Unfortunately for forensic lab specialists (and perhaps fortunately for criminals), footwear impression evidence is usually not as specific as fingerprints. Typical analysis by forensic examiners occurs in two stages. First, specialists look at class characteristics, examining brand, model, identifying logos and size. Second, they look at accidentals, or post-manufacturing cuts, scrapes, holes and debris that accumulate on a shoe sole.
If both the class characteristics and the accidentals of a suspect’s shoe line up exactly with prints taken from the crime scene, then the lab work is complete. However, for a lot of cases, it’s not that simple. A footprint left at the crime scene may have been low quality, degraded by weather or other events, or the suspect could have attached smaller soles to the base of their shoe to confuse investigators—which was the calling card of Theodore Kaczynski, the Unabomber. In these cases, examiners pair footwear evidence with a random match probability to communicate the level of uncertainty associated with the results.
Thus, say Jared Murray and Neil Spencer, the strength of shoe print evidence is actually based on probability—which is an area the statistics experts know well.
"Any quantitative measure of the strength of evidence of a shoeprint match will be highly sensitive to underlying probability models," said Murray, professor of statistics at the University of Texas at Austin. "Small changes in modeling assumptions can shift these measures by orders of magnitude, so it is vital to get them right."
Murray and Spencer’s study, published in the Annals of Applied Statistics, focuses on how contact surfaces—the areas of the shoe soles that touch the ground (toes and heels, especially)—affect the distribution of accidentals. The researchers used the Jerusalem Shoeprint Accidentals Database (JESA), which contains information on 386 men’s shoes, to test several of their new mathematical methods.
They took test impressions for each shoe using orange powder on the soles, pressing them into clear film, then photographing the residual orange impressions left on the film. The images were then smoothed and de-noised to isolate the contact surface. The researchers found their models more successfully fit the location of accidentals on shoes than current models—and it did so quicker.
Current models demand analysis of one specific shoe at a time and are not scalable to all types of shoes. Murray and Spencer, on the other hand, suggest a more general and scalable approach based on a Bayesian hierarchical model that pools information across many contact surfaces at once. In this way, examiners can infer general trends and capture commonalities spanning a broad variety of shoes.
“We model the spatial distribution of accidentals on a shoe sole as a point process, treating the sole’s tread pattern as a covariate,” the researchers write in their paper.
The importance and value of explicitly incorporating the contact surface when modeling accidental distributions cannot be understated.
“We were the first to do so, and it resulted in a major improvement over the traditional models,” the researchers say.
Murray and Spencer said the upgraded model is not ready to be rolled out to crime labs, just yet. In fact, it may never be officially launched as both experts say they expect data collection and data sources to continue to grow, opening the opportunity for even more sophisticated models to capture the relationship between contact surfaces and accidentals more accurately.
Photo: Left to right: A photo of a shoe’s sole, a raw image of a test impression and the contact surface obtained from a standardized test impression. Credit: Jared Murray