# 3D Object Localization in 3D CT Volumes

## Introduction

This project was inspired from the paper by Criminisi et al. from Microsoft Research. In the paper, they proposed an approach in which they apply random regression forests to predict the location of anatomical structures in CT scans. They use a data set of 100 torso CT scans, which differ highly in several aspects (e.g. scanner type, resolution, organ size and pose, etc.). For these scans, the 3D bounding boxes for the organs of interest are computed at first to generate the ground truth. The bounding boxes are parametrized by the positions of the front upper left corner and back lower right corner.

## Regression Forests

A random regression forest consists of bunch of decision trees where each node in a tree splits the incoming datapoints according to random feature selection and random splits on those selected features, However, a decision is made at each node to pick the best randomly chosen split criteria. Hence, decision trees are binary trees, which recursively partition the input space into two subsets. This allows a partitioning of a complex problem into smaller, simpler problems. Every resulting subset contains a model to predict the output. For regression trees this is a regression function, which returns a real-valued prediction.

## Preprocessing

Since the goal is to find the axis aligned bounding boxes for the femur, a parametrization is chosen, which fully describes the bounding boxes. To do so, for each bounding box, a vector

## Training

The training phase of the regression forest starts at the root node of each tree. The nodes of the regression trees are recursively divided by splitting up all the voxels contained in the node into two disjunct sets of voxels. The voxels at given node are separated by the following test function: ξ > f(v; θj). Each voxel is passed to the left or to the right child if the test function evaluates to true or respectively to false. The function f defines the feature response of a particular voxel v for a feature θj. The quality of the split is measured by the information gain, which is defined based on the entropy H(S) as