## 3 Materials and Methods
### SPI-Net Architecture
#### 3.2.1 Geometric Features Branch  
According to the universal approximation theorem [65], any bounded function can be approximated as well as one wants with a shallow Neural Network containing only one hidden layer. As such, one may even use a trivial feed-forward neural network such as a Multi-Layer Perceptron (MLP) to model sequences, like any other type of data. For the Geometric Features branch, we use the simplest form of an auto-encoder: a trivial feed-forward non-recurrent neural network to reconstruct an action according to the evolution of the Euclidean distances of five given key-points over time: Torso, Left  
Knees. The given key-points were selected in order to extract specific information for the model such as pedestrian's orientation or pedestrian's dynamics over time. A considerable amount of literature has been published on modeling pedestrian's attention towards the environment as an input to infer their crossing intention [66; 67; 68; 69; 70; 71; 72], mainly by focusing on specific key-points such as the head and more specifically its orientation. [PERSON] et al. [70] show that across all the possible forms of attention and communication a pedestrian could use, the most notable one is to look in the direction of the approaching vehicle: for a collision incoming within the next few seconds, pedestrians always tend to look at the vehicle before crossing [16]. Therefore, such head orientation input is not necessarily useful for the particular task of intention prediction since it is almost always recurrent information. In that regard, [PERSON] et al. [69] report that head detection is not particularly useful for the particular task of intention prediction. Similar results were reported in [15]: specifically focusing on the head for modeling pedestrian's attention does not seem to bring better performance for the task of intention prediction. Key-points such as elbows or wrists were considered as well in order to capture specific attention behaviors of pedestrians relying on hand gestures to communicate their intention of crossing to the driver. However, it has been shown that pedestrians mainly use explicit communication such as hand gestures to signal gratitude or dissatisfaction following the driver's action [71]. Such a specific gesture happens too late for our current intention prediction task as the pedestrian would be already either crossing or not at that time. In fact, [PERSON] et al. [72] discovered that evident attention indicators used by humans for inferring crossing intentions such as the head orientation of pedestrians are not always sufficient. Even more, they concluded that _\"a lack of information about the pedestrian's posture and body movement results in a delayed detection of the pedestrians changing their crossing intention\"_. In conformity with this conclusion, we chose to capture different information for the Geometric features branch. Instead of extracting pedestrian's awareness features towards its environment, we try to capture pedestrian's orientation features and pedestrian's dynamics features over time based on relative distances of their key-points. Therefore the torso and shoulders key-points are preferred over the head, elbows or wrists to model the pedestrian orientation towards his environment. Furthermore, knee key-points are taken into consideration in order to determine if the given pedestrian is walking or standing in the scene and therefore capture the dynamics. By selecting a lower amount of key-points than the ones available in the complete body structure, we reduce the inference time of the Geometric features branch without degrading its quality for classification. To avoid redundancy in our distances matrix and to minimize the geometric branch input size, we use the Joint Collection Distances (JCD) [73; 35] feature to represent our vector of distances over time.