Scalable spatial point process models for forensic footwear analysis

2026-01-30

arXiv.org

AI Summary

This study addresses the need to quantify the rarity of “accidental characteristics”—such as scratches and wear patterns—in footwear impressions from crime scenes, thereby enabling a scientifically grounded assessment of their evidential weight in forensic contexts. To this end, the authors propose a hierarchical Bayesian model that treats accidental features as a spatial point process and captures their local dependence on sole tread patterns through a spatially varying coefficient framework. A latent Gaussian model combined with Integrated Nested Laplace Approximation (INLA) is employed to facilitate computationally efficient inference at scale. Empirical evaluation demonstrates that the proposed approach significantly outperforms existing methods on held-out test data, yielding improved accuracy in footwear comparison and enhanced reliability in forensic evidence evaluation.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Shoe print evidence recovered from crime scenes plays a key role in forensic investigations. By examining shoe prints, investigators can determine details of the footwear worn by suspects. However, establishing that a suspect's shoes match the make and model of a crime scene print may not be sufficient. Typically, thousands of shoes of the same size, make, and model are manufactured, any of which could be responsible for the print. Accordingly, a popular approach used by investigators is to examine the print for signs of ``accidentals,''i.e., cuts, scrapes, and other features that accumulate on shoe soles after purchase due to wear. While some patterns of accidentals are common on certain types of shoes, others are highly distinctive, potentially distinguishing the suspect's shoe from all others. Quantifying the rarity of a pattern is thus essential to accurately measuring the strength of forensic evidence. In this study, we address this task by developing a hierarchical Bayesian model. Our improvement over existing methods primarily stems from two advancements. First, we frame our approach in terms of a latent Gaussian model, thus enabling inference to be efficiently scaled to large collections of annotated shoe prints via integrated nested Laplace approximations. Second, we incorporate spatially varying coefficients to model the relationship between shoes'tread patterns and accidental locations. We demonstrate these improvements through superior performance on held-out data, which enhances accuracy and reliability in forensic shoe print analysis.

Problem

• forensic footwear analysis
• accidentals
• spatial point process
• evidential strength
• shoe print rarity

Innovation

• latent Gaussian model
• integrated nested Laplace approximations
• spatially varying coefficients
• point process
• forensic footwear analysis