# Image Registration Method Exhaustive

## Overview

This script demonstrates the use of the Exhaustive optimizer in the ImageRegistrationMethod to estimate a good initial rotation position.

Because gradient descent base optimization can get stuck in local minima, a good initial transform is critical for reasonable results. Search a reasonable space on a grid with brute force may be a reliable way to get a starting location for further optimization.

The initial translation and center of rotation for the transform is initialized based on the first principle moments of the intensities of the image. Then in either 2D or 3D a Euler transform is used to exhaustively search a grid of the rotation space at a certain step size. The resulting transform is a reasonable guess where to start further registration.

## Code

```#!/usr/bin/env python

import SimpleITK as sitk
import sys
import os
from math import pi

def command_iteration(method):
if method.GetOptimizerIteration() == 0:
print("Scales: ", method.GetOptimizerScales())
print(
f"{method.GetOptimizerIteration():3} "
+ f"= {method.GetMetricValue():7.5f} "
+ f": {method.GetOptimizerPosition()}"
)

if len(sys.argv) < 4:
print(
"Usage:",
sys.argv[0],
"<fixedImageFilter> <movingImageFile>",
"<outputTransformFile>",
)
sys.exit(1)

R = sitk.ImageRegistrationMethod()

R.SetMetricAsMattesMutualInformation(numberOfHistogramBins=50)

sample_per_axis = 12
if fixed.GetDimension() == 2:
tx = sitk.Euler2DTransform()
# Set the number of samples (radius) in each dimension, with a
# default step size of 1.0
R.SetOptimizerAsExhaustive([sample_per_axis // 2, 0, 0])
# Utilize the scale to set the step size for each dimension
R.SetOptimizerScales([2.0 * pi / sample_per_axis, 1.0, 1.0])
elif fixed.GetDimension() == 3:
tx = sitk.Euler3DTransform()
R.SetOptimizerAsExhaustive(
[
sample_per_axis // 2,
sample_per_axis // 2,
sample_per_axis // 4,
0,
0,
0,
]
)
R.SetOptimizerScales(
[
2.0 * pi / sample_per_axis,
2.0 * pi / sample_per_axis,
2.0 * pi / sample_per_axis,
1.0,
1.0,
1.0,
]
)

# Initialize the transform with a translation and the center of
# rotation from the moments of intensity.
tx = sitk.CenteredTransformInitializer(fixed, moving, tx)

R.SetInitialTransform(tx)

R.SetInterpolator(sitk.sitkLinear)

outTx = R.Execute(fixed, moving)

print("-------")
print(outTx)
print(f"Optimizer stop condition: {R.GetOptimizerStopConditionDescription()}")
print(f" Iteration: {R.GetOptimizerIteration()}")
print(f" Metric value: {R.GetMetricValue()}")

sitk.WriteTransform(outTx, sys.argv[3])

if "SITK_NOSHOW" not in os.environ:
resampler = sitk.ResampleImageFilter()
resampler.SetReferenceImage(fixed)
resampler.SetInterpolator(sitk.sitkLinear)
resampler.SetDefaultPixelValue(1)
resampler.SetTransform(outTx)

out = resampler.Execute(moving)

simg1 = sitk.Cast(sitk.RescaleIntensity(fixed), sitk.sitkUInt8)
simg2 = sitk.Cast(sitk.RescaleIntensity(out), sitk.sitkUInt8)
cimg = sitk.Compose(simg1, simg2, simg1 // 2.0 + simg2 // 2.0)
sitk.Show(cimg, "ImageRegistrationExhaustive Composition")
```