# CAPformer: Pedestrian Crossing Action Prediction Using Transformer

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## Abstract

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## 1. Introduction

#### 1.1. Context

#### 1.2. Motivation

## 2. Related Work

#### 2.1. JAAD

#### 2.2. TITAN and STIP

#### 2.3. PIE

#### 2.4. PePScenes

#### 2.5. Benchmark

## 3. Proposed Approach

#### 3.1. Problem Formulation

#### 3.2. System Description

#### 3.2.1. Video Encoder Branch

#### 3.2.2. Kinematics Encoder Branch

**ViT encoder**: similar to the one proposed in [34] for image classification. It applies a layer normalization on the embedded input before forwarding it into a multi-head attention layer. Its output is added to the original embedded input through a residual connection. After that, another layer normalization is applied and forwarded to a multi-layer perceptron composed of two linear layers with a Gaussian error linear units (GELU) activation between them. After another residual connection, the output of the layer is used as input for the next layer. The L layer’s output is summarized and the resulting vector is forwarded through a layer normalization and a simple feed-forward layer. Dropout is applied through all the processes, after every feed-forward layer, except for the last one. The diagram of this architecture is shown in Figure 2b;**Vanilla transformer encoder**: using the original proposed encoder in [7]. The main difference with the previous one is the application of layer normalization. Instead of applying it to embedded input, it is applied to the output of the second residual connection. The diagram of this architecture is shown in Figure 2c. Another difference is the usage of ReLU activation instead of GELU in the multi-layer perceptron.

#### 3.2.3. Feature Fusion Block

**Concatenation through fully connected**: The output of the video encoder is concatenated with the output of the kinematics encoder. This is forwarded through a multi-layer perceptron with one hidden layer, dropout regularization, and a ReLU activation. The output dimension of this layer corresponds to the number of classes;

#### 3.3. Training

#### 3.3.1. Datasets

**JAAD**[9]: This dataset is composed of 346 short clips (only 323 are used, excluding low resolution and adverse weather or night ones) recorded in several countries using different cameras. Two variants of the annotations are used in the benchmark: ${\mathrm{JAAD}}_{\mathrm{beh}}$ and ${\mathrm{JAAD}}_{\mathrm{all}}$. ${\mathrm{JAAD}}_{\mathrm{beh}}$ includes only pedestrians with behavioral annotations: 495 crossing and 191 non-crossing, giving rise to 374 non-crossing and 1760 crossing samples. ${\mathrm{JAAD}}_{\mathrm{all}}$ comprises the entire set of pedestrians in the sequences, adding 2100 non-crossing pedestrian far from the road, resulting in 6853 non-crossing and 1760 crossing sequence samples. The sequence samples from pedestrian tracks are extracted using a sliding window approach with an $80\%$ of overlap between them. Bounding boxes are manually annotated and provided for each pedestrian track. However, ego-vehicle state information is not measured, and the only related annotation is the categorical ego-vehicle state. Since this annotation is not used in the original results in the benchmark, we decided not to include it in our ranking process;**PIE**[26]: This dataset is composed of a continuous recording session in Toronto, Canada, spanning 6 hours during the day in clear weather. In addition to bounding boxes, as in the case of JAAD, PIE provides real measurements of the ego-vehicle state, obtained using an On-Board Diagnostics (OBD) sensor. As in the case of the benchmark, we decided to include this information as input for some of the trained models in both experiments and the ranking process. It contains 512 crossing and 1322 non-crossing pedestrians, which leads to 3576 non-crossing and 1194 crossing samples, using an overlap of $60\%$.

#### 3.3.2. Loss

#### 3.3.3. Optimizer

#### 3.3.4. Hardware and Software Details

## 4. Experimental Setup

#### 4.1. Data Ablation Study

#### 4.1.1. Bounding Boxes Image Cropping Strategies

#### 4.1.2. Bounding Box Coordinates Preprocessing

**Center coordinates and height**: we obtain the center coordinates of the bounding box and its height. We did not include the width to avoid redundancy, as we include it as a measure related to the distance between ego-vehicle and pedestrian;**Center coordinates and height including speed**: in addition to the above features, we include the speed of change of center coordinates and height.

#### 4.1.3. Pose Keypoints Missing Data

#### 4.1.4. Ego-Vehicle Speed Controversy

#### 4.1.5. Input Features Combinations

#### 4.1.6. Data Augmentation Applied

**Horizontal flip**: apply a random horizontal flip on the image plane;**Roll rotation**: apply a roll rotation of the 3D sequence, which is equivalent to applying a 2D rotation on each image in the sequence;**Color jittering**: apply a random change in brightness, contrast, saturation, and hue of the input sequence.

#### 4.1.7. Combined Datasets Training

#### 4.2. Model Ablation Study

#### 4.2.1. Pre-Trained Backbones

#### 4.2.2. Different Transformer Encoders

#### 4.3. Benchmark

**Multi-stream RNN (MultiRNN)**[44]: Two stream architecture which combines two RNN streams, one for odometry prediction (includes a CNN encoder for including visual features) and the other for bounding box prediction. Instead of predicting future bounding boxes, it is modified to predict the future pedestrian crossing action;**C3D**[45]: 3D convolutional model which combines 3D convolutional layers and 3D max-pooling layers. It uses only the pedestrian bounding box cropped regions from RGB video sequences as input data;**Inflated 3D (I3D)**[41]: 3D convolutional model based on 2D CNN inflation, where filters and pooling kernels are expanded into 3D. It uses as input optical flow sequence information, extracted from pedestrian bounding box cropped regions;**PCPA**[8]: best performing model in the benchmark. Multi-branch model with four branches. The first branch is based on C3D network and encodes input RGB video sequence extracted by cropping pedestrian bounding boxes. The other three branches consist of RNNs. The information is fussed using attention at the temporal level and the branch (modality) level.

- Query, key and value size is the same ${d}_{q,k,v}\equiv d=256$;
- Number of self-attention heads ${n}_{heads}=8$;
- Number of transformer encoders $L=2$;
- Multi-layer perceptron hidden layer dimension ${d}_{mlp}=384$;
- Dropout rate, applied after embedding and the MLP block ${p}_{drop}=0.1$.

#### 4.4. Model Hyperparameters

- PIE dataset used for training;
- Batch size of 16 samples;
- Local box warp used as the pre-processing for bounding boxes crops;
- TimeSformer used as backbone, pre-trained on SSv2 and fine-tuned. The output vector size of 1024;
- Fusion strategy: concatenation;
- Input sequence length $N=16$;
- Learning rate with value ${10}^{-4}$ for the fusion and kinematic encoder and ${10}^{-5}$ for the video backbone;
- Input image dimension of $112\times 112\times 3$;
- Weight decay of ${10}^{-3}$.

#### 4.5. Metrics

## 5. Results

#### 5.1. Preprocessing

#### 5.1.1. Image Input Nature and Size

#### 5.1.2. Bounding Box Coordinates Preprocessing

#### 5.1.3. Different Combinations of Input Features

#### 5.1.4. Data Augmentation

#### 5.2. Combined Datasets Training

#### 5.3. Different Encoder Strategies

#### 5.4. Benchmark

#### 5.5. Qualitative Results

## 6. Discussion

## 7. Conclusions and Future Work

- Train and test models in a combination of different available behavior datasets and analyze it in an unrelated scenario to see its generalization capabilities;
- Research deeper in the usage of data augmentation techniques in the training of multi-branch models;
- Consider the development of virtual scenarios to include more crossing cases and fight data imbalance;
- Explore new features from datasets, such as labeled information from the environment (e.g., the relative relationship between vehicles, crosswalk position, traffic signals). These new features will be 2D or 3D, depending on the availability of datasets in the literature;
- Experimentation with different data cleaning strategies in training time, applying a maximum occlusion level, pedestrian minimum size, etc.;
- Simulate real case scenario to find new weaknesses and strengths in available models.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Detailed model diagram. B stands for batch size, N is the sequence length, H is image height, W is image width, BBs is bounding boxes coordinates.

**Figure 2.**Detailed diagrams of embedding procedure and transformer encoder architectures. MHA stands for multi-head attention, LN for layer normalization, MLP for multi-layer perceptron. Grey part of embedding diagram corresponds to the class token, which is used in ViT encoder.

0.325 | 0.325 | 0.325 |

(a) b | (b) b | (c) b |

0.24 | 0.24 | 0.24 | 0.24 |

(a) b | (b) b | (c) b | (d) b |

**Figure 4.**Histogram showing the number of pedestrian tracks for each range of ego-vehicle speed in the benchmark data (TTE from 30 to 60 frames).

0.49 | 0.49 |

(a) b | (b) b |

**Figure 5.**Correct predictions in different test cases obtained from RubiksNet trained model. Green and red borders represent crossing and not crossing behavior, respectively.

**Figure 6.**Incorrect predictions in different test cases obtained from RubiksNet trained model. Green and red borders represent crossing and not crossing behavior, respectively.

**Table 1.**Information about the two datasets included in the benchmark. # of ann. fr. refers to the number of annotated frames; ${\mathrm{S}}_{\mathrm{NC}}$ and ${\mathrm{S}}_{\mathrm{C}}$ refers to the number of non-crossing and crossing pedestrians, respectively; Ego-veh. mot. refers to ego-vehicle motion.

# of ann. fr. | ${\mathbf{S}}_{\mathbf{NC}}$ | ${\mathbf{S}}_{\mathbf{C}}$ | Diff. Weather | Diff. Loc. | Ego-Veh. Mot. | |
---|---|---|---|---|---|---|

JAAD | 75 K | 495 | 2291 | Yes | Yes | No |

PIE | 293 K | 512 | 1322 | No | No | Yes |

F1 | P | R | AUC | |
---|---|---|---|---|

box | $0.212{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.078}$ | $0.309{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.081}$ | $0.189{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.069}$ | $0.542{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.014}$ |

box warp | $\mathbf{0}.\mathbf{454}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.040}$ | $\mathbf{0}.\mathbf{532}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $\mathbf{0}.\mathbf{417}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.055}$ | $\mathbf{0}.\mathbf{636}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ |

context | $0.387{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.017}$ | $0.531{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.037}$ | $0.318{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.025}$ | $0.599{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.006}$ |

surround | $0.379{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.070}$ | $0.431{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.072}$ | $0.350{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.071}$ | $0.607{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.022}$ |

F1 | P | R | AUC | |
---|---|---|---|---|

$112\times 112$ | $0.454{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.040}$ | $0.532{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $0.417{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.055}$ | $0.636{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ |

$224\times 224$ | $\mathbf{0}.\mathbf{528}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.020}$ | $\mathbf{0}.\mathbf{572}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.021}$ | $\mathbf{0}.\mathbf{507}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.042}$ | $\mathbf{0}.\mathbf{636}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.011}$ |

**Table 4.**Results obtained using different pre-processing strategies for bounding box coordinates. h refers to bounding box height; ${x}^{\prime},{y}^{\prime},{h}^{\prime}$ refers to speed of $x,y$ coordinates and height, respectively; subscripts $tl,br,c$ refers to top-left, bottom-right and center coordinates of the bounding box.

Mode | F1 | P | R | AUC |
---|---|---|---|---|

Only image | $0.454{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.040}$ | $0.532{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $\mathbf{0}.\mathbf{417}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.055}$ | $0.636{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ |

${x}_{tl},{y}_{tl},{x}_{br},{y}_{br}$ | $0.425{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.023}$ | $0.550{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.020}$ | $0.358{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.035}$ | $0.620{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.011}$ |

${x}_{c},{y}_{c},h$ | $\mathbf{0}.\mathbf{456}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.031}$ | $\mathbf{0}.\mathbf{587}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.031}$ | $0.403{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.052}$ | $\mathbf{0}.\mathbf{639}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ |

${x}_{c},{y}_{c},h,{x}_{c}^{\prime},{y}_{c}^{\prime},{h}^{\prime}$ | $0.355{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.067}$ | $0.462{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.078}$ | $0.300{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.066}$ | $0.600{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.022}$ |

**Table 5.**Different input combinations metrics. Abbr. I: Bounding boxes image crops, B: bounding boxes coordinates, P: pose keypoints, S: ego-vehicle speed.

Input | F1 | P | R | AUC | |||
---|---|---|---|---|---|---|---|

I | B | P | S | ||||

🗸 | $0.160{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.049}$ | $0.428{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.115}$ | $0.108{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.038}$ | $0.535{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.011}$ | |||

🗸 | 🗸 | $0.011{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.007}$ | $0.204{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.140}$ | $0.006{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.004}$ | $0.502{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.002}$ | ||

🗸 | 🗸 | 🗸 | $0.737{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.004}$ | $0.660{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.011}$ | $\mathbf{0}.\mathbf{837}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ | $0.833{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.003}$ | |

🗸 | 🗸 | $\mathbf{0}.\mathbf{746}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.003}$ | $\mathbf{0}.\mathbf{698}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.017}$ | $0.806{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.016}$ | $0.833{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.002}$ | ||

🗸 | $0.454{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.040}$ | $0.532{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $0.417{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.055}$ | $0.636{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ | |||

🗸 | 🗸 | $0.456{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.031}$ | $0.587{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.031}$ | $0.403{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.052}$ | $0.639{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ | ||

🗸 | 🗸 | 🗸 | $0.454{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.030}$ | $0.533{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.020}$ | $0.403{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.039}$ | $0.633{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | |

🗸 | 🗸 | 🗸 | 🗸 | $0.716{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.010}$ | $0.695{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.016}$ | $0.748{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.032}$ | $0.808{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.010}$ |

🗸 | 🗸 | 🗸 | $0.726{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.007}$ | $0.665{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.014}$ | $0.803{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.017}$ | $0.821{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.006}$ | |

🗸 | 🗸 | $0.468{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.022}$ | $0.542{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ | $0.420{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.034}$ | $0.640{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.011}$ | ||

🗸 | 🗸 | 🗸 | $0.726{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.009}$ | $0.701{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.012}$ | $0.759{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.028}$ | $0.815{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.009}$ | |

🗸 | 🗸 | $0.701{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ | $0.685{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.017}$ | $0.731{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.040}$ | $0.798{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ | ||

🗸 | $0.000{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.000}$ | $0.000{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.000}$ | $0.000{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.000}$ | $0.500{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.000}$ | |||

🗸 | 🗸 | $0.734{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.002}$ | $0.644{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.004}$ | $0.854{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.004}$ | $\mathbf{0}.\mathbf{834}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.001}$ | ||

🗸 | $0.743{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.003}$ | $0.680{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.010}$ | $0.819{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.011}$ | $0.834{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.002}$ |

**Table 6.**Results of different data augmentation strategies. Abbr. C: Color jittering, F: horizontal flip (left to right), R: 2D rotation (roll angle), I: image bounding box crop, B: bounding box coordinates.

Augm. | Input | F1 | P | R | AUC |
---|---|---|---|---|---|

− | I | $0.454{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.040}$ | $0.532{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $0.417{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.055}$ | $0.636{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ |

I+B | $0.456{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.031}$ | $\mathbf{0}.\mathbf{587}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.031}$ | $0.403{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.052}$ | $0.639{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ | |

C | I | $0.446{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.032}$ | $0.572{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.020}$ | $0.385{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.050}$ | $0.634{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.016}$ |

I+B | $0.473{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.016}$ | $0.544{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.011}$ | $0.422{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.022}$ | $0.641{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.008}$ | |

F | I | $0.475{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.011}$ | $0.585{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ | $0.405{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.020}$ | $0.644{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.005}$ |

I+B | $0.443{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.029}$ | $0.557{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.026}$ | $0.390{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.049}$ | $0.630{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.014}$ | |

F+R+C | I | $0.469{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $\mathbf{0}.\mathbf{600}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $0.390{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.024}$ | $0.643{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.007}$ |

I+B | $\mathbf{0}.\mathbf{513}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.025}$ | $0.562{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ | $\mathbf{0}.\mathbf{484}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.044}$ | $\mathbf{0}.\mathbf{667}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | |

R | I | $\mathbf{0}.\mathbf{504}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.012}$ | $0.567{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.017}$ | $\mathbf{0}.\mathbf{458}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.018}$ | $\mathbf{0}.\mathbf{659}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.007}$ |

I+B | $0.434{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.048}$ | $0.572{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.027}$ | $0.383{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.063}$ | $0.631{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.021}$ |

**Table 7.**Combined dataset training experiment. Abbr. P: PIE, J: JAAD. Train and Test columns refer to the dataset used for training and testing, respectively.

Train | Test | F1 | P | R | AUC |
---|---|---|---|---|---|

P+J | P | $0.427{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.035}$ | $0.478{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.023}$ | $0.419{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.055}$ | $0.615{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ |

J | $0.566{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.020}$ | $0.540{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.026}$ | $0.635{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.055}$ | $0.756{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.018}$ | |

P | P | $0.454{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.040}$ | $0.532{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $0.416{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.068}$ | $0.636{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ |

J | $0.207{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.021}$ | $0.171{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.012}$ | $0.275{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.043}$ | $0.500{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ |

**Table 8.**Different transformer encoder configurations experiment. Abbr. mean: output average strategy, flat: output flattening strategy.

F1 | P | R | AUC | ||
---|---|---|---|---|---|

− | − | $0.454{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.040}$ | $0.532{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.015}$ | $0.417{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.055}$ | $0.636{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ |

ViT [34] | mean | $0.456{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.031}$ | $\mathbf{0}.\mathbf{587}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.031}$ | $0.403{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.052}$ | $0.639{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.013}$ |

flat | $0.415{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.042}$ | $0.532{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.029}$ | $0.352{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.048}$ | $0.617{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.020}$ | |

Vanilla [7] | mean | $\mathbf{0}.\mathbf{519}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.014}$ | $0.557{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.019}$ | $\mathbf{0}.\mathbf{500}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.034}$ | $\mathbf{0}.\mathbf{669}{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.008}$ |

flat | $0.431{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.039}$ | $0.571{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.018}$ | $0.367{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.052}$ | $0.628{\scriptstyle \phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.017}$ |

**Table 9.**Comparison of our proposed model and the best-performing models in benchmark [8]. Abbr. M is modality attention; C is concatenation; T is temporal attention; I refers to bounding box image crops; B refers to bounding box coordinates; S refers to ego-vehicle speed and P refers to pose keypoints. Rows with darker background correspond to PCPA models trained by us.

Model | Backbone | Fusion | Input | PIE | ${\mathbf{JAAD}}_{\mathbf{beh}}$ | ${\mathbf{JAAD}}_{\mathbf{all}}$ | |||
---|---|---|---|---|---|---|---|---|---|

F1 | AUC | F1 | AUC | F1 | AUC | ||||

Ours | TimeSformer | M | I,B,S | 0.761 | 0.844 | 0.763 | 0.545 | 0.557 | 0.728 |

C | 0.779 | 0.853 | 0.743 | 0.552 | 0.514 | 0.701 | |||

RubiksNet | M | 0.749 | 0.839 | 0.752 | 0.589 | 0.630 | 0.782 | ||

C | 0.738 | 0.828 | 0.691 | 0.549 | 0.618 | 0.778 | |||

C3D | M,T | I,B | 0.750 | 0.851 | 0.615 | 0.577 | 0.614 | 0.802 | |

C3D | – | I | 0.520 | 0.670 | 0.750 | 0.510 | 0.650 | 0.810 | |

MultiRNN | GRU | – | B, S * | 0.710 | 0.800 | 0.740 | 0.500 | 0.580 | 0.790 |

I3D | – | O | 0.720 | 0.830 | 0.750 | 0.510 | 0.630 | 0.800 | |

PCPA | C3D | C | I,B,S,P | 0.730 | 0.830 | 0.630 | 0.480 | 0.580 | 0.800 |

M | 0.750 | 0.840 | 0.680 | 0.490 | 0.620 | 0.830 | |||

T | 0.770 | 0.860 | 0.710 | 0.480 | 0.620 | 0.790 | |||

M,T | 0.770 | 0.860 | 0.710 | 0.500 | 0.680 | 0.860 | |||

0.735 | 0.834 | 0.630 | 0.484 | 0.530 | 0.779 | ||||

I,B | 0.723 | 0.820 | 0.613 | 0.486 | 0.522 | 0.780 |

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## Share and Cite

**MDPI and ACS Style**

Lorenzo, J.; Alonso, I.P.; Izquierdo, R.; Ballardini, A.L.; Saz, Á.H.; Llorca, D.F.; Sotelo, M.Á.
CAPformer: Pedestrian Crossing Action Prediction Using Transformer. *Sensors* **2021**, *21*, 5694.
https://doi.org/10.3390/s21175694

**AMA Style**

Lorenzo J, Alonso IP, Izquierdo R, Ballardini AL, Saz ÁH, Llorca DF, Sotelo MÁ.
CAPformer: Pedestrian Crossing Action Prediction Using Transformer. *Sensors*. 2021; 21(17):5694.
https://doi.org/10.3390/s21175694

**Chicago/Turabian Style**

Lorenzo, Javier, Ignacio Parra Alonso, Rubén Izquierdo, Augusto Luis Ballardini, Álvaro Hernández Saz, David Fernández Llorca, and Miguel Ángel Sotelo.
2021. "CAPformer: Pedestrian Crossing Action Prediction Using Transformer" *Sensors* 21, no. 17: 5694.
https://doi.org/10.3390/s21175694