how to crop the detected face image in opencv java

OpenCV has region of interest functions which you may find useful. If you are using the cv::Mat then you could use something like the following.

// Take your Final Detected Image
image;

// These values need to be your determined face rect values
cv::Rect myROI(x, y,width, height);

// Crop the full image to that image contained by the rectangle myROI
// Note that this doesn't copy the data
cv::Mat croppedImage = image(myROI);

import org.opencv.core.Core;
import org.opencv.core.Mat;
import org.opencv.core.MatOfRect;
import org.opencv.core.Point;
import org.opencv.core.Rect;
import org.opencv.core.Scalar;
import org.opencv.core.Size;
import org.opencv.highgui.Highgui;
import static org.opencv.highgui.Highgui.imwrite;
import org.opencv.imgproc.Imgproc;
import org.opencv.objdetect.CascadeClassifier;

public class FaceDetector {
    private static Mat cropImage;

public static void main(String[] args)throws Exception {
    int x = 0,y = 0,height = 0,width = 0;

    System.loadLibrary(Core.NATIVE_LIBRARY_NAME);
        System.out.println("\nRunning FaceDetector");

//CascadeClassifier faceDetector = new CascadeClassifier(FaceDetector.class.getResource("haarcascade_frontalface_alt.xm    l").getPath());
CascadeClassifier faceDetector = new CascadeClassifier(Snapshot.class.getResource("haarcascade_frontalface_alt.xml").getPath().substring(1));
Mat image = Highgui.imread("C:\\image.jpg");

faceDetector.detectMultiScale(image, face_Detections);
System.out.println(String.format("Detected %s faces",  face_Detections.toArray().length));

Rect rect_Crop=null;
for (Rect rect : face_Detections.toArray()) {
    Core.rectangle(image, new Point(rect.x, rect.y), new Point(rect.x + rect.width, rect.y + rect.height),
            new Scalar(0, 255, 0));
    rectCrop = new Rect(rect.x, rect.y, rect.width, rect.height);
}
       
 Mat image_roi = new Mat(image,rectCrop);
  Highgui.imwrite("C:\\cropimage_912.jpg",image_roi);

}}