## 2 Methodology
### Friction Testing and Model Development  
The study area for this project is the City of Edmonton, known for its cold and lengthy winter season with frequent snowfall events. These weather characteristics make it an ideal location for this study as it allows us to collect images of road surfaces with varying degrees of contaminant presence and their corresponding friction values. Furthermore, it also provides us with the collision record needed to make a binary collision model. In the past three years (2019, 2020, and 2021), the City of Edmonton has experienced an average of 18,370 total crashes, 1922 minor injuries, 253 serious injuries, and 14 fatalities [13]. These events have been shown to be more frequent during the winter months, with 59.1% of crashes occurring between October and March [14].  
In total, 128 friction tests were performed over the course of four days (18, 19, and 25 January and 4 February 2022) alongside 10 h of dash camera road footage. An example of the road surface imagery recorded is shown in Figure 2a. Note that the actual input of the model is a cropped, transformed version of this image (shown in Figure 2b). This transformation converts the cropped image into a top-down view of the road surface.  
Figure 1: Proposed framework.  
These tests were performed after maintenance activities as a response to snowfall events that occurred on 17 January (7.3 mm), 24 January (2.4 mm), and 3 February (2.6 mm). Figure 3 depicts the locations visited during friction testing. Regarding the test procedure itself, it involved reaching a speed of 30 km/h, followed by the driver fully initiating the brakes until the vehicle came to a complete stop. During this braking process, a device called the Vericom VC4000 measured the friction coefficient through changes in the longitudinal G-force. Note that Feb 04 did not produce any additional friction measurements due to a device malfunctioning.  
Using the collected friction data and winter road surface footage, a friction model was developed using the decision tree algorithm in combination with four feature extraction techniques: road condition classification (bare, two-track, one-track, and fully snow-covered), image thresholding, local binary patterns, and a gray level co-occurrence  
Figure 3: Generated continuous friction values and the selected section for interpolator evaluation (red box). The map shown is powered by ESRI. Sources: City of Edmonton, Esri Canada, Esri, HERE, Garmin, SafeGraph, Geotechnologies, Inc., METI/NASA, USGS, EPA, USDA, NRCan, Parks Canada [15].  
Figure 2: Example of the road surface images collected and the processed image used as model input.  
matrix. The generated predictors were a mixture of texture features that describe the general state of the image (e.g., contrast) and task-specific features that describe the degree of contaminant presence on the road surface. Through these predictors, the decision tree algorithm formulated a relationship between these extracted features and their corresponding friction value with an RMSE of 0.0759 and a root mean squared percentage error (RMSPE) of 19.6% [16]. This model was used to create the dataset needed for interpolator evaluation and collision likelihood model development.