<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def find_center(self, image, threshold=0.1, verbose=True):
 """ Find the center of a galaxy. If the algorithm is successful the (x, y) coordinates in this `~photutils.isophote.EllipseGeometry` (i.e. the ``x0`` and ``y0`` attributes) instance will be modified. The isophote fit algorithm requires an initial guess for the galaxy center (x, y) coordinates and these coordinates must be close to the actual galaxy center for the isophote fit to work. This method provides can provide an initial guess for the galaxy center coordinates. See the **Notes** section below for more details. Parameters image : 2D `~numpy.ndarray` The image array. Masked arrays are not recognized here. This assumes that centering should always be done on valid pixels. threshold : float, optional The centerer threshold. To turn off the centerer, set this to a large value (i.e. >> 1). The default is 0.1. verbose : bool, optional Whether to print object centering information. The default is `True`. Notes ----- The centerer function scans a 10x10 window centered on the (x, y) coordinates in the `~photutils.isophote.EllipseGeometry` instance passed to the constructor of the `~photutils.isophote.Ellipse` class. If any of the `~photutils.isophote.EllipseGeometry` (x, y) coordinates are `None`, the center of the input image frame is used. If the center acquisition is successful, the `~photutils.isophote.EllipseGeometry` instance is modified in place to reflect the solution of the object centerer algorithm. In some cases the object centerer algorithm may fail even though there is enough signal-to-noise to start a fit (e.g. objects with very high ellipticity). In those cases the sensitivity of the algorithm can be decreased by decreasing the value of the object centerer threshold parameter. The centerer works by looking where a quantity akin to a signal-to-noise ratio is maximized within the 10x10 window. The centerer can thus be shut off entirely by setting the threshold to a large value (i.e. >> 1; meaning no location inside the search window will achieve that signal-to-noise ratio). """


        self._centerer_mask_half_size = len(IN_MASK) / 2
        self.centerer_threshold = threshold

        # number of pixels in each mask
        sz = len(IN_MASK)
        self._centerer_ones_in = np.ma.masked_array(np.ones(shape=(sz, sz)),
                                                    mask=IN_MASK)
        self._centerer_ones_out = np.ma.masked_array(np.ones(shape=(sz, sz)),
                                                     mask=OUT_MASK)
        self._centerer_in_mask_npix = np.sum(self._centerer_ones_in)
        self._centerer_out_mask_npix = np.sum(self._centerer_ones_out)

        # Check if center coordinates point to somewhere inside the frame.
        # If not, set then to frame center.
        shape = image.shape
        _x0 = self.x0
        _y0 = self.y0
        if (_x0 is None or _x0 < 0 or _x0 >= shape[1] or _y0 is None or
                _y0 < 0 or _y0 >= shape[0]):
            _x0 = shape[1] / 2
            _y0 = shape[0] / 2

        max_fom = 0.
        max_i = 0
        max_j = 0

        # scan all positions inside window
        window_half_size = 5
        for i in range(int(_x0 - window_half_size),
                       int(_x0 + window_half_size) + 1):
            for j in range(int(_y0 - window_half_size),
                           int(_y0 + window_half_size) + 1):

                # ensure that it stays inside image frame
                i1 = int(max(0, i - self._centerer_mask_half_size))
                j1 = int(max(0, j - self._centerer_mask_half_size))
                i2 = int(min(shape[1] - 1, i + self._centerer_mask_half_size))
                j2 = int(min(shape[0] - 1, j + self._centerer_mask_half_size))

                window = image[j1:j2, i1:i2]

                # averages in inner and outer regions.
                inner = np.ma.masked_array(window, mask=IN_MASK)
                outer = np.ma.masked_array(window, mask=OUT_MASK)
                inner_avg = np.sum(inner) / self._centerer_in_mask_npix
                outer_avg = np.sum(outer) / self._centerer_out_mask_npix

                # standard deviation and figure of merit
                inner_std = np.std(inner)
                outer_std = np.std(outer)
                stddev = np.sqrt(inner_std**2 + outer_std**2)

                fom = (inner_avg - outer_avg) / stddev

                if fom > max_fom:
                    max_fom = fom
                    max_i = i
                    max_j = j

        # figure of merit > threshold: update geometry with new coordinates.
        if max_fom > threshold:
            self.x0 = float(max_i)
            self.y0 = float(max_j)

            if verbose:
                log.info("Found center at x0 = {0:5.1f}, y0 = {1:5.1f}"
                         .format(self.x0, self.y0))
        else:
            if verbose:
                log.info('Result is below the threshold -- keeping the '
                         'original coordinates.')