Depth Map Normalization
Normalize a depth map to [0, 1] range using min-max normalization.
Depth maps often need normalization for visualization or as input to neural networks. Min-max normalization maps values to [0, 1]:
Znorm=Zmax−ZminZ−Zmin
where:
- Zmin and Zmax are the minimum and maximum depths in the map
- Closest points (small Z) become 0 (black in visualization)
- Farthest points (large Z) become 1 (white in visualization)
Note: If all depths are equal, the normalized result is all zeros.
Example:
normalize_depth([[1, 2], [3, 4]])
[[0.0, 0.3333], [0.6667, 1.0]]
Normalizing depth map:
- min = 1, max = 4, range = 3 (1-1)/3 = 0.0 (2-1)/3 = 0.3333 (3-1)/3 = 0.6667 (4-1)/3 = 1.0
Constraints:
- depth_map: 2D array of depth values
- Return normalized depth map with values in [0, 1], rounded to 4 decimal places
- Background Knowledge
Depth maps store the distance from the camera to the scene at each pixel, usually as a 2D array (e.g., a NumPy array) of real numbers. In raw form, these values can be in arbitrary units and ranges (e.g., [0.3, 12.7] meters, or sensor-specific disparity units), which makes them hard to visualize or feed directly into neural networks.
Normalization rescales values into a standard range, commonly [0, 1]. Min–max normalization does this linearly:
Znorm=Zmax−ZminZ−ZminThis preserves the relative ordering of depths (closer vs farther) but changes their scale. After normalization:
- Minimum depth becomes 0 (black in grayscale visualization).
- Maximum depth becomes 1 (white).
- All intermediate values are proportionally mapped in between.
In practice, depth normalization is important because many neural network architectures assume inputs roughly in [0, 1] or [-1, 1]. It also prevents large numerical ranges from dominating gradients or causing instability during training.
- Algorithm / Approach
The general pattern here is:
- Scan once over the depth map to find the minimum and maximum values.
- Apply the min–max formula to each element to map the entire array to [0, 1].
- Handle the degenerate case where all values are identical (so Zmax−Zmin=0): by definition in this problem, return all zeros.
Conceptually, this is a simple elementwise transformation with precomputed global statistics (min and max).
- Step-by-Step Strategy
Assume the depth map is stored in a 2D array Z (e.g., NumPy, PyTorch, etc.):
- Compute min and max
- Z_min = min(Z) over all pixels.
- Z_max = max(Z) over all pixels.
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