deepE_noCorrs_Pytorch

.		.

You can download the pre-trained model from here

The fundamental matrix can estimate the poses of two given frame in the real world environment by providing the rotation matrix and translation matrix of the second frame comparing to the first frame. Therefore, the fundamental matrix can provide valuable information for reconstructing 3D scene.

This project is trying to estimate the essential matrix from two input images following the paper Deep Fundamental Matrix Estimation without Correspondences (DeepFMat_NoCorrs).

Introduction

The paper DeepFMat_NoCorrs was attemping to estimate the fundamental matrix between a pair of images. The estimation of matrix is directly predicted by the network without finding any corresponses between two input images.

For this project, by making use of the idea and the network from the paper, I want to estimate the essential matrix between two frames in the monocular system.

Fundamental Matrix, Essential Matrix and Epipolar Geometry

When a 3D point is viewed by two different camera at two different viewpoints, its projections onto the 2D scenes of stereo cameras are correlated by the Fundamental Matrix. For example if x is the projection of 3D point X in the epipolar environment on the camera 1, x' is the projection of 3D point X on the camera 2. The correlation between them is:

. F. x = 0

However, in this project, I just wanted to know the relative orientation of 2 given images from the monocular camera. Therefore, the essential matrix is used.

. E. x = 0

Network and Dataset

Network

The network is obtained as the POS model from the paper Deep Fundamental Matrix Estimation without Correspondences. It is described below.

Convolution Layer	Fully Connected Layer

The normalize layer is ETR-Norm, which is to divide the F-matrix by its last entry.

Dataset

The dataset is obtained from Kitti Odometry dataset in grayscale. There are 22 sequences, in which 11 sequences are provided with ground truth trajectories. Thus, those 11 sequences are splitted into train and validation sets. Because of the limited number of sequences, k-fold cross-validation is used to find the optimal train and validation sets. From my experience, the sequences 00, 01, and 02 are used for validation set, and the sequences 03-11 are used for the train set.

Data Directory Structure

DATASET ROOT
|
+-- sequences                               # sequences folder
|       |
|       -------00                           # sequence folder
|             |
|             +----  image_0                # grayscale camera folder
|             |      |
|             |      +--- 000000.png        # frame 0000000
|             |      .
|             |      .
|             |      +--- nnnnnn.png        # frame nnnnnn 
|             |
|             +---- image_1                  # colored camera folder 
|             |      +--- 000000.png        # frame 0000000
|             |      .
|             |      .
|             |      +--- nnnnnn.png        # frame nnnnnn 
|             |
|             +--- calib.txt                # cabliration config 
|             |
|             +--- times.txt                # time stamp for each frame
|
+-- poses                                   # poses folder
       |
       +--- 00.txt                          # poses for the sequence 00
       .
       .
       +--- nn.txt                          # poses for the sequence nn

Demo

An example from Test set	Feature Matching

1. The numbers on the left hand side are the average of distances of corresponses to their associating epipoline.
2. The number on the right hand side is the loss, which is the error between the predicted result and the ground truth, in the example epoch.

Conclusion

The results from validation and test sets look promising. However, due to the limitation of my GPU memory, I can only train the model on the small size of images that is 32x32.

For the future work, I want to train the model on larger sizes of images by combining multiple GPUs.