Peak detection in a noisy 2d array

I'm trying to get python to return, as close as possible, the center of the most obvious clustering in an image like the one below:

In my previous question I asked how to get the global maximum and the local maximums of a 2d array, and the answers given worked perfectly. The issue is that the center estimation I can get by averaging the global maximum obtained with different bin sizes is always slightly off than the one I would set by eye, because I'm only accounting for the biggest bin instead of a group of biggest bins (like one does by eye).

I tried adapting the answer to this question to my problem, but it turns out my image is too noisy for that algorithm to work. Here's my code implementing that answer:

import numpy as np
from scipy.ndimage.filters import maximum_filter
from scipy.ndimage.morphology import generate_binary_structure, binary_erosion
import matplotlib.pyplot as pp

from os import getcwd
from os.path import join, realpath, dirname

# Save path to dir where this code exists.
mypath = realpath(join(getcwd(), dirname(__file__)))
myfile = 'data_file.dat'

x, y = np.loadtxt(join(mypath,myfile), usecols=(1, 2), unpack=True)
xmin, xmax = min(x), max(x)
ymin, ymax = min(y), max(y)

rang = [[xmin, xmax], [ymin, ymax]]
paws = []

for d_b in range(25, 110, 25):
    # Number of bins in x,y given the bin width 'd_b'
    binsxy = [int((xmax - xmin) / d_b), int((ymax - ymin) / d_b)]

    H, xedges, yedges = np.histogram2d(x, y, range=rang, bins=binsxy)
    paws.append(H)


def detect_peaks(image):
    """
    Takes an image and detect the peaks usingthe local maximum filter.
    Returns a boolean mask of the peaks (