import java.awt.geom.*;

static Path2D.Float alphaToShape(BufferedImage img) {

  BWImage bw = getAlphaChannel(img);

  Image2B alpha = new Image2B(bw);

  int w = alpha.w(), h = alpha.h();

  Path2D.Float path = new Path2D.Float();

  int x = w/2;

  int y = -1;

  while (y < h && !alphaToShape_isInteresting(alphaToShape_getQuadrant(alpha, x, y))) ++y;

  int x1 = x, y1 = y;

  path.moveTo(x, y);

  new HashSet<Pt> seen;

  while (seen.add(new Pt(x, y))) {

    int q = alphaToShape_getQuadrant(alpha, x, y);

    Pt next = null;

    for (Pt p : neighborhood8(x, y)) 

      if (!seen.contains(p) && alphaToShape_isInteresting(alphaToShape_getQuadrant(alpha, p.x, p.y))) {

      next = p;

      break;

    }

    if (next == null) break;

    x = next.x;

    y = next.y;

    path.lineTo(x+1, y+1);

  }

  ret path;

}

sbool alphaToShape_isInteresting(int q) {

  ret q != 0 && q != 0x1111;

}

static int alphaToShape_getQuadrant(Image2B img, int x, int y) {

  ret (alphaToShape_getQuadrant_getPixel(img, x, y) ? 0x1000 : 0) +

    (alphaToShape_getQuadrant_getPixel(img, x+1, y) ? 0x0100 : 0) +

    (alphaToShape_getQuadrant_getPixel(img, x, y+1) ? 0x0010 : 0) +

    (alphaToShape_getQuadrant_getPixel(img, x+1, y+1) ? 0x0001 : 0);

}

static bool alphaToShape_getQuadrant_getPixel(Image2B img, int x, int y) {

  ret x >= 0 && x < img.w && y >= 0 && y < img.h && img.getPixel(x, y);

}