Let’s have a look at the CT Slice Localization dataset by Graf et al. (2011) as part of my series on exploring less known datasets.
Contents
Dataset exploration
Let’s load the dataset to understand the basic idea behind it.
import time
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
# not gentlemen-like but it helps to keep the notebook clean ;)
import warnings
warnings.simplefilter('ignore')
filepath_input_data = "./data/slice_localization_data.csv"
input_data = pd.read_csv(filepath_input_data)
display(input_data.head(5))
display(input_data.tail(5))
display(input_data.describe())
| patientId | value0 | value1 | value2 | value3 | value4 | value5 | value6 | value7 | value8 | ... | value375 | value376 | value377 | value378 | value379 | value380 | value381 | value382 | value383 | reference | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | -0.25 | ... | -0.25 | 0.980381 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | 21.803851 |
| 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | -0.25 | ... | -0.25 | 0.977008 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | 21.745726 |
| 2 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | -0.25 | ... | -0.25 | 0.977008 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | 21.687600 |
| 3 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | -0.25 | ... | -0.25 | 0.977008 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | 21.629474 |
| 4 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | -0.25 | ... | -0.25 | 0.976833 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.25 | -0.25 | 21.571348 |
| patientId | value0 | value1 | value2 | value3 | value4 | value5 | value6 | value7 | value8 | ... | value375 | value376 | value377 | value378 | value379 | value380 | value381 | value382 | value383 | reference | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 53495 | 96 | 0.591906 | 0.357764 | 0.000000 | 0.000000 | 0.552321 | 0.795304 | 0.946697 | 0.952227 | 0.84395 | ... | 0.00 | 0.0 | 0.0 | 0.000000 | 0.000000 | 0.0 | 0.0 | 0.00 | 0.00 | 29.290398 |
| 53496 | 96 | 0.612313 | 0.000000 | 0.000000 | 0.000000 | 0.864160 | 0.820531 | 0.000000 | 0.938813 | 0.94374 | ... | 0.00 | 0.0 | 0.0 | 0.000000 | 0.000000 | 0.0 | 0.0 | 0.00 | 0.00 | 27.945721 |
| 53497 | 96 | 0.612313 | 0.000000 | 0.000000 | 0.000000 | 0.864160 | 0.820531 | 0.000000 | 0.938813 | 0.94374 | ... | 0.00 | 0.0 | 0.0 | 0.000000 | 0.000000 | 0.0 | 0.0 | 0.00 | 0.00 | 27.945721 |
| 53498 | 96 | 0.634921 | 0.904555 | 0.956087 | 0.980208 | 0.157664 | 0.000000 | -0.250000 | -0.250000 | -0.25000 | ... | -0.25 | 0.0 | 0.0 | 0.994967 | 0.806688 | 0.0 | 0.0 | -0.25 | -0.25 | 14.582997 |
| 53499 | 96 | 0.654321 | 0.891021 | 0.882244 | 0.979282 | 0.000000 | 0.000000 | -0.250000 | -0.250000 | -0.25000 | ... | -0.25 | 0.0 | 0.0 | 0.994671 | 0.000000 | 0.0 | 0.0 | -0.25 | -0.25 | 14.498955 |
| patientId | value0 | value1 | value2 | value3 | value4 | value5 | value6 | value7 | value8 | ... | value375 | value376 | value377 | value378 | value379 | value380 | value381 | value382 | value383 | reference | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | ... | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 | 53500.000000 |
| mean | 47.075701 | 0.059627 | 0.071558 | 0.145819 | 0.218728 | 0.274762 | 0.276189 | 0.204531 | 0.062281 | -0.042025 | ... | -0.029404 | 0.182913 | 0.320112 | 0.359373 | 0.342889 | 0.266091 | 0.083049 | -0.031146 | -0.154524 | 47.028039 |
| std | 27.414240 | 0.174243 | 0.196921 | 0.300270 | 0.359163 | 0.378862 | 0.369605 | 0.351294 | 0.292232 | 0.268391 | ... | 0.085817 | 0.383333 | 0.463517 | 0.478188 | 0.471811 | 0.437633 | 0.279734 | 0.098738 | 0.122491 | 22.347042 |
| min | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | -0.250000 | -0.250000 | -0.250000 | -0.250000 | ... | -0.250000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | -0.250000 | -0.250000 | -0.250000 | 1.738733 |
| 25% | 23.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | -0.250000 | ... | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | -0.250000 | 29.891607 |
| 50% | 46.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | ... | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | -0.250000 | 43.987893 |
| 75% | 70.000000 | 0.000000 | 0.000000 | 0.000000 | 0.446429 | 0.684477 | 0.662382 | 0.441412 | 0.000000 | 0.000000 | ... | 0.000000 | 0.000000 | 0.996286 | 0.999677 | 0.999560 | 0.949478 | 0.000000 | 0.000000 | 0.000000 | 63.735059 |
| max | 96.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 0.998790 | 0.996468 | 0.999334 | 1.000000 | 1.000000 | ... | 0.961279 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 0.999857 | 0.996839 | 0.942851 | 97.489115 |
The data contains a no labels. Hence, we have to read the documentation on the UCI ML repository. The first colum is the patient ID, the last one is the location of the slice ranging from 0 to 180 where 0 denotes a slice at the top of the head. The other columns represent two histrograms. The first one is the histogram of bone structure of a slice and the second one of detected air inclusions. Lets visualize both histograms: bone structure and air inclusions. Therefore, we have to extract some information from the dataset:
inputrange_0 = []
for i in range(240):
inputrange_0.append("value"+str(i))
bone_structure_histogram_mean = []
for i in input_data[inputrange_0]:
bone_structure_histogram_mean.append(input_data[i].describe()["mean"])
bone_structure_histogram_std = []
for i in input_data[inputrange_0]:
bone_structure_histogram_std.append(input_data[i].describe()["std"])
x = [i for i in range(len(bone_structure_histogram_mean))]
bones_lower_bound = np.subtract(bone_structure_histogram_mean,bone_structure_histogram_std)
bones_upper_bound = np.add(bone_structure_histogram_mean,bone_structure_histogram_std)
plt.figure(figsize=(10,7))
plt.plot(bone_structure_histogram_mean, color="black")
plt.fill_between(x,bones_lower_bound,bones_upper_bound,color="gray")
plt.xlabel("")
plt.ylabel("")
plt.title("Bone structure histogram - mean values and std")
plt.tight_layout()
plt.show()
inputrange_1 = []
for i in range(240,384):
inputrange_1.append("value"+str(i))
air_inclusions_histogram_mean = []
for i in input_data[inputrange_1]:
air_inclusions_histogram_mean.append(input_data[i].describe()["mean"])
air_inclusions_histogram_std = []
for i in input_data[inputrange_1]:
air_inclusions_histogram_std.append(input_data[i].describe()["std"])
x = [i for i in range(len(air_inclusions_histogram_mean))]
air_lower_bound = np.subtract(air_inclusions_histogram_mean,air_inclusions_histogram_std)
air_upper_bound = np.add(air_inclusions_histogram_mean,air_inclusions_histogram_std)
plt.figure(figsize=(10,7))
plt.plot(air_inclusions_histogram_mean, color="black")
plt.fill_between(x,air_lower_bound,air_upper_bound,color="gray")
plt.xlabel("")
plt.ylabel("")
plt.title("Air inclusions histogram - mean values and std")
plt.tight_layout()
plt.show()
Both histograms seem to cover a wide variety of ranges.
Preprocessing and ML algorithms
Let’s do some more scaling to aim for fast convergence:
from sklearn.preprocessing import MaxAbsScaler
input_data.drop(["patientId"],axis=1, inplace=True)
input_data_scaled_df = input_data.copy()
scaler = MaxAbsScaler()
input_data_scaled = scaler.fit_transform(input_data)
input_data_scaled_df.loc[:,:] = input_data_scaled
display(input_data_scaled_df.head(3))
# We are dealing with physics/real-world meaning here, hence we need the unscaled values
extract_scaling_function = np.ones((1,input_data_scaled_df.shape[1]))
extract_scaling_function = scaler.inverse_transform(extract_scaling_function)
# split data into X and y
y_df = input_data_scaled_df['reference'].copy()
X_df = input_data_scaled_df.copy()
X_df.drop('reference', axis=1, inplace=True)
from sklearn.model_selection import GridSearchCV, train_test_split
X_train, X_test, y_train, y_test = train_test_split(X_df.values, y_df.values,test_size=0.2, random_state=42, shuffle=True)
As machine learning algorithms, we can use exactly the same as used for this regression problem on predicting concrete compressive strength.
Results
After a few hours of training, we will end up with these results:
It looks like the deepest neural network predicts the CT slice position best.
References
F. Graf, H.-P. Kriegel, M. Schubert, S. Poelsterl, A. Cavallaro
2D Image Registration in CT Images using Radial Image Descriptors
In Medical Image Computing and Computer-Assisted Intervention (MICCAI),
Toronto, Canada, 2011.