How can I scale/interpolate an image with indexed values smoothly?-CodePudding

I am wanting to scale grayscale images (input masks, really) with discrete values up smoothly. The values in these images are indexes that represent arbitrary concepts (e.g. "terrain types"; they are usually indices into a table), rather than values on a continuous scale, so they can't be averaged or blended in any way.

Do there exist algorithms that can do this with a more pleasing result than nearest-neighbour, which results in a very blocky, pixelated result? I am looking for something that will at least produce more rounded results, and hopefully there are even algorithms that approximate a higher resolution version of the shapes made by the pixels.

I've researched the subject, but I can't find anything. There is plenty about linear or cubic interpolation, etc., but that won't work for indexed values. The only algorithm I ever see mentioned that does not try to average values is nearest-neighbour. But there must be more?

Using colour here for clarity. I do of course understand that the preferred result here is impossible; I'm not asking for something that reconstitutes destroyed information, just hoping for something that will at least guestimate something smoother than the first result.

CodePudding user response：

One thing you could try is to extract a polygon for the boundary of each uniformly-colored region, then upscale and draw the polygon in the output image. You won’t create neatly rounded edges, but you will avoid the stair-case effect of the nearest neighbor interpolation. Upscaling polygons should avoid gaps between the regions too.

CodePudding user response：

I guess that smoothing the shape for each value individually is a way to avoid undesired mixed value.

To handle values individually, here, I started with your nearest-neighbour image v, and create 3 image { A.bmp, B.bmp, C.bmp } by hand. (each image has only 1 color region and background is black. e.g. A.bmp is below:)

After smoothing the shape for each image, draw these shapes to one result image buffer with different color.

//I use C   and OpenCV
int main()
{
    const std::string FileNames[3] = { "A.bmp", "B.bmp", "C.bmp" };
    const cv::Scalar ResultShowColor[3] = { cv::Scalar(0,255,255), cv::Scalar(0,255,0), cv::Scalar(0,0,255) };
    cv::Mat Imgs[3];

    const int KernelSize = 15;
    for( int i=0; i<3;   i )
    {
        Imgs[i] = cv::imread( FileNames[i], cv::IMREAD_GRAYSCALE );
        if( Imgs[i].empty() )return 0;

        cv::threshold( Imgs[i], Imgs[i], 32, 255, cv::THRESH_BINARY );
        cv::GaussianBlur( Imgs[i], Imgs[i], cv::Size(KernelSize,KernelSize), 0 );
        cv::threshold( Imgs[i], Imgs[i], 255*0.5, 255, cv::THRESH_BINARY );
        cv::imshow( FileNames[i], Imgs[i] );
    }

    cv::Mat ResultImg = cv::Mat::zeros( Imgs[0].size(), CV_8UC3 );
    for( int i=0; i<3;   i )
    {
        ResultImg.setTo( ResultShowColor[i], Imgs[i] );
    }
    cv::imshow( "ResultImg", ResultImg );

    if( cv::waitKey() == 's' ){ cv::imwrite( "ResultImg.png", ResultImg );  }
    return 0;
}

This is result:

Yes, this result is not enough. Gaps exist at the boundaries of shapes. Therefore some ingenuity is required... but I post this because it might be some hint for you.