OpenCV: refine contours that are similar to rectangles

I was working on rectangle detection software, that should detect any rectangle on a given surface. After doing some research I came up with the following:

Apply Gaussian Blur on grayscale image

Detect Edges with Canny, using Otsu thresholds

MorphEx with rect

Findcontours

This yields decent results, however in some cases contour is not perfect. Which can be seen in the following images original image , detected contours.

I was thinking about convex hull, but then even the contours that aren't rectangles may be misinterpreted as rectangles. Maybe continue the contours in a straight line and calculate intersection points?

I am stuck. Any tips on how to refine the contours?

Here's the code for reference (Java on Android):

    detectedEdges = grayImg.clone();
    Size size = new Size(9, 9);

    Imgproc.GaussianBlur(grayImg, grayImg, size, 0);

    double otsu = Imgproc.threshold(grayImg.clone(),new Mat(),0,255,Imgproc.THRESH_BINARY|Imgproc.THRESH_OTSU);

    Imgproc.Canny(grayImg, detectedEdges, otsu/2, otsu);
    Mat kernel = Imgproc.getStructuringElement(Imgproc.MORPH_RECT, new Size(4,4));
    Imgproc.morphologyEx(detectedEdges.clone(),detectedEdges,Imgproc.MORPH_CLOSE,kernel);
    contours = new ArrayList<>();

    Imgproc.findContours(detectedEdges.clone(),contours,new Mat(),Imgproc.RETR_EXTERNAL,Imgproc.CHAIN_APPROX_SIMPLE);

    if (contours.size() == 0) {
        Toast.makeText(getApplicationContext(), "No contours found", Toast.LENGTH_SHORT).show();
        return null;
    }

    for(MatOfPoint c : contours){
        MatOfPoint2f contour = new MatOfPoint2f(c.toArray());

        double length  = Imgproc.arcLength(contour,true);
        Imgproc.approxPolyDP(contour,contour,0.02*length,true);
        if(contour.total() == 4){
            //found a rect! DO something
        }
    }

    Imgproc.drawContours(grayImg,contours,-1,new Scalar(255,225,255), 2);

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