosaur footprint is approximately 230mm long and has a 60mm region where a distinct imprint that appears to show details of the skin texture is found. This is not the only section where this feature is found, but is the clearest in detail and is the focus for this study.

Texture measurements were made with WPI’s scanning laser microscope (SLM) in two regions, one in the imprint and one the unmarked stone adjacent to the imprint. The sampling interval for the measurements was 10 micrometers.

Analysis and discussion:

These two regions are analyzed using Sfrax and three kinds of results are plotted:

1. area versus scale, comparing the relative areas of the two regions versus scale;
2. complexity, or the slope of the relative area plots, versus scale, comparing the complexities of the two regions; and
3. the scale-based F-test of the complexity versus scale, or the mean square ratio of the comparing the complexities of the vs. scale, indicating the differentiability of the two regions by complexity as a function of scale

The area-scale plots show that at scales above 106µm^2 (or 1mm^2) the two regions are similar with respect to area-scale relations. The differences between the two regions are clear at lower scales, and it is clear that there is more variability in the imprint region. At scales below 103µm^2, the slopes of the plots from the adjacent stone and imprint approach each other, indicating that the complexities in these two regions are similar.

The complexity vs. scale plots allows us to view the complexity-scale relations for the two regions, and appears to confirm that the complexities become similar at lower scales. The F-test versus scale plots show quantitatively that at scales above about 4mm^2 and below about 500µm^2 the complexities of the two regions are becoming more difficult to differentiate with confidence levels above 99.9%.

Conclusion:

This suggests that at scales somewhere below about 500µm^2 the dinosaur footprint has not changed the texture of the stone, so that this is an indication of the resolution of the foot print, or finest scale at which information can be obtained with this level of confidence concerning the texture and movement of the dinosaur’s foot sole.

Figures shown below: Various images of the skin imprint of the dinosaur footprint.

A 7 cm square photograph

A 2 cm square photograph

A 2 cm square photo simulation

A profile height topographical image.

Results:

Click a graph for a larger view:

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Last modified: September 13, 2007 10:00:04