java - 图像的单应变换

Question

这是我的示例图片

我想根据红色标记点对图像进行如下变换。

我实现了此处描述的公式:http://www.corrmap.com/features/homography_transformation.php

但是我的输出是:

输出图像中的黑噪声过多。这是我的java代码

import java.awt.image.BufferedImage;
import java.io.IOException;
import java.util.ArrayList;
import Jama.Matrix;
import java.io.File;
import javax.imageio.ImageIO;

public class ImageWarp {
        private double x1, y1, x2, y2, x3, y3, x4, y4, X1, Y1, X2, Y2, X3, Y3, X4,
                        Y4;

        public static void main(String[] args) throws IOException {
            ImageWarp iw = new ImageWarp();

            BufferedImage img = ImageIO.read(new File("C:\\Users\\mohar\\Documents\\NetBeansProjects\\Test3\\src\\notebook.jpg"));
            ArrayList<Coordinate> coords = new ArrayList<>();
            coords.add(new Coordinate(39, 206));
            coords.add(new Coordinate(218, 29));
            coords.add(new Coordinate(541, 153));
            coords.add(new Coordinate(417, 417));

            BufferedImage output = iw.getCropedImage(img, coords, 500, 500);
            ImageIO.write(output, "jpg", new File("C:\\Users\\mohar\\Documents\\NetBeansProjects\\Test3\\src\\output.jpg"));
        }

        public BufferedImage getCropedImage(BufferedImage imgBuffer,
                        ArrayList<Coordinate> cornersCordinate, int imageWidth,
                        int imageHeight) throws IOException {

                x1 = Math.abs(cornersCordinate.get(0).getX());
                y1 = Math.abs(cornersCordinate.get(0).getY());
                x2 = Math.abs(cornersCordinate.get(1).getX());
                y2 = Math.abs(cornersCordinate.get(1).getY());
                x3 = Math.abs(cornersCordinate.get(2).getX());
                y3 = Math.abs(cornersCordinate.get(2).getY());
                x4 = Math.abs(cornersCordinate.get(3).getX());
                y4 = Math.abs(cornersCordinate.get(3).getY());
                X1 = 0;
                Y1 = 0;
                X2 = imageWidth - 1;
                Y2 = 0;
                X3 = imageWidth - 1;
                Y3 = imageHeight - 1;
                X4 = 0;
                Y4 = imageHeight - 1;

                double M_a[][] = { { x1, y1, 1, 0, 0, 0, -x1 * X1, -y1 * X1 },
                                { x2, y2, 1, 0, 0, 0, -x2 * X2, -y2 * X2 },
                                { x3, y3, 1, 0, 0, 0, -x3 * X3, -y3 * X3 },
                                { x4, y4, 1, 0, 0, 0, -x4 * X4, -y4 * X4 },
                                { 0, 0, 0, x1, y1, 1, -x1 * Y1, -y1 * Y1 },
                                { 0, 0, 0, x2, y2, 1, -x2 * Y2, -y2 * Y2 },
                                { 0, 0, 0, x3, y3, 1, -x3 * Y3, -y3 * Y3 },
                                { 0, 0, 0, x4, y4, 1, -x4 * Y4, -y4 * Y4 }, };

                double M_b[][] = { { X1 }, { X2 }, { X3 }, { X4 }, { Y1 }, { Y2 },
                                { Y3 }, { Y4 }, };

                Matrix A = new Matrix(M_a);
                Matrix B = new Matrix(M_b);
                Matrix C = A.solve(B);
                double a = C.get(0, 0);
                double b = C.get(1, 0);
                double c = C.get(2, 0);
                double d = C.get(3, 0);
                double e = C.get(4, 0);
                double f = C.get(5, 0);
                double g = C.get(6, 0);
                double h = C.get(7, 0);

                int width = imgBuffer.getWidth();
                int height = imgBuffer.getHeight();

                BufferedImage output = new BufferedImage(imageWidth, imageHeight,
                                BufferedImage.TYPE_INT_RGB);
                for (int i = 0; i < width; i++) {
                        for (int j = 0; j < height; j++) {
                                if (isInside(i, j)) {
                                        int x = (int) (((a * i) + (b * j) + c) / ((g * i) + (h * j) + 1));
                                        int y = (int) (((d * i) + (e * j) + f) / ((g * i) + (h * j) + 1));
                                        int p = imgBuffer.getRGB(i, j);
                                        output.setRGB(x, y, p);
                                }
                        }
                }

                return output;
        }

        private boolean isInside(int x, int y) {

                double apd = Math.abs(0.5 * (x1 * y + x * y4 + x4 * y1 - x * y1 - x4
                                * y - x1 * y4));
                double dpc = Math.abs(0.5 * (x4 * y + x * y3 + x3 * y4 - x * y4 - x3
                                * y - x4 * y3));
                double cpb = Math.abs(0.5 * (x3 * y + x * y2 + x2 * y3 - x * y3 - x2
                                * y - x3 * y2));
                double pba = Math.abs(0.5 * (x * y2 + x2 * y1 + x1 * y - x2 * y - x1
                                * y2 - x * y1));
                double rec = Math.abs(0.5 * (x1 * y2 + x2 * y3 + x3 * y4 + x4 * y1 - x2
                                * y1 - x3 * y2 - x4 * y3 - x1 * y4));

                if ((apd + dpc + cpb + pba) > rec) {
                        return false;
                } else {
                        return true;
                }
        }

}

class Coordinate {
    private double x;
    private double y;

    public Coordinate(double x, double y) {
        this.x = x;
        this.y = y;
    }



    public double getX() {
        return x;
    }

    public double getY() {
        return y;
    }


}

Answer 1

如 beaker 所述,

For each point in the original image you're calculating its position in the destination image. That would miss a lot of points. It would be better to calculate the value of each pixel in the destination image interpolated from the original image.

为避免这种情况，您可以为每个点使用向后映射 (x',y') 到 (x, y)。

这是您修改后的可行代码

public class ImageWarp {
    private double x1, y1, x2, y2, x3, y3, x4, y4, X1, Y1, X2, Y2, X3, Y3, X4,
            Y4;

    public BufferedImage getCropedImage(BufferedImage imgBuffer,
            ArrayList<Coordinate> cornersCordinate, int imageWidth,
            int imageHeight) throws IOException {

        X1 = Math.abs(cornersCordinate.get(0).getX());
        Y1 = Math.abs(cornersCordinate.get(0).getY());
        X2 = Math.abs(cornersCordinate.get(1).getX());
        Y2 = Math.abs(cornersCordinate.get(1).getY());
        X3 = Math.abs(cornersCordinate.get(2).getX());
        Y3 = Math.abs(cornersCordinate.get(2).getY());
        X4 = Math.abs(cornersCordinate.get(3).getX());
        Y4 = Math.abs(cornersCordinate.get(3).getY());
        x1 = 0;
        y1 = 0;
        x2 = imageWidth - 1;
        y2 = 0;
        x3 = imageWidth - 1;
        y3 = imageHeight - 1;
        x4 = 0;
        y4 = imageHeight - 1;

        double M_a[][] = { { x1, y1, 1, 0, 0, 0, -x1 * X1, -y1 * X1 },
                { x2, y2, 1, 0, 0, 0, -x2 * X2, -y2 * X2 },
                { x3, y3, 1, 0, 0, 0, -x3 * X3, -y3 * X3 },
                { x4, y4, 1, 0, 0, 0, -x4 * X4, -y4 * X4 },
                { 0, 0, 0, x1, y1, 1, -x1 * Y1, -y1 * Y1 },
                { 0, 0, 0, x2, y2, 1, -x2 * Y2, -y2 * Y2 },
                { 0, 0, 0, x3, y3, 1, -x3 * Y3, -y3 * Y3 },
                { 0, 0, 0, x4, y4, 1, -x4 * Y4, -y4 * Y4 }, };

        double M_b[][] = { { X1 }, { X2 }, { X3 }, { X4 }, { Y1 }, { Y2 },
                { Y3 }, { Y4 }, };

        Matrix A = new Matrix(M_a);
        Matrix B = new Matrix(M_b);
        Matrix C = A.solve(B);
        double a = C.get(0, 0);
        double b = C.get(1, 0);
        double c = C.get(2, 0);
        double d = C.get(3, 0);
        double e = C.get(4, 0);
        double f = C.get(5, 0);
        double g = C.get(6, 0);
        double h = C.get(7, 0);


        BufferedImage output = new BufferedImage(imageWidth, imageHeight,
                BufferedImage.TYPE_INT_RGB);
        for (int i = 0; i < imageWidth; i++) {
            for (int j = 0; j < imageHeight; j++) {
                    int x = (int) (((a * i) + (b * j) + c) / ((g * i) + (h * j) + 1));
                    int y = (int) (((d * i) + (e * j) + f) / ((g * i) + (h * j) + 1));
                    int p = imgBuffer.getRGB(x, y);
                    output.setRGB(i, j, p);
            }
        }

        return output;
    }
}

进一步了解可以看this .