Java 中的离散小波变换在图像中创建白点

Question

在我的Java程序中，图像被加载到程序中，然后使用离散小波变换进行变换，所得系数用作输出图像的图片数据。

但是，如果我对例如卡通图像进行变换，则在近似子带中的暗边缘上会出现白点：http://imgur.com/kLXyBvd

这是 forwardDWT 的代码：

private int[][] transformPixels(int[][] pixels, int widthHeight) {
    double[][] temp_bank = new double[widthHeight][widthHeight];
    double a1 = -1.586134342;
    double a2 = -0.05298011854;
    double a3 = 0.8829110762;
    double a4 = 0.4435068522;

    // Scale coeff:
    double k1 = 0.81289306611596146; // 1/1.230174104914
    double k2 = 0.61508705245700002;// 1.230174104914/2
    for (int i = 0; i < 2; i++) {
        for (int col = 0; col < widthHeight; col++) {
            // Predict 1
            for (int row = 1; row < widthHeight - 1; row += 2) {
                pixels[row][col] += a1 * (pixels[row - 1][col] + pixels[row + 1][col]);
            }
            pixels[widthHeight - 1][col] += 2 * a1 * pixels[widthHeight - 2][col];

            // Update 1
            for (int row = 2; row < widthHeight; row += 2) {
                pixels[row][col] += a2 * (pixels[row - 1][col] + pixels[row + 1][col]);
            }
            pixels[0][col] += 2 * a2 * pixels[1][col];

            // Predict 2
            for (int row = 1; row < widthHeight - 1; row += 2) {
                pixels[row][col] += a3 * (pixels[row - 1][col] + pixels[row + 1][col]);
            }
            pixels[widthHeight - 1][col] += 2 * a3 * pixels[widthHeight - 2][col];

            // Update 2
            for (int row = 2; row < widthHeight; row += 2) {
                pixels[row][col] += a4 * (pixels[row - 1][col] + pixels[row + 1][col]);
            }
            pixels[0][col] += 2 * a4 * pixels[1][col];
        }

        for (int row = 0; row < widthHeight; row++) {
            for (int col = 0; col < widthHeight; col++) {
                if (row % 2 == 0)
                    temp_bank[col][row / 2] = k1 * pixels[row][col];
                else
                    temp_bank[col][row / 2 + widthHeight / 2] = k2 * pixels[row][col];

            }
        }

        for (int row = 0; row < widthHeight; row++) {
            for (int col = 0; col < widthHeight; col++) {
                pixels[row][col] = (int) temp_bank[row][col];
            }
        }
    }
    return pixels;
}

这是使用提升方案实现的 CDF9/7 fitlerbanks 的 DWT，类似于 JPEG2000 中的 DWT。

该算法有两个限制：

只能处理灰度数据
图片的宽度和高度必须相同并且是2^n的乘积，例如256x256、512x512 等

因为也可能是灰度值计算错误，这里是加载图像的其他代码，开始转换，将 rgb 值转换为灰度值并转换回 rgb：

public BufferedImage openImage() throws InvalidWidthHeightException {
    try {
        int returnVal = fc.showOpenDialog(panel);
        if (returnVal == JFileChooser.APPROVE_OPTION) {
            File file = fc.getSelectedFile();
            BufferedImage temp = ImageIO.read(file);
            if (temp == null)
                return null;
            int checkInt = temp.getWidth();
            boolean check = (checkInt & (checkInt - 1)) == 0;
            if (checkInt != temp.getHeight() & !check)
                throw new InvalidWidthHeightException();
            int widthandHeight = temp.getWidth();
            image = new BufferedImage(widthandHeight, widthandHeight, BufferedImage.TYPE_BYTE_GRAY);
            Graphics g = image.getGraphics();
            g.drawImage(temp, 0, 0, null);
            g.dispose();

            return image;

        }
    } catch (IOException e) {
        System.out.println("Failed to load image!");
    }
    return null;

}

public void transform(int count) {
    int[][] pixels = getGrayValues(image);
    int transformedPixels[][];
    int width = pixels.length;
    transformedPixels = transformPixels(pixels, width);
    width/=2;

    for (int i = 1; i < count + 1; i++) {
        transformedPixels = transformPixels(transformedPixels, width);
        width/=2;
    }
    width = pixels.length;
    transformedImage = new BufferedImage(width, width, BufferedImage.TYPE_BYTE_GRAY);
    for (int x = 0; x < width; x++) {
        for (int y = 0; y < width; y++) {
            transformedImage.setRGB(x, y, tranformToRGB(transformedPixels[x][y]));
        }
    }

}

private int tranformToRGB(double d) {
    int value = (int) d;
    if (d < 0)
        d = 0;
    if (d > 255)
        d = 255;
    return 0xffffffff << 24 | value << 16 | value << 8 | value;
}

private int[][] getGrayValues(BufferedImage image2) {
    int[][] res = new int[image.getHeight()][image.getWidth()];
    int r, g, b;
    for (int i = 0; i < image.getWidth(); i++) {
        for (int j = 0; j < image.getHeight(); j++) {
            int value = image2.getRGB(i, j);
            r = (value >> 16) & 0xFF;
            g = (value >> 8) & 0xFF;
            b = (value & 0xFF);
            res[i][j] = (r + g + b) / 3;
        }
    }
    return res;
}

注意：因为图像的宽度和高度应该是相同的，所以我有时只是将宽度也用作高度。

编辑：正如@stuhlo 所建议的，我在 forwardDWT 中添加了对近似子带值的检查：

for (int row = 0; row < widthHeight; row++) {
            for (int col = 0; col < widthHeight; col++) {
                if (row % 2 == 0) {
                    double value = k1 * pixels[row][col];
                    if (value > 255)
                        value = 255;
                    if (value < 0)
                        value = 0;
                    temp_bank[col][row / 2] = value;
                } else {
                    temp_bank[col][row / 2 + widthHeight / 2] = k2 * pixels[row][col];
                }
            }
        }

不幸的是，现在水平细节的子栏变成黑色了。

Answer 1

您的问题是由于子带样本需要比原始图像样本更多的比特来存储。

我建议使用更大的数据类型来存储子带样本并将它们归一化为 8 位值以供显示。

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