In these sets of experiments, we repeated the same procedure described in the previous post with only one difference. So, please see the details in the previous post. The difference is the way that we partitioned the patches into training and validation sets. We obtained patches from 8 simulation images from Field2. Then, randomly pick 1/8 of patches and put them into validation set. The remaining patches formed the training set.

** Note:** Best and Worst cases are chosen by comparing the average bubble error in a patch.

**Quantitative Metrics:** In order to compare success of different experiments, we decide the use the followings:

**Quantitative Metric1** = \[ L1Loss(z**f_0 – x**f_0) \]

**Quantitative Metric2** = \[ MSELossLoss(z**f_0 – x**f_0) \]

where f_0 is a gaussian kernel with sigma =1.

* Note*: Both f and f_0 are in pixel coordinates.

** Experiment 1: **learning rate=1e-5, sigma of kernel f=1, regularizer parameter=0.01

**Average quantitative metric1** is 19.645459

**Average metric1 per bubble** is 0.7747

**Average quantitative metric2** is 0.981560

**Average metric2 per bubble** is 0.0384

Worst Case in terms of Per Bubble Error: Center Location(x,z) = 34.53 mm and 10.85 mm, Average Metric1 per bubble: 1.31, Average Metric2 per bubble: : 0.0756

Best Case in terms of Per Bubble Error:Center Location(x,z) = 19.75 mm and 44.37 mm , Quantitative Metric1: 0.511, Quantitative Metric2: 0.0173

** Experiment 2:** learning rate=1e-5, sigma of kernel f=1, regularizer parameter=0.005

**Average quantitative metric1** is 20.352445

**Average metric1 per bubble** is 0.802987

**Average quantitative metric2** is 0.985063

**Average metric2 per bubble** is 0.038526

Worst Case in terms of Per Bubble Error:Center Location(x,z) = 29.61 mm and 9.87 mm , Average Metric1 per bubble: : 1.235, Average Metric2 per bubble: : 0.0755

Best Case in terms of Per Bubble Error:Center Location(x,z) = 24.68 mm and 33.53 mm , Average Metric1 per bubble: : 0.538, Average Metric2 per bubble: : 0.0134

** Experiment 3:** learning rate=1e-5, sigma of kernel f=1.5, regularizer parameter=0.01

**Average quantitative metric1** is 18.815349

**Average metric1 per bubble** is 0.742511

**Average quantitative metric2** is 0.936104

**Average metric2 per bubble** is 0.036656

Worst Case in terms of Per Bubble Error:Center Location(x,z) = 2.50 mm and 13.81 mm , Average Metric1 per bubble: : 1.1237, Average Metric2 per bubble: : 0.071355

Best Case in terms of Per Bubble Error:Center Location(x,z) = 12.36 mm and 41.41 mm , Average Metric1 per bubble: : 0.522, Average Metric2 per bubble: : 0.0179

** Experiment 4:** learning rate=1e-5, sigma of kernel f=1.5, regularizer parameter=0.005

**Average quantitative metric1** is 19.907855

**Average metric1 per bubble** is 0.785045

**Average quantitative metric2** is 0.928157

**Average metric2 per bubble** is 0.036292

Worst Case in terms of Per Bubble Error:Center Location(x,z) = 2.50 mm and 17.76 mm , Average Metric1 per bubble: : 1.175, Average Metric2 per bubble: : 0.068

Best Case in terms of Per Bubble Error:Center Location(x,z) = 24.68 mm and 33.53 mm , Average Metric1 per bubble: : 0.519, Average Metric2 per bubble: : 0.0144

** Experiment 5:** learning rate=1e-5, sigma of kernel f=2, regularizer parameter=0.01

**Average quantitative metric1** is 19.071611

**Average metric1 per bubble** is 0.753008

**Average quantitative metric2** is 1.000624

**Average metric2 per bubble** is 0.039267

Worst Case in terms of Per Bubble Error:Center Location(x,z) = 2.50 mm and 13.81 mm , Average Metric1 per bubble: 1.045525, Average Metric2 per bubble: 0.065981

Best Case in terms of Per Bubble Error:Center Location(x,z) = 17.27 mm and 27.61 mm , Average Metric1 per bubble: 0.571219, Average Metric2 per bubble: 0.0237

** Experiment 6:** learning rate=1e-5, sigma of kernel f=2, regularizer parameter=0.005

**Average quantitative metric1** is 19.766309

**Average metric1 per bubble** is 0.780344

**Average quantitative metric2** is 0.954419

**Average metric2 per bubble** is 0.037464

Worst Case in terms of Per Bubble Error:Center Location(x,z) = 34.53 mm and 22.68 mm , Average Metric1 per bubble: 1.182416, Average Metric2 per bubble: 0.063596

Best Case in terms of Per Bubble Error:Center Location(x,z) = 22.21 mm and 37.47 mm , Average Metric1 per bubble: 0.561, Average Metric1 per bubble: 0.01984

The above results are for disabled random shuffling in training phase. The below table results are obtained using random shuffle.

sigma of f | \(\lambda \) | learning rate | number of epochs | batch size | Q1 | Q2 | Q1 per bubble | Q2 per bubble | % gap between training and validation | |

exp1 | 1 | 0.01 | 1e-5 | 300 | 1 | 16.241709 | 0.817596 | 0.638174 | 0.031777 | 112 |

exp2 | 1 | 0.005 | 1e-5 | 300 | 1 | 16.662992 | 0.774843 | 0.657008 | 0.030192 | 151 |

exp3 | 1.5 | 0.01 | 1e-5 | 300 | 1 | 16.189029 | 0.805056 | 0.637 | 0.031413 | 48.5 |

exp4 | 1.5 | 0.005 | 1e-5 | 300 | 1 | 16.565583 | 0.772228 | 0.652627 | 0.030147 | 91.3 |

exp5 | 2 | 0.01 | 1e-5 | 300 | 1 | 17.008482 | 0.878161 | 0.669787 | 0.034329 | 22 |

exp6 | 2 | 0.005 | 1e-5 | 300 | 1 | 18.784188 | 0.928413 | 0.742285 | 0.036475 | 54.6 |