Semester

Fall

Date of Graduation

2023

Document Type

Thesis

Degree Type

MS

College

Eberly College of Arts and Sciences

Department

Forensic and Investigative Science

Committee Chair

Jacqueline Speir

Committee Member

Casper Venter

Committee Member

Tina Moroose

Committee Member

Matthew Marvin

Abstract

The recovery of known-source shoes for the purpose of comparison to crime scene impressions often occurs with a temporal lag. During this passage of time, the outsole can be altered due to continued wear. These changes may impact forensically relevant characteristics of use known as randomly acquired characteristics (RACs). Continued wear may cause the formation of new RACs, cause RACs to undergo some degree of geometric change, and/or lead to the loss of formerly existing RACs. Consequently, the correspondence between a test impression from a known mated shoe with continued wear and a questioned impression with less wear deposited at a scene may diminish. In order to systematically examine these changes, the acquisition, retention, and geometric change of RACs were investigated as a function of step-count. Eight participants were recruited to walk in a new pair of Nike Quest 3 shoes on a fixed route for 10 collections at 20K step-intervals up to a maximum of 200K total steps of use. Between each step-interval, high quality exemplars were created, digitized, and registered. The corresponding outsole was examined for the presence of RACs using oblique illumination and 4X magnification, and each feature’s geometry was traced using Adobe Photoshop Elements 10. In addition, one pair of shoes was remarked in replicate for each of the 10 step-intervals to inform uncertainty of detection and measurement, forming a quality control (QC) dataset.

RACs were tracked from the time of their acquisition through a total of 200K steps. The average gain in RAC count increased at a rate of 1.6X to 2.0X to 2.4X for 40K, 60K, and 80K steps of additional wear, respectively. However, uncertainty demonstrated that acquisition equal to or less than two RACs is likely attributed to variability in analyst detection. Likewise, the average loss, when normalized by the number of RACs present, increased at a rate of 1.6X to 2.0X to 2.3X for 40K, 60K and 80K steps of additional wear, respectively. Unlike the uncertainty reported for RAC gain, the quality assurance methodology used in this study effectively limited (nearly) all missed detections. As a result, variability in RAC loss as a function of missed analyst detection cannot be quantified, but is believed to be negligible.

For the purpose of detecting the spatial distribution of RAC acquisition and loss, 20 heatmaps were populated as a function of cumulative wear. Comparison of the spatial distributions of RACs for both acquisition and loss suggests possible clustering, with a slight increase in the number of RACs gained in the medial edge of the toe, and lost in the lateral toe and heel, for later step-intervals.

With the aim of quantifying the geometric change of RACs through continued wear and cumulative use, probability density functions and receiver operating characteristic (ROC) curves were generated to compare the numerical similarity --- based on average Hausdorff distance (HA) --- between known mated (KM) RACs that differ with wear, versus all other known non-mated (KNM) RACs in the dataset. If uncertainty in the method and the ability of the analyst to repeatedly trace RACs known to be identical is ignored, then across all step-interval differences (up to 180K) and cumulative wear (up to 200K of total steps), there was a 0.86 probability that mated RACs which persisted through continued wear were more numerically similar to themselves than non-mates. Moreover, for 20K steps of additional wear for a lightly-worn shoe versus a well-worn shoe, this probability was relatively constant (0.95 - 0.90), failing to detect any differences over the life of the shoe (at least up until 200K steps of use). However, for increasing additional steps, the probability of a randomly selected RAC being deemed more similar to a worn version of itself as opposed to a non-mated RAC decreased by about 4% for every 20K steps of additional wear between 20K and 100K total steps. When considering uncertainty in the analyst's ability to repeatedly mark RACs known to be identical, 95% of the QC mated RACs had a numerical similarity score less than 1.12 HA units. At 20K steps of additional wear, nearly 75% of the KMs-with-wear distribution overlapped with the KM-QC scores indicating either no substantial change based on wear, or an inability for this method to detect any difference due to wear. Another 10% of scores for KMs-with-wear were less than KNM scores, but 15% were actually greater (suggesting a numerical false exclusion). For all scores where a false exclusion between known mates is more numerically likely, the ratio of KMs-with-wear versus KNM scores was 19% for 20K additional steps. This value increased to 20%, 30% and 35% for 40K, 60K and 80K steps of additional wear, respectively.

In order to assess the effect of continued wear and cumulative age on the degree of global (or impression-wide) self-similarity, vectors of RAC area per spatial bin were transformed using principal component analysis (PCA), whereafter accuracy in group membership was evaluated using cosine similarity (CS) and linear discriminant analysis (LDA). When using CS as a classifier, source association accuracy decreased by approximately 6% for 20K - 100K steps of use (72%, 66%, 61%, 54%, 50%). This matches intuition in that a greater degree of continued wear will result in lower self-similarity. Lower classification accuracy was observed for earlier cumulative step-intervals, until at least six RACs were acquired to generate sufficient differentiation. These findings were corroborated with a hold-one-out validation (HOOV) using LDA as a classifier, such that self-association accuracy was below 75% until 160K steps were accrued. Additionally, little-to-no increase in classification accuracy was observed when a participant's left/right shoe designation was ignored. In other words, RAC maps for a left or right shoe worn by a single participant were not more similar than other close non-mates in this dataset. For the wear-induced deviation in self-similarity using CS and LDA, at least 8% and 23% (respectively) could be attributed to the combined method and/or analyst's variation in marking. Thus, greater global self-similarity than that reported may exist for moderately-worn shoes (perhaps as high as 80% for 20K steps of wear accumulated after 100K and measured using CS, and >>90% after 160K total steps when using LDA).

In summary, this research quantified RAC (i.) acquisition, (ii.) loss, (iii.) spatial distribution, and (iv.) numerical geometric similarity --- as well as (v.) global impression-wide self-similarity --- for a specific make/model of shoe, tracked over 200K steps of total wear, as worn by an opportunistic set of participants, walking a single/specific terrain. Results indicate a relatively equal rate of acquisition and normalized loss with increasing wear, such that loss can dominate for shoes with a greater number of initial RACs while acquisition can dominate for lightly-worn shoes with few RACs. In addition, there is evidence that approximately 15% of KMs-with-wear will start to exhibit changes in RAC geometry with 20K additional steps of wear that numerically cause them appear more similar to KNMs. As the step-interval difference increases to a total of 80K, this rises to approximately 25%. Finally, global self-similarity after 20K steps is very poor for new/lightly-worn shoes (owning to the lack of features on which to form a valid association), but this metric is generally greater than 80% for moderately-to-well-worn shoes (100K for CS and 160K for LDA). Naturally, as the number of steps walked between the collection of two test-impressions increases, similarity decreases. If the outcomes observed in this study persist with other datasets that include other shoe makes/models, participants, and terrains, then the results frame the range of variation in RAC number and self-similarity with less-worn mates that a forensic footwear examiner might reasonably expect between test impressions that differ in total wear.

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