### SGM Algorithm Implementation in Python
The Semi-Global Matching (SGM) algorithm is widely used for dense stereo matching due to its efficiency and accuracy. In the context of computer vision, this method computes disparity maps from a pair of rectified images.
A typical implementation involves several key steps including cost computation, path aggregation along multiple directions, and final optimization or post-processing stages[^1].
Below demonstrates an example of how one might implement parts of the SGM process using Python with libraries such as NumPy:
```python
import numpy as np
import cv2
def compute_cost_volume(left_img, right_img, max_disparity):
height, width = left_img.shape[:2]
cost_volume = np.zeros((height, width, max_disparity), dtype=np.float32)
for d in range(max_disparity):
shifted_right = np.roll(right_img, -d, axis=1)
diff = abs(left_img[:, :width-d] - shifted_right[:, :width-d])
cost_volume[:, d:, d] = np.sum(diff, axis=-1)
return cost_volume
def aggregate_costs(cost_volume, P1, P2):
paths = []
num_paths = 8 # Typically use eight-path aggregation
for direction in range(num_paths):
aggregated_cost = cost_volume.copy()
for i in range(1, cost_volume.shape[0]):
prev_min = np.minimum(aggregated_cost[i-1], aggregated_cost[i]+P2)
aggregated_cost[i] += np.where(
aggregated_cost[i] == aggregated_cost[i-1],
P1,
prev_min.min(axis=-1)[..., None]
)
paths.append(aggregated_cost)
total_aggregation = sum(paths)/len(paths)
return total_aggregation
left_image = cv2.imread('path_to_left_image', 0)
right_image = cv2.imread('path_to_right_image', 0)
max_disp = 64
cost_vol = compute_cost_volume(left_image, right_image, max_disp)
aggr_cost = aggregate_costs(cost_vol, 10, 120)
disparity_map = np.argmin(aggr_cost, axis=2).astype(np.uint8)
cv2.imwrite('disparity.png', disparity_map * (255 / max_disp))
```
This code snippet provides only part of what would be required for a full SGM pipeline but covers fundamental aspects like computing initial costs between image pairs at different disparities and aggregating these costs across various scanline orientations[^3].
For more advanced implementations that include optimizations found within modern variants of SGM algorithms, consulting specialized literature on the subject may prove beneficial since those sources often contain detailed explanations alongside optimized source codes tailored towards specific applications.
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