sinterface IIntegralImage extends MakesBufferedImage {
  public int getWidth();
  public int getHeight();

  // get value for 1 channel
  // normal range [0; pixelCount*256)
  public double getIntegralValue(int x, int y, int channel);
    
  // gets value of the 3 channels
  // normal range [0; pixelCount*256*3)
  default double getIntegralValue(int x, int y) {
    ret getIntegralValue(x, y, 0)
      + getIntegralValue(x, y, 1)
      + getIntegralValue(x, y, 2);
  }
  
  default double rectSum(int x1, int y1, int x2, int y2, int channel) {
    double bottomLeft  = getIntegralValue(x1-1, y2-1, channel);
    double bottomRight = getIntegralValue(x2-1, y2-1, channel);
    double topLeft     = getIntegralValue(x1-1, y1-1, channel);
    double topRight    = getIntegralValue(x2-1, y1-1, channel);
    ret bottomRight+topLeft-topRight-bottomLeft;
  }
  
  default double rectSum(int x1, int y1, int x2, int y2) {
    double bottomLeft  = getIntegralValue(x1-1, y2-1);
    double bottomRight = getIntegralValue(x2-1, y2-1);
    double topLeft     = getIntegralValue(x1-1, y1-1);
    double topRight    = getIntegralValue(x2-1, y1-1);
    ret bottomRight+topLeft-topRight-bottomLeft;
  }
  
  default IIntegralImage clip(int x, int y, int w, int h) {
    ret IIVirtualClip(this, x, y, w, h);
  }
}