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import matplotlib.pyplot as plt
import numpy as np
import SimpleITK as sitk
from armscan_env.config import get_config
from armscan_env.envs.rewards import anatomy_based_rwd
from armscan_env.util.visualizations import show_slices

config = get_config()

Simple Clustering and Linear Sweep Search

Loading the dataset:

volume = sitk.ReadImage(config.get_single_labelmap_path(1))
volume_img = sitk.GetArrayFromImage(volume)
print(f"{volume_img.shape=}")

size = np.array(volume.GetSize()) * np.array(volume.GetSpacing())
print(f"{size=} mm")
transversal_extent = (0, size[0], 0, size[2])
longitudinal_extent = (0, size[1], 0, size[2])
frontal_extent = (0, size[0], size[1], 0)

volume_img.shape=(61, 864, 606)
size=array([150.0486095 , 213.93069077,  61.        ]) mm

)In this notebook, we are going to explain the process of searching the carpal tunnel along one axis using a simple clustering algorithm. The first step is to visualize the data to understand the anatomy of the hand at the level of the carpal tunnel. We will then use a simple clustering algorithm to identify the number of features present in each image. Based on the number of features and their relative positions, we will be able to identify the carpal tunnel, basing on its anatomical description.

Since we are not changing the orientation of the slices along the hand, we are bound to a sub-optimal visualization along the axis on which the images have been stacked. This is not exactly transversal to the carpal tunnel, so our anatomical description will be relative to this suboptimal orientation. However, we can still demonstrate that the anatomical description of the region of interest is enough to optimize the navigation.

The following images are slices in proximity of the carpal tunnel area.

show_slices(data=volume_img, start=690, end=20, lap=1, extent=transversal_extent)
plt.show()

The values of the labels are going to be used to identify the clusters of tissues and reason about the anatomy seen in the image.

tissues = {
    "bones": 1,
    "tendons": 2,
    "ulnar": 3,
}

The function cluster_iter is going to be used to identify the clusters of tissues in the image. It iterates over the tissues in the dictionary and identifies the clusters of each tissue. The clustering algorithm uses a center-symmetric filter to identify clusters of neighboring pixels with the same value. The algorithm is based on the label function from the scipy.ndimage package. The function returns a dictionary with the clusters of tissues and the center of each of them.

from armscan_env.clustering import cluster_iter
from armscan_env.util.visualizations import show_clusters

clusters_679 = cluster_iter(tissues, volume_img[:, 679, :].T)
fig = show_clusters(clusters_679, volume_img[:, 679, :].T, extent=transversal_extent)
fig.set_xlabel("X [mm]")
fig.set_ylabel("Z [mm]")
plt.show()

Visualizing slices of the hand at different levels, is going to make clear why it is enough to reason about the anatomy of one slice to identify the region of interest. The function anatomy_based_rwd calculates the score of each image. This offers an observable reward, which can be used to optimize the navigation problem with classical search methods as well as with RL algorithms. The score is based on the number of clusters recognized for each tissue, which should be equal to the n_landmarks parameter. If some of the tissues are not present at all, this is more hardly penalized, because it means that the navigation is far off. Moreover, the score takes into account the position of the landmarks: in particular it checks whether the ulnar artery lies underneath the tendons clusters or not. The score is then normalized to sum up to one.

We tuned the score function to our sub-optimal region of interest: it returns a zero loss for the slice showing the described anatomical conformation.

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# Create a figure and a gridspec with two rows and two columns
fig = plt.figure(constrained_layout=True, figsize=(12, 6))
gs = fig.add_gridspec(2, 3)

# Add subplots
ax1 = fig.add_subplot(gs[:, 0])
ax2 = fig.add_subplot(gs[0, 1])
ax3 = fig.add_subplot(gs[0, 2])
ax4 = fig.add_subplot(gs[1, 1])
ax5 = fig.add_subplot(gs[1, 2])


ax1.axhline(y=418, color="red", linestyle="--", label=f"Horizontal Line at Z-index = {418}")
ax1.axhline(y=601, color="red", linestyle="--", label=f"Horizontal Line at Z-index = {601}")
ax1.axhline(y=679, color="red", linestyle="--", label=f"Horizontal Line at Z-index = {679}")
ax1.axhline(y=739, color="red", linestyle="--", label=f"Horizontal Line at Z-index = {739}")
ax1.imshow(volume_img[35, :, :], label="Hand")
ax1.set_xlabel("x: pixels")
ax1.set_ylabel("z: pixels")
ax1.legend()

clusters_418 = cluster_iter(tissues, volume_img[:, 418, :].T)
show_clusters(clusters_418, volume_img[:, 418, :].T, ax2, extent=transversal_extent)
reward_418 = anatomy_based_rwd(clusters_418, n_landmarks=(7, 5, 1))
ax2.text(
    0.95,
    0.1,
    f"Reward: {reward_418:.2f}",
    horizontalalignment="right",
    verticalalignment="bottom",
    transform=ax2.transAxes,
    bbox=dict(facecolor="white", alpha=0.5, edgecolor="black", boxstyle="round,pad=1"),
)
ax2.set_title("Slice 418")
ax2.axis("off")

clusters_601 = cluster_iter(tissues, volume_img[:, 601, :].T)
show_clusters(clusters_601, volume_img[:, 601, :].T, ax3, extent=transversal_extent)
reward_601 = anatomy_based_rwd(clusters_601, n_landmarks=(7, 5, 1))
ax3.text(
    0.95,
    0.1,
    f"Reward: {reward_601:.2f}",
    horizontalalignment="right",
    verticalalignment="bottom",
    transform=ax3.transAxes,
    bbox=dict(facecolor="white", alpha=0.5, edgecolor="black", boxstyle="round,pad=1"),
)
ax3.set_title("Slice 601")
ax3.axis("off")

show_clusters(clusters_679, volume_img[:, 679, :].T, ax4, extent=transversal_extent)
reward_679 = anatomy_based_rwd(clusters_679, n_landmarks=(7, 5, 1))
ax4.text(
    0.95,
    0.1,
    f"Reward: {reward_679:.2f}",
    horizontalalignment="right",
    verticalalignment="bottom",
    transform=ax4.transAxes,
    bbox=dict(facecolor="white", alpha=0.5, edgecolor="black", boxstyle="round,pad=1"),
)
ax4.set_title("Slice 679")
ax4.axis("off")

clusters_739 = cluster_iter(tissues, volume_img[:, 739, :].T)
show_clusters(clusters_739, volume_img[:, 739, :].T, ax5, extent=transversal_extent)
reward_739 = anatomy_based_rwd(clusters_739, n_landmarks=(7, 5, 1))
ax5.text(
    0.95,
    0.1,
    f"Reward: {reward_739:.2f}",
    horizontalalignment="right",
    verticalalignment="bottom",
    transform=ax5.transAxes,
    bbox=dict(facecolor="white", alpha=0.5, edgecolor="black", boxstyle="round,pad=1"),
)
ax5.set_title("Slice 739")
ax5.axis("off")

plt.show()

The clustering algorithm does not just give us information about the number of tissues clusters, but also about their position. Hence, it is possible to reason about the orientation of the image and the relation of the tissues to one another.

clusters_679 = cluster_iter(tissues, volume_img[:, 679, :].T)

bones_centers = [cluster.center for _, cluster in enumerate(clusters_679.bones)]
ligament_centers = [cluster.center for _, cluster in enumerate(clusters_679.tendons)]

bones_center = np.mean(bones_centers, axis=0)
print("bones_center: ", bones_center)
ligament_center = np.mean(ligament_centers, axis=0)
print("ligament_center: ", ligament_center)
ulnar_center = clusters_679.ulnar[0].center
print("ulnar_center: ", ulnar_center)

bones_center:  [289.53353614  36.76763969]
ligament_center:  [312.05577456  30.23236792]
ulnar_center:  (268.2307692307692, 22.26923076923077)

anatomy_based_rwd(clusters_679, n_landmarks=(7, 5, 1))

-0.0

Performing a linear sweep search along the axis of the hand, we can identify the optimal region that returns a zero loss. We can also see that the loss converges to zero as we approach the optimal region.

sweep_loss = []
zero_loss_clusters = []

for i in range(volume_img.shape[1]):
    clusters = cluster_iter(tissues, volume_img[:, i, :].T)
    loss = anatomy_based_rwd(clusters, n_landmarks=(7, 5, 1))
    sweep_loss.append(loss)
    if loss == 0:
        zero_loss_clusters.append(clusters)
    print(f"Loss for slice {i}: {sweep_loss[i]}")

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Loss for slice 815: -0.17948717948717952
Loss for slice 816: -0.17948717948717952
Loss for slice 817: -0.1282051282051282
Loss for slice 818: -0.15384615384615385
Loss for slice 819: -0.1282051282051282
Loss for slice 820: -0.1282051282051282
Loss for slice 821: -0.1282051282051282
Loss for slice 822: -0.1282051282051282
Loss for slice 823: -0.15384615384615385
Loss for slice 824: -0.15384615384615385
Loss for slice 825: -0.15384615384615385
Loss for slice 826: -0.15384615384615385
Loss for slice 827: -0.15384615384615385
Loss for slice 828: -0.15384615384615385
Loss for slice 829: -0.1282051282051282
Loss for slice 830: -0.10256410256410256
Loss for slice 831: -0.1282051282051282
Loss for slice 832: -0.1282051282051282
Loss for slice 833: -0.1282051282051282
Loss for slice 834: -0.15384615384615385
Loss for slice 835: -0.15384615384615385
Loss for slice 836: -0.1282051282051282
Loss for slice 837: -0.15384615384615385
Loss for slice 838: -0.15384615384615385
Loss for slice 839: -0.1282051282051282
Loss for slice 840: -0.1282051282051282
Loss for slice 841: -0.1282051282051282
Loss for slice 842: -0.1282051282051282
Loss for slice 843: -0.15384615384615385
Loss for slice 844: -0.17948717948717952
Loss for slice 845: -0.20512820512820512
Loss for slice 846: -0.17948717948717952
Loss for slice 847: -0.17948717948717952
Loss for slice 848: -0.17948717948717952
Loss for slice 849: -0.15384615384615385
Loss for slice 850: -0.15384615384615385
Loss for slice 851: -0.15384615384615385
Loss for slice 852: -0.15384615384615385
Loss for slice 853: -0.5128205128205128
Loss for slice 854: -0.5128205128205128
Loss for slice 855: -0.15384615384615385
Loss for slice 856: -0.15384615384615385
Loss for slice 857: -0.15384615384615385
Loss for slice 858: -0.15384615384615385
Loss for slice 859: -0.20512820512820512
Loss for slice 860: -0.15384615384615385
Loss for slice 861: -0.15384615384615385
Loss for slice 862: -0.15384615384615385
Loss for slice 863: -0.15384615384615385

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plt.plot(range(len(sweep_loss)), sweep_loss, marker="o")

plt.xlabel("Slice index")
plt.ylabel("Score")
plt.title("Score along axial slices")

plt.show()

We can visualize the slices that return a zero loss to check whether this approach is valid.

zero_loss_indices = np.where(np.array(sweep_loss) == 0)[0]
print(f"{len(zero_loss_indices)} indices return a zero loss: ", zero_loss_indices)

nrows = 1
ncols = len(zero_loss_indices) // nrows
indices_to_display = nrows * ncols

if indices_to_display > 0:
    fig, axes = plt.subplots(nrows=nrows, ncols=ncols, figsize=(20, 10))
    axes = axes.flatten()
    for i, idx in enumerate(zero_loss_indices[:indices_to_display]):
        axes[i] = show_clusters(
            tissue_clusters=zero_loss_clusters[i],
            slice=volume_img[:, idx, :].T,
            extent=transversal_extent,
            aspect=2,
            ax=axes[i],
        )
        axes[i].set_title(f"Index: {idx}, Loss: {sweep_loss[idx]:.2f}")
        axes[i].axis("off")

    plt.show()

4 indices return a zero loss:  [667 674 679 682]

As we can see, the results are quite promising, but the clustering algorithm is not really identifying the clusters robustly. There are some clusters that are not separated because they have connected pixels. Moreover, it is not possible to tune the clustering algorithm for an expected size, preventing outliers to be detected.

clusters_668 = cluster_iter(tissues, volume_img[:, 668, :].T)
show_clusters(clusters_668, volume_img[:, 668, :].T, extent=transversal_extent, aspect=2)
plt.axis("off")
plt.show()

In the next notebook, we will show the performance using a different clustering algorithm.