how to remove straight lines or non-curvical lines in a canny image

A simple approach would be:

1. Find connected components
2. Find the minimum oriented bounding box
3. Compute the aspect ratio of the box, and check if it’s too much elongated.

On your image, I marked in red almost straight lines, and in green the curved lines. You can play with the threshold on the aspect ratio:

Code:

#include<opencv2/opencv.hpp>
using namespace cv;


int main()
{
    // Load image
    Mat1b img = imread("path_to_img", IMREAD_GRAYSCALE);

    // Create output image
    Mat3b out;
    cvtColor(img, out, COLOR_GRAY2BGR);

    // Find contours
    vector<vector<Point>> contours;
    findContours(img.clone(), contours, RETR_LIST, CHAIN_APPROX_NONE);

    for (const auto& contour : contours)
    {
        // Find minimum area rectangle
        RotatedRect rr = minAreaRect(contour);

        // Compute aspect ratio
        float aspect_ratio = min(rr.size.width, rr.size.height) / max(rr.size.width, rr.size.height);

        // Define a threshold on the aspect ratio in [0, 1]
        float thresh = 0.2f;

        Vec3b color;
        if (aspect_ratio < thresh) { 
            // Almost straight line
            color = Vec3b(0,0,255); // RED
        }
        else {
            // Curved line
            color = Vec3b(0, 255, 0); // GREEN
        }

        // Color output image
        for (const auto& pt : contour) {
            out(pt) = color;
        }
    }

    imshow("Out", out);
    waitKey();

    return 0;
}