How to Erode the border and get rectangel shape?

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You can solve it out by either of the two method explained below.

First method.

• Convert to Gray.

• Threshold the image.

• Find the biggest contour in the threshold image, which will represent boundary of your object.

• Find the convexHull of the biggest contour.

• Compute the largest rectangle inside the convex polygon. See a good explanation here

Second method.

This one is relatively simple compared to above.

• Convert to Gray.
• Threshold the image
• Find biggest contour to segment object region and draw contour to new Mat.

• Apply morphologyEx, here we use morphological Opening . And another thing is that we will use larger kernel size along one direction(x or y) to remove unwanted boarder in your image.

• After morphology apply findcontours() and boundingRect() for final segmentation.

Source code

#include <iostream>
#include "opencv2/opencv.hpp"

using namespace std;
using namespace cv;

int main(){

//Load image convert to gray scale and threshold
Mat tmp,thr;
Mat src=imread("test.bmp",1);
blur( src, src, Size( 7, 7 ), Point(-1,-1) );
cvtColor(src,tmp,CV_BGR2GRAY);
threshold(tmp,thr,180,255,THRESH_BINARY);
imshow("thr",thr);

    //Find biggest contour to segment exact object
    vector< vector <Point> > contours; // Vector for storing contour
    vector< Vec4i > hierarchy;
    int largest_contour_index=0;
    int largest_area=0;
    Mat dst(src.rows,src.cols,CV_8UC1,Scalar::all(0)); //create destination image

     findContours( thr, contours, hierarchy,CV_RETR_EXTERNAL, CV_CHAIN_APPROX_SIMPLE ); // Find the contours in the image
     for( int i = 0; i< contours.size(); i++ ) // iterate through each contour.
      {
       double a=contourArea( contours[i],false);  //  Find the area of contour
       if(a>largest_area){
       largest_area=a;
       largest_contour_index=i;                //Store the index of largest contour
       }
      }

     drawContours( dst,contours, largest_contour_index, Scalar(255,255,255),CV_FILLED, 8, hierarchy ); // Draw the largest contour using previously stored index.
     imshow("contour",dst);

     //Apply morphological opening operation to eliminate unwanted region.
     Size kernalSize (7,100); //kernal size may change for differnt image
     Mat element = getStructuringElement (MORPH_RECT, kernalSize, Point(1,1)  );
     morphologyEx( dst, dst, MORPH_OPEN, element );

     //find bounding box after morphology.
     findContours( dst, contours, hierarchy,CV_RETR_EXTERNAL, CV_CHAIN_APPROX_SIMPLE ); // Find the contours in the image always only one contour
     Rect rect=boundingRect(contours[0]);

     //Crop the rsult
     Mat crop=src(rect);
     imshow("Cropped",crop);
     rectangle( src, rect, Scalar(0,0,255), 1, 8, 0 );
     imshow("src",src);
     waitKey();

}

Result for sample2.bmp

Size kernalSize (7,100);

Source image

Largest contour

After morphology

Result

And for your first image Sample.bmp you need to change the kernel like

Size kernalSize (100,7);

And here is the result I got with the above kernel