Java - Problems with normal map generation

Question

Hello, I have a problem in generating a normal texture map, I wonder if there is any way to "soften" tone transitions.

Original image (left) and generated map (right) As you can see, the generated map has "steps" in almost all color tone transitions.

The map generation code:

public static BufferedImage[] getNormal(BufferedImage source, int contrast, int brightness, float smoothness, float power) {
        BufferedImageOp op = new RescaleOp(contrast / 100f, brightness, null);
        BufferedImage input = op.filter(toGrayscale(source), null);
        BufferedImage output = new BufferedImage(input.getWidth(), input.getHeight(), BufferedImage.TYPE_INT_RGB);
        WritableRaster outRaster = output.getRaster();

        for (int y = 1; y < output.getHeight() - 1; y++) {
            for (int x = 1; x < output.getWidth() - 1; x++) {
                Vec3d xNormal = new Vec3d(1, 0, power * Math.sin(Math.atan((input.getRGB(x - 1, y) - input.getRGB(x + 1, y)))));
                Vec3d yNormal = new Vec3d(0, 1, power * Math.sin(Math.atan((input.getRGB(x, y - 1) - input.getRGB(x, y + 1)))));

                Vec3d normal = new Vec3d();
                normal.cross(xNormal, yNormal);
                normal.normalize();

                int[] rgb = {
                        (int) (((normal.x + 1f) / 2) * 255),
                        (int) (((normal.y + 1f) / 2) * 255),
                        (int) (((normal.z + 1f) / 2) * 255)
                };

                outRaster.setPixel(x, y, rgb);
            }
        }

        output.setData(outRaster);
        return new BufferedImage[]{input, output};
    }

This is my doubt, I am already grateful.