This code segment functions to: Resize an input image while maintaining aspect ratio, ensuring the minimum dimension matches a specified target size and selecting appropriate interpolation methods based on scaling direction.

```python
[TASK_BEGIN]
def min_resize(x, m):
    H, W = x.shape[0], x.shape[1]
    current_min = min(H, W)
    if current_min == m:
        return x
    ratio = m / current_min
    new_H = int(round(H * ratio))
    new_W = int(round(W * ratio))
    if m < current_min:
        interpolation = cv2.INTER_AREA
    else:
        interpolation = cv2.INTER_LANCZOS4
    return cv2.resize(x, (new_W, new_H), interpolation=interpolation)
[TASK_END]
```