First, sort points by -coordinate. Then remove dominated points: if point A's required square completely contains point B's required square, remove B. Point B will be covered whenever A is. After cleanup, the remaining points have a special structure: their required squares are nested in a specific way.
If in sorted order, point 's required square starts at a smaller -coordinate. The problem becomes: partition the cleaned points into segments, where each segment is covered by one square photo. Find the lowest total area, accounting for overlap between adjacent photos.