Compute Depth Map from Disparity

mediumPRODepth EstimationComputer Vision 1

Given a disparity map, focal length $f$ , and baseline $b$ , compute the depth map using the stereo depth equation.

In a rectified stereo system, depth $Z$ is inversely proportional to disparity $d$ :

$Z = \frac{f \cdot b}{d}$

where:

$f$ is the focal length in pixels
$b$ is the baseline distance between cameras
$d$ is the disparity (difference in x-coordinates between left and right images)

For zero disparity (no correspondence found), set the depth to infinity (float('inf')).

Return the depth map as a 2D list with values rounded to 4 decimal places.

Example

Input

disparity_map = [[10, 20, 0],
                 [5, 15, 25]]
focal_length = 500.0
baseline = 0.1

Output

[[5.0, 2.5, inf], [10.0, 3.3333, 2.0]]

Reasoning

Inputs: disparity_map is a $2 \times 3$ grid of disparities in pixels: how far each point shifts horizontally between the two images. focal_length is $f = 500$ pixels and baseline is $b = 0.1$ , the distance between the two cameras.
Shared numerator: every pixel uses the same product $f \cdot b = 500 \times 0.1 = 50$ , so each depth is just $Z = 50 / d$ .
Top row: $50/10 = 5.0$ and $50/20 = 2.5$ . The third pixel has $d = 0$ : no match was found, so its depth is defined as infinity, inf, rather than dividing by zero.
Bottom row: $50/5 = 10.0$ , $50/15 = 3.3333\ldots$ which rounds to $3.3333$ at 4 decimal places, and $50/25 = 2.0$ .
Output: the same $2 \times 3$ shape, [[5.0, 2.5, inf], [10.0, 3.3333, 2.0]].
Notice: depth is inversely proportional to disparity. Doubling $d$ from 10 to 20 halves $Z$ from 5.0 to 2.5, so the pixel that shifts most ( $d = 25$ ) is the closest point and zero shift means infinitely far.

Constraints

disparity_map: 2D list of floats (disparity values >= 0)
focal_length: float (focal length in pixels)
baseline: float (baseline distance)
Return: 2D list of floats (depth values)
Zero disparity -> float('inf')
Round to 4 decimal places
Use pure Python

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Background Knowledge

The problem revolves around the concept of depth estimation in computer vision, specifically using stereo vision. Stereo vision is a technique used to estimate the depth of a scene by analyzing the disparity between two images taken from slightly different viewpoints, typically from a stereo camera setup. The disparity map, which is given in the problem, represents the difference in x-coordinates between corresponding points in the left and right images.

The stereo depth equation, $Z = \frac{f \cdot b}{d}$ , is fundamental to understanding how depth is calculated from disparity. Here, $Z$ is the depth of the point, $f$ is the focal length of the camera in pixels, $b$ is the baseline distance between the cameras, and $d$ is the disparity. This equation shows that depth is inversely proportional to disparity, meaning that as disparity increases (objects appear closer in the images), the calculated depth decreases, indicating the object is closer to the camera.

Understanding the parameters involved is crucial. The focal length $f$ affects how much the camera "zooms" into the scene, the baseline $b$ affects the stereo effect and thus the depth perception, and the disparity $d$ is the measurable difference that we use to calculate depth. In real-world applications, accurately calculating these values is essential for tasks like robotics, autonomous vehicles, and 3D reconstruction.

Algorithm/Approach

The general approach to solving this problem involves applying the stereo depth equation to each pixel in the disparity map. This requires iterating over the disparity map, applying the equation for each non-zero disparity value to calculate the depth, and handling the case where disparity is zero (indicating no correspondence and thus infinite depth).

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