Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Mapping with math

03.12.2002


In an unexpected meeting of the minds, two Dartmouth professors from disparate fields have come together to solve a problem: how to make accurate models of remote landscapes from photographs.


Dartmouth Professors Hany Farid (left) and Arjun Heimsath have found a way to create 3-D models of remote regions using only 2-D photographs



Arjun Heimsath, Assistant Professor of Earth Sciences, and Hany Farid, Assistant Professor of Computer Science, have found a way to create three-dimensional models of remote regions using only two-dimensional digital photographs. Once built, these models make it easier for researchers to predict landslides, erosion rates and other geomorphic events.

"It started after I got back from one of my trips to Nepal," says Heimsath. "I wasn’t able to survey the area I wanted because it was so hard to get to on foot. I’d seen Hany’s work, and I wondered if he could create the models I needed from photographs."


Usually, global positioning systems, satellite technology and other intensive surveying techniques are used to create digital elevation models, or DEMs. These methods are sometimes expensive, time consuming, or physically impossible to carry out in some parts of the world, and the equipment can be cumbersome, explains Heimsath. Farid, whose research focuses on image processing and computer vision, immediately realized he could help.

"We sketched out the idea on a napkin over lunch," says Farid. "I asked Arjun to take some photographs on his next trip, and we tested our theory within about three weeks. It didn’t really work at first, but it worked well enough to keep going."

Their collaboration resulted in a paper that appeared in the November 2002 issue of the Mathematical Geology Journal, which describes a new method to obtain DEMs, without walking through poison oak, navigating rough or unstable terrain, or hauling around big, expensive and delicate equipment.

"With our method, you breeze in with a digital camera, and with relative ease, you get the DEM," says Heimsath.

On any single photograph there is not enough information to calculate the DEM, explains Farid. But with at least three images of the same region, taken from slightly different vantage points, you can capture all the necessary data. Once the images are in the computer, the researcher has to manually pick spots on each picture that correspond, such as identifying the same shrub, the same boulder, and so on.

"After you pick somewhere between 50 and 100 points, the mathematical algorithm takes over and automatically estimates the elevation map," says Farid.

Farid explains that much of the math they utilized was developed for other applications. What he and Heimsath added were constraints unique to the surface geometry of the Earth’s surface. These constraints help to better condition or fine-tune the mathematical algorithms.

"One of the strikingly elegant aspects of our method is that you’ve got the pictures," says Heimsath, "so you know what your output is supposed to look like. If you run this model and you get something that doesn’t look like the picture, then you know you’ve done something wrong."

The algorithms are not without limitations, however. And the researchers caution that their methodology hasn’t been rigorously field tested yet. One limitation is the type of landscape being modeled. Ideally, the ground surface shouldn’t be covered in vegetation. In order for the calculations to work, the photos have to clearly illustrate the ground. Also, when taking the photos, the researcher needs a good point of view taken from a little distance away.

"It’s no good to be looking at the area you want to map from below. It’s better if you are on a hillside adjacent to the area, across the valley or on a nearby ridge," says Heimsath. Both researchers agree that it was a fun collaborative project.

"What was nice about the work, and what’s representative of Dartmouth, is that I’m taking tools from the mathematics and computer vision community," says Farid, "and applying them to a real-world problem that Arjun works on. It was just a good fit and a natural partnership. The fact that we live next door to each other helped maintain the momentum."

From the original lunch in the cafe to publication took about eight months. Farid and Heimsath say it’s probably the quickest project they’ve ever worked on. The next step is to move from theory to real-life application. Two of their students, Deane Somerville, from Sherborn, Mass., and Layne Moffett, from Tulsa, Okla., both Dartmouth undergraduates from the Class of ’05, plan to travel to New Zealand in January to test the theory. The students will go to areas that have already been surveyed by conventional methods, and take digital photos to see if the new methodology compares to what’s known. If it doesn’t, they can immediately return to the field and take some more pictures for more tests. In addition to publishing their paper in the Mathematical Geology Journal, Farid and Heimsath will present their research at the American Geophysical Union’s annual meeting in December.

Farid’s research is funded by the National Science Foundation and an Alfred P. Sloan Fellowship. Heimsath is also supported by the National Science Foundation.

SUSAN KNAPP | EurekAlert!
Further information:
http://www.dartmouth.edu/~news
http://www.dartmouth.edu/~news/releases/dec02/mathmap.shtml

More articles from Earth Sciences:

nachricht Water - as the underlying driver of the Earth’s carbon cycle
17.01.2017 | Max-Planck-Institut für Biogeochemie

nachricht Modeling magma to find copper
13.01.2017 | Université de Genève

All articles from Earth Sciences >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Interfacial Superconductivity: Magnetic and superconducting order revealed simultaneously

Researchers from the University of Hamburg in Germany, in collaboration with colleagues from the University of Aarhus in Denmark, have synthesized a new superconducting material by growing a few layers of an antiferromagnetic transition-metal chalcogenide on a bismuth-based topological insulator, both being non-superconducting materials.

While superconductivity and magnetism are generally believed to be mutually exclusive, surprisingly, in this new material, superconducting correlations...

Im Focus: Studying fundamental particles in materials

Laser-driving of semimetals allows creating novel quasiparticle states within condensed matter systems and switching between different states on ultrafast time scales

Studying properties of fundamental particles in condensed matter systems is a promising approach to quantum field theory. Quasiparticles offer the opportunity...

Im Focus: Designing Architecture with Solar Building Envelopes

Among the general public, solar thermal energy is currently associated with dark blue, rectangular collectors on building roofs. Technologies are needed for aesthetically high quality architecture which offer the architect more room for manoeuvre when it comes to low- and plus-energy buildings. With the “ArKol” project, researchers at Fraunhofer ISE together with partners are currently developing two façade collectors for solar thermal energy generation, which permit a high degree of design flexibility: a strip collector for opaque façade sections and a solar thermal blind for transparent sections. The current state of the two developments will be presented at the BAU 2017 trade fair.

As part of the “ArKol – development of architecturally highly integrated façade collectors with heat pipes” project, Fraunhofer ISE together with its partners...

Im Focus: How to inflate a hardened concrete shell with a weight of 80 t

At TU Wien, an alternative for resource intensive formwork for the construction of concrete domes was developed. It is now used in a test dome for the Austrian Federal Railways Infrastructure (ÖBB Infrastruktur).

Concrete shells are efficient structures, but not very resource efficient. The formwork for the construction of concrete domes alone requires a high amount of...

Im Focus: Bacterial Pac Man molecule snaps at sugar

Many pathogens use certain sugar compounds from their host to help conceal themselves against the immune system. Scientists at the University of Bonn have now, in cooperation with researchers at the University of York in the United Kingdom, analyzed the dynamics of a bacterial molecule that is involved in this process. They demonstrate that the protein grabs onto the sugar molecule with a Pac Man-like chewing motion and holds it until it can be used. Their results could help design therapeutics that could make the protein poorer at grabbing and holding and hence compromise the pathogen in the host. The study has now been published in “Biophysical Journal”.

The cells of the mouth, nose and intestinal mucosa produce large quantities of a chemical called sialic acid. Many bacteria possess a special transport system...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

12V, 48V, high-voltage – trends in E/E automotive architecture

10.01.2017 | Event News

2nd Conference on Non-Textual Information on 10 and 11 May 2017 in Hannover

09.01.2017 | Event News

Nothing will happen without batteries making it happen!

05.01.2017 | Event News

 
Latest News

Water - as the underlying driver of the Earth’s carbon cycle

17.01.2017 | Earth Sciences

Interfacial Superconductivity: Magnetic and superconducting order revealed simultaneously

17.01.2017 | Materials Sciences

Smart homes will “LISTEN” to your voice

17.01.2017 | Architecture and Construction

VideoLinks
B2B-VideoLinks
More VideoLinks >>>