Ellipses Experiments

The structure of all experiments is very similar:

• generate a fully synthetic data-set, including:
  • ground truth (positions of the ellipses in pixel-space);
  • noisy observations (background with random pixels plus ellipses);
• split data-set into training and validation;
• define an intuitive "upstream" criterion (non-differentiable: argmax over predictions to determine the most likely position of the ellipse);
• define parameterized NN-based model to find the ellipses;
• perform hyperparameter search;
• visualize results.

Experiments

• finding the single pixel, which is the "center" of a solid ellipse on a noisy background: notebook;
• finding the single pixel, which is the "center" of a hollow ellipse ("doughnut") on a noisy background: notebook;
• finding the single pixel on each frame tracking the position of the "center" of a hollow "continious" (present in every frame) ellipse on a noisy background including other random (appearing and disappearing on each frame) hollow-ellipses: notebook.

Small data-sets

Synthetic data used in the experiments was intentially very limited:

• 300 frames with solid ellipse;
• 300 frames with hollow ellipse;
• 30 movies with 250 frames each.

This presented an interesting challenge of finding models with very low capacity.

The best results were achieved using transfer learning

Transfer learning

Steps:

1. Trained 207-parameters model through 100 epochs for detecting solid ellipses, and achieved mean distance from the label of 2.6 pixels. Verified that model achieves similar performance from different initializations.
2. Trained a model with 516-parameters through 100 epochs to detect hollow ellipse, and achieved mean distance from the label of 13.5 pixels. This 516-parameters model incorporates the 207-parameters model from the first step, which was frozen initially. Verified that model achieves similar performance from different initializations of the trainable part. Model was then fine-tuned with all parameters unfrozen to achieve 11.8-pixels mean distance.
3. Trained a model with 2126 parameters (of these, 516 were carried over from step 2 and were initially frozen) through 100 epochs to detect moving hollow ellipses among the noise, which also consisted of hollow ellipses. Achieved mean distance of 16.2. Fine-tuning didn't improve results.
4. Trained the same model as in step 3 (2126) from scratch: with all parameters unfrozen and without using any pre-trained parameters. After 1000 epochs this model demonstrated to be unstable in training. Its best result was 24.4-pixels mean distance.

Conclusion: transfer learning allowed to achieve useful results with extremely small data-set and very small training time.