可以使用颜色量化将图像中的颜色数量减少到更小的预定义调色板中。然后，可以将此缩小调色板中的主色用作背景色。

import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import javax.imageio.ImageIO;

public class Main {
    public static void main(String[] args) {
        try {
            // Load the image
            BufferedImage image = ImageIO.read(new File("image.jpg"));

            // Convert the image to a palette image with a predefined number of colors
            image = ImageUtil.quantize(image, 16);

            // Get the palette for the image
            int[] palette = image.getColorModel().getRGBs();

            // Calculate the dominant color in the palette
            int rTotal = 0;
            int gTotal = 0;
            int bTotal = 0;
            for (int i = 0; i < palette.length; i++) {
                int r = (palette[i] >> 16) & 0xFF;
                int g = (palette[i] >> 8) & 0xFF;
                int b = palette[i] & 0xFF;
                rTotal += r;
                gTotal += g;
                bTotal += b;
            }
            int numColors = palette.length;
            int dominantColor = (rTotal / numColors << 16) | (gTotal / numColors << 8) | (bTotal / numColors);

            // Set the background color to the dominant color
            String backgroundColor = String.format("#%06X", dominantColor);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}

ImageUtil类是我提供的一个实用程序类，用于将图像转换为调色板图像。下面是ImageUtil类的代码：

import java.awt.image.BufferedImage;
import java.awt.image.IndexColorModel;

public class ImageUtil {
    public static BufferedImage quantize(BufferedImage image, int numColors) {
        // Convert the image to a palette image with the specified number of colors
        BufferedImage paletteImage = new BufferedImage(image.getWidth(), image.getHeight(), BufferedImage.TYPE_BYTE_INDEXED);
        IndexColorModel colorModel = (IndexColorModel) paletteImage.getColorModel();
        int[] palette = new int[numColors];
        for (int i = 0; i < numColors; i++) {
            palette[i] = colorModel.getRGB(i);
        }
        paletteImage.setRGB(0, 0, image.getWidth(), image.getHeight(), image.getRGB(0, 0, image.getWidth(), image.getHeight(), null, 0, image.getWidth()), 0, image.getWidth());
        return paletteImage;
    }
}