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Convert Rectified Disparity to Z-Depth

EasyGeometry, Equations 📚 Computer Vision 1

Implement a function to calculate depth Z from given disparity d, focal length f, and baseline B in a rectified stereo setup. This conversion is crucial in depth estimation tasks, where understanding the relationship between disparity and depth is essential.

The concept of rectified stereo involves two cameras with parallel image planes, allowing for a straightforward calculation of depth from disparity. The disparity is the difference in pixels between the same point in the left and right images, while depth is the actual distance of the point from the camera. The formula Z = (f × B) / d represents this inverse proportionality, where f is the focal length and B is the baseline, or the distance between the two cameras.

Here are the steps to calculate depth Z:

Check if the disparity d is valid (greater than 0).
If d is valid, use the formula to calculate Z.
Handle the case where d is invalid (less than or equal to 0).

Z = \frac{f \times B}{d}

This technique is widely used in robotics and autonomous vehicles for 3D reconstruction and obstacle detection.

Example:

Input:

d=10, f=500, B=1

Output:

50.0

Reasoning:

Check if disparity is valid: $d = 10 > 0$ , so proceed with calculation
Apply the depth formula: $Z = \frac{f \times B}{d} = \frac{500 \times 1}{10}$
Compute the result: $Z = \frac{500}{10} = 50.0$
Return the calculated depth value: 50.0

Constraints:

- Input parameters: disparity d (float), focal length f (float), and baseline B (float)
- Valid ranges: d > 0, f > 0, B > 0
- Output format: Return depth Z as a float with a precision of 1 decimal place
- Special conditions: If d is invalid (less than or equal to 0), the function should handle this case and return an appropriate value or error message
- Assumptions: The input parameters are valid for a rectified stereo setup and the formula Z = (f × B) / d applies

More from Computer Vision 1

Semi-Global Matching Cost AggregationHard Compute Depth Map from DisparityMedium Stereo Rectification CheckEasy Oriented BRIEF DescriptorHard Gaussian Scale SpaceMedium

1. Background Knowledge

Stereo depth estimation relies on triangulation between two camera views. For rectified stereo images with parallel optical axes:

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

where:

$Z$ = depth (distance from camera)
$f$ = focal length in pixels
$B$ = baseline (distance between cameras)
$d$ = disparity (pixel difference between left/right images)

Key insight: Disparity is inversely proportional to depth. Near objects have large disparity; far objects have small disparity.

2. Algorithm Approach

Direct formula application with edge case handling:

Check for zero/negative disparity (infinite depth)
Apply $Z = fB/d$

3. Step-by-Step Strategy

Handle edge case: if $d \leq 0$ , return infinity (1e9)
Compute $Z = f \times B / d$
Return rounded result

4. Common Pitfalls

Division by zero when disparity is 0
Confusing units (f in pixels, B in meters, Z in meters)
Negative disparity handling

5. Time & Space Complexity

Aspect	Complexity
Time	O(1)
Space	O(1)

solution.py

Python 3.13

Test Results

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