Maximum sum rectangle in a 2D matrix

Given a 2D array, find the maximum sum subarray in it. For example, in the following 2D array, the maximum sum subarray is highlighted with blue rectangle and sum of this subarray is 29.

class Solution {
    public int kadane(int[] arr) {
        int curr_sum = 0;
        int max = Integer.MIN_VALUE;
        for (int x : arr) {
            curr_sum += x;
            max = Math.max(max, curr_sum);
            if (curr_sum < 0)
                curr_sum = 0;
        }
        return max;
    }

    public int maxSumSubmatrix(int[][] matrix) {
        if (matrix.length == 0)
            return 0;
        int ans = Integer.MIN_VALUE;
        for (int i = 0; i < matrix[0].length; i++) {
            int[] sum = new int[matrix.length];
            for (int j = i; j < matrix[0].length; j++) {
                for (int k = 0; k < matrix.length; k++)
                    sum[k] += matrix[k][j];
                int bestSum = kadane(sum);
                ans=Math.max(ans,bestSum);
            }
        }
        return ans;
    }
}