给定M*N尺寸图像像素选择状态，生成选择区域多边形集合的高效算法问询

Great question! When it comes to generating a polygon set for selected pixel regions in an M×N binary image, Marching Squares (and its optimized variants) stands out as one of the most efficient, practical algorithms around. Let’s dive into why it works so well, how it operates, and some tweaks to make it even better:

Why It’s Efficient #

• Linear Time Complexity: It runs in O(M×N) time, meaning it processes each pixel (or more precisely, each 2×2 pixel block) exactly once. No redundant computations, perfect for grid-based image data.
• Direct Contour Generation: Unlike edge detection + contour stitching pipelines, it outputs continuous polygon vertices directly as it traverses the image—no extra steps to piece together fragmented edges.
• Low Memory Overhead: It only needs to track the current contour’s vertices and a small state buffer, no need for large intermediate data structures beyond the original image.

How It Works (Simplified) #

Marching Squares operates on 2×2 pixel grids:

• Traverse the image from top-left to bottom-right, checking every overlapping 2×2 pixel block.
• For each block, map the 4-pixel selected/unselected state (16 possible combinations total) to a pre-defined edge pattern.
• Each pattern tells you exactly where to place polygon vertices along the block’s edges. Connect these vertices sequentially, and you’ll form closed, continuous outlines for all selected regions—including holes (unselected areas inside selected regions).

If you’re working with extra-large images or need parallelization, these variants are worth considering:

• Jump Flooding-Based Contour Extraction: This can leverage GPU or multi-threaded CPU processing to speed up contour detection. It uses "jump propagation" to spread contour information across the grid, cutting down on redundant checks and bringing effective time complexity closer to O(M×N/k) where k is the number of parallel cores.
• Moore Neighbor Tracing + Polygon Simplification: For images with simple, single-connected selected regions, Moore’s algorithm traces the contour directly by following pixel neighbors. After generating the raw vertex sequence, use the Ramer-Douglas-Peucker algorithm to strip out redundant vertices (simplifying the polygon without losing shape). This is lightning-fast for small or simple images, though you’ll need extra logic to handle multi-connected holes.

• Handling Holes: Marching Squares naturally generates both outer (selected region boundaries) and inner (hole boundaries) contours—no extra code needed to distinguish them.
• Coordinate Precision: By default, vertices are placed at half-integer coordinates (e.g., (0.5, 0)), which represent the actual boundary between pixels. If you need integer pixel coordinates, you can adjust the vertex calculation, but half-integers are more accurate for geometric operations.
• Closed Polygons: Always ensure each contour’s start and end vertices match to form a closed polygon—critical for rendering, collision detection, or any downstream use.

• Edge Detection (Canny) + Contour Stitching: Requires two separate steps (edge detection first, then contour assembly) which adds overhead. Marching Squares skips the middleman.
• Seed Fill + Contour Tracing: Seed fill identifies selected regions, but you still need a separate contour tracing step to generate polygons—adding extra computation that Marching Squares avoids.

内容的提问来源于stack exchange，提问作者razor3x