Geometry extraction from trajectories

I have some trajectories of people moving in a given geometry. For example

In this example, the geometry was added manually, a process I would like to automatize: The question is then: How to generate an approximation of the walls, shown as black lines in the picture above?

Code

Here is my Ansatz: count, in a grid, where people go (or not go), and hence identify the empty grid cells. That would tell me where is inside and outside the geometry. Assuming Tx and Ty hold the coordinates of all trajectory points:

from scipy import stats
dx = 0.1
xbins = np.arange(geominX, geomaxX + dx, dx)
ybins = np.arange(geominY, geomaxY + dx, dx)
ret = stats.binned_statistic_2d(
        Tx,
        Ty,
        None,
        "count",
        bins=[xbins, ybins]
    )

Plotting the counts per cell (ret.statistic) yields:

Now, from this, I calculated the points in the geometry with non-empty counts:

X = ret.x_edge + dx/2
Y = ret.y_edge + dx/2
x, y = np.meshgrid(X[:-1], Y[:-1])
xx = x[ret.statistic.T != 0]
yy = y[ret.statistic.T != 0]
plt.plot(xx, yy, ".")

which gives for dx=0.1 the following result:

For the sake of explanation, I'd like to give another example of a bottleneck, where the boundaries of the geometry, the black lines, are added manually.

Problem

This is now the point where I'm stuck and need some help. Do you have any idea how I could proceed from here and automatically identify a rough approximation of the geometry's boundaries?

Data

In case of trajectories are needed, here are two links to the above-used trajectories:

• Crossing
• Bottlenck

EDIT (using OpenCV)

Thanks to @BlackBeans comment, I tried the following:

1. plot the trajectories with white on black background and save image:

# with a big marker size
ax.plot(d[:, 2], d[:, 3], "o", ms=10, color="white")

2. In the next step, read the image and find the contours:

img = cv2.imread("trajecotries.png", cv2.IMREAD_GRAYSCALE)
_, binary_img = cv2.threshold(img, 225, 255, cv2.THRESH_BINARY_INV)
contours, _ = cv2.findContours(binary_img, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)
cnt = contours[1]
final_image = cv2.drawContours(img, [cnt], 0, (178,34,34), 2)

That brings me closer to my goal. However, the contours are not in original coordinates, but rather some numbers relative to the image.