Cumulative Sum Channel

Overview

For images with directional structure (seismic sections, depth profiles, medical slices), a cumulative sum along the vertical axis encodes positional context that a CNN would otherwise need many layers to learn. Mean-subtract first to center around zero, then cumsum to create a gradient-like channel that captures trends. Normalize by standard deviation to keep values in a stable range.

Quick Start

import numpy as np

def add_cumsum_channel(img, border=5):
    center_mean = img[border:-border, border:-border].mean()
    csum = (img.astype(np.float32) - center_mean).cumsum(axis=0)
    csum -= csum[border:-border, border:-border].mean()
    csum /= max(1e-3, csum[border:-border, border:-border].std())
    return csum

# Stack as additional channel
images_2ch = np.zeros((N, H, W, 2), dtype=np.float32)
for i in range(N):
    images_2ch[i, ..., 0] = images[i].squeeze() / 255.0
    images_2ch[i, ..., 1] = add_cumsum_channel(images[i].squeeze())

Workflow

1. Compute center-region mean of grayscale image (exclude border pixels)
2. Subtract mean and compute cumulative sum along vertical axis
3. Re-center and normalize by center-region standard deviation
4. Stack as additional input channel alongside the original image

Key Decisions

• Border exclusion: ignores edge artifacts when computing statistics
• Vertical axis: captures top-to-bottom structure; use axis=1 for horizontal
• Normalization: prevents cumsum values from dominating pixel values in the network
• When useful: seismic data, depth profiles, cross-section images — any domain with vertical gradients

References

• UNet with depth