Determine the age of the tree by the number of circles

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Merry Christmas. Here's your present... The ring count that I get is 70. Make sure to mark my answer as correct, if you find that it works for you. :)

Here is a cropped version of your input image, which contains only the necessary data:

Here is the C++ code to count the rings:

#include <opencv2/opencv.hpp>
using namespace cv;
#pragma comment(lib, "opencv_world340.lib")

#include <iostream>
using namespace std;

int main(void)
{
    Mat frame = imread("rings_slice.png");

    if (frame.empty())
    {
        cout << "Error loading image file" << endl;
        return -1;
    }

    cvtColor(frame, frame, CV_BGR2GRAY);

    adaptiveThreshold(frame, frame, 255, ADAPTIVE_THRESH_GAUSSIAN_C, THRESH_BINARY, 11, 2);

    // Use centre column
    int column_index = frame.cols / 2;

    int ring_count = 0;

    // Start with the second row
    for (int i = 1; i < frame.rows; i++)
    {
        // If this pixel is white and the previous pixel is black
        if (255 == frame.at<unsigned char>(i, column_index) && 0 == frame.at<unsigned char>(i - 1, column_index))
            ring_count++;
    }

    cout << ring_count << endl;

    return 1;
}

Alternatively, here is the Python code:

import numpy as np
import cv2
import sys

frame = cv2.imread("rings_slice.png")

if frame is None:
    print('Error loading image')
    exit()

frame = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)

frame = cv2.adaptiveThreshold(frame, 255, cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY, 11, 2)

rows = frame.shape[0]
cols = frame.shape[1]

# Use centre column
column_index = cols / 2

ring_count = 0;

# Start with the second row
for i in range(1, rows):
    # If this pixel is white and the previous pixel is black
    if 255 == frame[i, column_index] and 0 == frame[i - 1, column_index]:
        ring_count += 1;

print ring_count