コード例 #1
0
 def do_measurements(self, workspace, image_name, object_name, 
                     center_object_name, center_choice,
                     bin_count_settings, dd):
     '''Perform the radial measurements on the image set
     
     workspace - workspace that holds images / objects
     image_name - make measurements on this image
     object_name - make measurements on these objects
     center_object_name - use the centers of these related objects as
                   the centers for radial measurements. None to use the
                   objects themselves.
     center_choice - the user's center choice for this object:
                   C_SELF, C_CENTERS_OF_OBJECTS or C_EDGES_OF_OBJECTS.
     bin_count_settings - the bin count settings group
     d - a dictionary for saving reusable partial results
     
     returns one statistics tuple per ring.
     '''
     assert isinstance(workspace, cpw.Workspace)
     assert isinstance(workspace.object_set, cpo.ObjectSet)
     bin_count = bin_count_settings.bin_count.value
     wants_scaled = bin_count_settings.wants_scaled.value
     maximum_radius = bin_count_settings.maximum_radius.value
     
     image = workspace.image_set.get_image(image_name,
                                           must_be_grayscale=True)
     objects = workspace.object_set.get_objects(object_name)
     labels, pixel_data = cpo.crop_labels_and_image(objects.segmented,
                                                    image.pixel_data)
     nobjects = np.max(objects.segmented)
     measurements = workspace.measurements
     assert isinstance(measurements, cpmeas.Measurements)
     if nobjects == 0:
         for bin in range(1, bin_count+1):
             for feature in (F_FRAC_AT_D, F_MEAN_FRAC, F_RADIAL_CV):
                 feature_name = (
                     (feature + FF_GENERIC) % (image_name, bin, bin_count))
                 measurements.add_measurement(
                     object_name, "_".join([M_CATEGORY, feature_name]),
                     np.zeros(0))
                 if not wants_scaled:
                     measurement_name = "_".join([M_CATEGORY, feature,
                                                  image_name, FF_OVERFLOW])
                     measurements.add_measurement(
                         object_name, measurement_name, np.zeros(0))
         return [(image_name, object_name, "no objects","-","-","-","-")]
     name = (object_name if center_object_name is None 
             else "%s_%s"%(object_name, center_object_name))
     if dd.has_key(name):
         normalized_distance, i_center, j_center, good_mask = dd[name]
     else:
         d_to_edge = distance_to_edge(labels)
         if center_object_name is not None:
             #
             # Use the center of the centering objects to assign a center
             # to each labeled pixel using propagation
             #
             center_objects=workspace.object_set.get_objects(center_object_name)
             center_labels, cmask = cpo.size_similarly(
                 labels, center_objects.segmented)
             pixel_counts = fix(scind.sum(
                 np.ones(center_labels.shape),
                 center_labels,
                 np.arange(1, np.max(center_labels)+1,dtype=np.int32)))
             good = pixel_counts > 0
             i,j = (centers_of_labels(center_labels) + .5).astype(int)
             if center_choice == C_CENTERS_OF_OTHER:
                 #
                 # Reduce the propagation labels to the centers of
                 # the centering objects
                 #
                 ig = i[good]
                 jg = j[good]
                 lg = np.arange(1, len(i)+1)[good]
                 center_labels = np.zeros(center_labels.shape, int)
                 center_labels[ig,jg] = lg
             cl,d_from_center = propagate(np.zeros(center_labels.shape),
                                          center_labels,
                                          labels != 0, 1)
             #
             # Erase the centers that fall outside of labels
             #
             cl[labels == 0] = 0
             #
             # If objects are hollow or crescent-shaped, there may be
             # objects without center labels. As a backup, find the
             # center that is the closest to the center of mass.
             #
             missing_mask = (labels != 0) & (cl == 0)
             missing_labels = np.unique(labels[missing_mask])
             if len(missing_labels):
                 all_centers = centers_of_labels(labels)
                 missing_i_centers, missing_j_centers = \
                                  all_centers[:, missing_labels-1]
                 di = missing_i_centers[:, np.newaxis] - ig[np.newaxis, :]
                 dj = missing_j_centers[:, np.newaxis] - jg[np.newaxis, :]
                 missing_best = lg[np.lexsort((di*di + dj*dj, ))[:, 0]]
                 best = np.zeros(np.max(labels) + 1, int)
                 best[missing_labels] = missing_best
                 cl[missing_mask] = best[labels[missing_mask]]
                 #
                 # Now compute the crow-flies distance to the centers
                 # of these pixels from whatever center was assigned to
                 # the object.
                 #
                 iii, jjj = np.mgrid[0:labels.shape[0], 0:labels.shape[1]]
                 di = iii[missing_mask] - i[cl[missing_mask] - 1]
                 dj = jjj[missing_mask] - j[cl[missing_mask] - 1]
                 d_from_center[missing_mask] = np.sqrt(di*di + dj*dj)
         else:
             # Find the point in each object farthest away from the edge.
             # This does better than the centroid:
             # * The center is within the object
             # * The center tends to be an interesting point, like the
             #   center of the nucleus or the center of one or the other
             #   of two touching cells.
             #
             i,j = maximum_position_of_labels(d_to_edge, labels, objects.indices)
             center_labels = np.zeros(labels.shape, int)
             center_labels[i,j] = labels[i,j]
             #
             # Use the coloring trick here to process touching objects
             # in separate operations
             #
             colors = color_labels(labels)
             ncolors = np.max(colors)
             d_from_center = np.zeros(labels.shape)
             cl = np.zeros(labels.shape, int)
             for color in range(1,ncolors+1):
                 mask = colors == color
                 l,d = propagate(np.zeros(center_labels.shape),
                                 center_labels,
                                 mask, 1)
                 d_from_center[mask] = d[mask]
                 cl[mask] = l[mask]
         good_mask = cl > 0
         if center_choice == C_EDGES_OF_OTHER:
             # Exclude pixels within the centering objects
             # when performing calculations from the centers
             good_mask = good_mask & (center_labels == 0)
         i_center = np.zeros(cl.shape)
         i_center[good_mask] = i[cl[good_mask]-1]
         j_center = np.zeros(cl.shape)
         j_center[good_mask] = j[cl[good_mask]-1]
         
         normalized_distance = np.zeros(labels.shape)
         if wants_scaled:
             total_distance = d_from_center + d_to_edge
             normalized_distance[good_mask] = (d_from_center[good_mask] /
                                               (total_distance[good_mask] + .001))
         else:
             normalized_distance[good_mask] = \
                 d_from_center[good_mask] / maximum_radius
         dd[name] = [normalized_distance, i_center, j_center, good_mask]
     ngood_pixels = np.sum(good_mask)
     good_labels = labels[good_mask]
     bin_indexes = (normalized_distance * bin_count).astype(int)
     bin_indexes[bin_indexes > bin_count] = bin_count
     labels_and_bins = (good_labels-1,bin_indexes[good_mask])
     histogram = coo_matrix((pixel_data[good_mask], labels_and_bins),
                            (nobjects, bin_count+1)).toarray()
     sum_by_object = np.sum(histogram, 1)
     sum_by_object_per_bin = np.dstack([sum_by_object]*(bin_count + 1))[0]
     fraction_at_distance = histogram / sum_by_object_per_bin
     number_at_distance = coo_matrix((np.ones(ngood_pixels),labels_and_bins),
                                     (nobjects, bin_count+1)).toarray()
     object_mask = number_at_distance > 0
     sum_by_object = np.sum(number_at_distance, 1)
     sum_by_object_per_bin = np.dstack([sum_by_object]*(bin_count+1))[0]
     fraction_at_bin = number_at_distance / sum_by_object_per_bin
     mean_pixel_fraction = fraction_at_distance / (fraction_at_bin +
                                                   np.finfo(float).eps)
     masked_fraction_at_distance = masked_array(fraction_at_distance,
                                                ~object_mask)
     masked_mean_pixel_fraction = masked_array(mean_pixel_fraction,
                                               ~object_mask)
     # Anisotropy calculation.  Split each cell into eight wedges, then
     # compute coefficient of variation of the wedges' mean intensities
     # in each ring.
     #
     # Compute each pixel's delta from the center object's centroid
     i,j = np.mgrid[0:labels.shape[0], 0:labels.shape[1]]
     imask = i[good_mask] > i_center[good_mask]
     jmask = j[good_mask] > j_center[good_mask]
     absmask = (abs(i[good_mask] - i_center[good_mask]) > 
                abs(j[good_mask] - j_center[good_mask]))
     radial_index = (imask.astype(int) + jmask.astype(int)*2 + 
                     absmask.astype(int)*4)
     statistics = []
     for bin in range(bin_count + (0 if wants_scaled else 1)):
         bin_mask = (good_mask & (bin_indexes == bin))
         bin_pixels = np.sum(bin_mask)
         bin_labels = labels[bin_mask]
         bin_radial_index = radial_index[bin_indexes[good_mask] == bin]
         labels_and_radii = (bin_labels-1, bin_radial_index)
         radial_values = coo_matrix((pixel_data[bin_mask],
                                     labels_and_radii),
                                    (nobjects, 8)).toarray()
         pixel_count = coo_matrix((np.ones(bin_pixels), labels_and_radii),
                                  (nobjects, 8)).toarray()
         mask = pixel_count==0
         radial_means = masked_array(radial_values / pixel_count, mask)
         radial_cv = np.std(radial_means,1) / np.mean(radial_means, 1)
         radial_cv[np.sum(~mask,1)==0] = 0
         for measurement, feature, overflow_feature in (
             (fraction_at_distance[:,bin], MF_FRAC_AT_D, OF_FRAC_AT_D),
             (mean_pixel_fraction[:,bin], MF_MEAN_FRAC, OF_MEAN_FRAC),
             (np.array(radial_cv), MF_RADIAL_CV, OF_RADIAL_CV)):
             
             if bin == bin_count:
                 measurement_name = overflow_feature % image_name
             else:
                 measurement_name = feature % (image_name, bin+1, bin_count)
             measurements.add_measurement(object_name,
                                          measurement_name,
                                          measurement)
         radial_cv.mask = np.sum(~mask,1)==0
         bin_name = str(bin+1) if bin < bin_count else "Overflow"
         statistics += [(image_name, object_name, bin_name, str(bin_count),
                         round(np.mean(masked_fraction_at_distance[:,bin]),4),
                         round(np.mean(masked_mean_pixel_fraction[:, bin]),4),
                         round(np.mean(radial_cv),4))]
     return statistics
コード例 #2
0
    def run_on_objects(self, object_name, workspace):
        """Run, computing the area measurements for a single map of objects"""
        objects = workspace.get_objects(object_name)
        assert isinstance(objects, cpo.Objects)
        #
        # Do the ellipse-related measurements
        #
        i, j, l = objects.ijv.transpose()
        centers, eccentricity, major_axis_length, minor_axis_length, \
            theta, compactness =\
            ellipse_from_second_moments_ijv(i, j, 1, l, objects.indices, True)
        del i
        del j
        del l
        self.record_measurement(workspace, object_name, F_ECCENTRICITY,
                                eccentricity)
        self.record_measurement(workspace, object_name, F_MAJOR_AXIS_LENGTH,
                                major_axis_length)
        self.record_measurement(workspace, object_name, F_MINOR_AXIS_LENGTH,
                                minor_axis_length)
        self.record_measurement(workspace, object_name, F_ORIENTATION,
                                theta * 180 / np.pi)
        self.record_measurement(workspace, object_name, F_COMPACTNESS,
                                compactness)
        is_first = False
        if len(objects.indices) == 0:
            nobjects = 0
        else:
            nobjects = np.max(objects.indices)
        mcenter_x = np.zeros(nobjects)
        mcenter_y = np.zeros(nobjects)
        mextent = np.zeros(nobjects)
        mperimeters = np.zeros(nobjects)
        msolidity = np.zeros(nobjects)
        euler = np.zeros(nobjects)
        max_radius = np.zeros(nobjects)
        median_radius = np.zeros(nobjects)
        mean_radius = np.zeros(nobjects)
        min_feret_diameter = np.zeros(nobjects)
        max_feret_diameter = np.zeros(nobjects)
        zernike_numbers = self.get_zernike_numbers()
        zf = {}
        for n, m in zernike_numbers:
            zf[(n, m)] = np.zeros(nobjects)
        if nobjects > 0:
            chulls, chull_counts = convex_hull_ijv(objects.ijv,
                                                   objects.indices)
            for labels, indices in objects.get_labels():
                to_indices = indices - 1
                distances = distance_to_edge(labels)
                mcenter_y[to_indices], mcenter_x[to_indices] =\
                         maximum_position_of_labels(distances, labels, indices)
                max_radius[to_indices] = fix(
                    scind.maximum(distances, labels, indices))
                mean_radius[to_indices] = fix(
                    scind.mean(distances, labels, indices))
                median_radius[to_indices] = median_of_labels(
                    distances, labels, indices)
                #
                # The extent (area / bounding box area)
                #
                mextent[to_indices] = calculate_extents(labels, indices)
                #
                # The perimeter distance
                #
                mperimeters[to_indices] = calculate_perimeters(labels, indices)
                #
                # Solidity
                #
                msolidity[to_indices] = calculate_solidity(labels, indices)
                #
                # Euler number
                #
                euler[to_indices] = euler_number(labels, indices)
                #
                # Zernike features
                #
                zf_l = cpmz.zernike(zernike_numbers, labels, indices)
                for (n, m), z in zip(zernike_numbers, zf_l.transpose()):
                    zf[(n, m)][to_indices] = z
            #
            # Form factor
            #
            ff = 4.0 * np.pi * objects.areas / mperimeters**2
            #
            # Feret diameter
            #
            min_feret_diameter, max_feret_diameter = \
                feret_diameter(chulls, chull_counts, objects.indices)

        else:
            ff = np.zeros(0)

        for f, m in ([(F_AREA, objects.areas), (F_CENTER_X, mcenter_x),
                      (F_CENTER_Y, mcenter_y), (F_EXTENT, mextent),
                      (F_PERIMETER, mperimeters), (F_SOLIDITY, msolidity),
                      (F_FORM_FACTOR, ff), (F_EULER_NUMBER, euler),
                      (F_MAXIMUM_RADIUS, max_radius),
                      (F_MEAN_RADIUS, mean_radius),
                      (F_MEDIAN_RADIUS, median_radius),
                      (F_MIN_FERET_DIAMETER, min_feret_diameter),
                      (F_MAX_FERET_DIAMETER, max_feret_diameter)] +
                     [(self.get_zernike_name((n, m)), zf[(n, m)])
                      for n, m in zernike_numbers]):
            self.record_measurement(workspace, object_name, f, m)
コード例 #3
0
    def run_on_objects(self,object_name, workspace):
        """Run, computing the area measurements for a single map of objects"""
        objects = workspace.get_objects(object_name)
        assert isinstance(objects, cpo.Objects)
        #
        # Do the ellipse-related measurements
        #
        i, j, l = objects.ijv.transpose()
        centers, eccentricity, major_axis_length, minor_axis_length, \
            theta, compactness =\
            ellipse_from_second_moments_ijv(i, j, 1, l, objects.indices, True)
        del i
        del j
        del l
        self.record_measurement(workspace, object_name,
                                F_ECCENTRICITY, eccentricity)
        self.record_measurement(workspace, object_name,
                                F_MAJOR_AXIS_LENGTH, major_axis_length)
        self.record_measurement(workspace, object_name, 
                                F_MINOR_AXIS_LENGTH, minor_axis_length)
        self.record_measurement(workspace, object_name, F_ORIENTATION, 
                                theta * 180 / np.pi)
        self.record_measurement(workspace, object_name, F_COMPACTNESS,
                                compactness)
        is_first = False
        if len(objects.indices) == 0:
            nobjects = 0
        else:
            nobjects = np.max(objects.indices)
        mcenter_x = np.zeros(nobjects)
        mcenter_y = np.zeros(nobjects)
        mextent = np.zeros(nobjects)
        mperimeters = np.zeros(nobjects)
        msolidity = np.zeros(nobjects)
        euler = np.zeros(nobjects)
        max_radius = np.zeros(nobjects)
        median_radius = np.zeros(nobjects)
        mean_radius = np.zeros(nobjects)
        min_feret_diameter = np.zeros(nobjects)
        max_feret_diameter = np.zeros(nobjects)
        zernike_numbers = self.get_zernike_numbers()
        zf = {}
        for n,m in zernike_numbers:
            zf[(n,m)] = np.zeros(nobjects)
        if nobjects > 0:
            chulls, chull_counts = convex_hull_ijv(objects.ijv, objects.indices)
            for labels, indices in objects.get_labels():
                to_indices = indices-1
                distances = distance_to_edge(labels)
                mcenter_y[to_indices], mcenter_x[to_indices] =\
                         maximum_position_of_labels(distances, labels, indices)
                max_radius[to_indices] = fix(scind.maximum(
                    distances, labels, indices))
                mean_radius[to_indices] = fix(scind.mean(
                    distances, labels, indices))
                median_radius[to_indices] = median_of_labels(
                    distances, labels, indices)
                #
                # The extent (area / bounding box area)
                #
                mextent[to_indices] = calculate_extents(labels, indices)
                #
                # The perimeter distance
                #
                mperimeters[to_indices] = calculate_perimeters(labels, indices)
                #
                # Solidity
                #
                msolidity[to_indices] = calculate_solidity(labels, indices)
                #
                # Euler number
                #
                euler[to_indices] = euler_number(labels, indices)
                #
                # Zernike features
                #
                zf_l = cpmz.zernike(zernike_numbers, labels, indices)
                for (n,m), z in zip(zernike_numbers, zf_l.transpose()):
                    zf[(n,m)][to_indices] = z
            #
            # Form factor
            #
            ff = 4.0 * np.pi * objects.areas / mperimeters**2
            #
            # Feret diameter
            #
            min_feret_diameter, max_feret_diameter = \
                feret_diameter(chulls, chull_counts, objects.indices)
            
        else:
            ff = np.zeros(0)

        for f, m in ([(F_AREA, objects.areas),
                      (F_CENTER_X, mcenter_x),
                      (F_CENTER_Y, mcenter_y),
                      (F_EXTENT, mextent),
                      (F_PERIMETER, mperimeters),
                      (F_SOLIDITY, msolidity),
                      (F_FORM_FACTOR, ff),
                      (F_EULER_NUMBER, euler),
                      (F_MAXIMUM_RADIUS, max_radius),
                      (F_MEAN_RADIUS, mean_radius),
                      (F_MEDIAN_RADIUS, median_radius),
                      (F_MIN_FERET_DIAMETER, min_feret_diameter),
                      (F_MAX_FERET_DIAMETER, max_feret_diameter)] +
                     [(self.get_zernike_name((n,m)), zf[(n,m)])
                       for n,m in zernike_numbers]):
            self.record_measurement(workspace, object_name, f, m) 
コード例 #4
0
 def do_measurements(self, workspace, image_name, object_name, 
                     center_object_name, bin_count,
                     dd):
     '''Perform the radial measurements on the image set
     
     workspace - workspace that holds images / objects
     image_name - make measurements on this image
     object_name - make measurements on these objects
     center_object_name - use the centers of these related objects as
                   the centers for radial measurements. None to use the
                   objects themselves.
     bin_count - bin the object into this many concentric rings
     d - a dictionary for saving reusable partial results
     
     returns one statistics tuple per ring.
     '''
     assert isinstance(workspace, cpw.Workspace)
     assert isinstance(workspace.object_set, cpo.ObjectSet)
     image = workspace.image_set.get_image(image_name,
                                           must_be_grayscale=True)
     objects = workspace.object_set.get_objects(object_name)
     labels, pixel_data = cpo.crop_labels_and_image(objects.segmented,
                                                    image.pixel_data)
     nobjects = np.max(objects.segmented)
     measurements = workspace.measurements
     assert isinstance(measurements, cpmeas.Measurements)
     if nobjects == 0:
         for bin in range(1, bin_count+1):
             for feature in (FF_FRAC_AT_D, FF_MEAN_FRAC, FF_RADIAL_CV):
                 measurements.add_measurement(object_name,
                                              M_CATEGORY + "_" + feature % 
                                              (image_name, bin, bin_count),
                                              np.zeros(0))
         return [(image_name, object_name, "no objects","-","-","-","-")]
     name = (object_name if center_object_name is None 
             else "%s_%s"%(object_name, center_object_name))
     if dd.has_key(name):
         normalized_distance, i_center, j_center, good_mask = dd[name]
     else:
         d_to_edge = distance_to_edge(labels)
         if center_object_name is not None:
             center_objects=workspace.object_set.get_objects(center_object_name)
             center_labels, cmask = cpo.size_similarly(
                 labels, center_objects.segmented)
             pixel_counts = fix(scind.sum(np.ones(center_labels.shape),
                                          center_labels,
                                          np.arange(1, np.max(center_labels)+1,dtype=np.int32)))
             good = pixel_counts > 0
             i,j = (centers_of_labels(center_labels) + .5).astype(int)
             ig = i[good]
             jg = j[good]
             center_labels = np.zeros(center_labels.shape, int)
             center_labels[ig,jg] = labels[ig,jg] ## TODO: This is incorrect when objects are annular.  Retrieves label# = 0
             cl,d_from_center = propagate(np.zeros(center_labels.shape),
                                          center_labels,
                                          labels != 0, 1)
         else:
             # Find the point in each object farthest away from the edge.
             # This does better than the centroid:
             # * The center is within the object
             # * The center tends to be an interesting point, like the
             #   center of the nucleus or the center of one or the other
             #   of two touching cells.
             #
             i,j = maximum_position_of_labels(d_to_edge, labels, objects.indices)
             center_labels = np.zeros(labels.shape, int)
             center_labels[i,j] = labels[i,j]
             #
             # Use the coloring trick here to process touching objects
             # in separate operations
             #
             colors = color_labels(labels)
             ncolors = np.max(colors)
             d_from_center = np.zeros(labels.shape)
             cl = np.zeros(labels.shape, int)
             for color in range(1,ncolors+1):
                 mask = colors == color
                 l,d = propagate(np.zeros(center_labels.shape),
                                 center_labels,
                                 mask, 1)
                 d_from_center[mask] = d[mask]
                 cl[mask] = l[mask]
         good_mask = cl > 0
         i_center = np.zeros(cl.shape)
         i_center[good_mask] = i[cl[good_mask]-1]
         j_center = np.zeros(cl.shape)
         j_center[good_mask] = j[cl[good_mask]-1]
         
         normalized_distance = np.zeros(labels.shape)
         total_distance = d_from_center + d_to_edge
         normalized_distance[good_mask] = (d_from_center[good_mask] /
                                           (total_distance[good_mask] + .001))
         dd[name] = [normalized_distance, i_center, j_center, good_mask]
     ngood_pixels = np.sum(good_mask)
     good_labels = objects.segmented[good_mask]
     bin_indexes = (normalized_distance * bin_count).astype(int)
     labels_and_bins = (good_labels-1,bin_indexes[good_mask])
     histogram = coo_matrix((image.pixel_data[good_mask], labels_and_bins),
                            (nobjects, bin_count)).toarray()
     sum_by_object = np.sum(histogram, 1)
     sum_by_object_per_bin = np.dstack([sum_by_object]*bin_count)[0]
     fraction_at_distance = histogram / sum_by_object_per_bin
     number_at_distance = coo_matrix((np.ones(ngood_pixels),labels_and_bins),
                                     (nobjects, bin_count)).toarray()
     object_mask = number_at_distance > 0
     sum_by_object = np.sum(number_at_distance, 1)
     sum_by_object_per_bin = np.dstack([sum_by_object]*bin_count)[0]
     fraction_at_bin = number_at_distance / sum_by_object_per_bin
     mean_pixel_fraction = fraction_at_distance / (fraction_at_bin +
                                                   np.finfo(float).eps)
     masked_fraction_at_distance = masked_array(fraction_at_distance,
                                                ~object_mask)
     masked_mean_pixel_fraction = masked_array(mean_pixel_fraction,
                                               ~object_mask)
     # Anisotropy calculation.  Split each cell into eight wedges, then
     # compute coefficient of variation of the wedges' mean intensities
     # in each ring.
     #
     # Compute each pixel's delta from the center object's centroid
     i,j = np.mgrid[0:labels.shape[0], 0:labels.shape[1]]
     imask = i[good_mask] > i_center[good_mask]
     jmask = j[good_mask] > j_center[good_mask]
     absmask = (abs(i[good_mask] - i_center[good_mask]) > 
                abs(j[good_mask] - j_center[good_mask]))
     radial_index = (imask.astype(int) + jmask.astype(int)*2 + 
                     absmask.astype(int)*4)
     statistics = []
     for bin in range(bin_count):
         bin_mask = (good_mask & (bin_indexes == bin))
         bin_pixels = np.sum(bin_mask)
         bin_labels = labels[bin_mask]
         bin_radial_index = radial_index[bin_indexes[good_mask] == bin]
         labels_and_radii = (bin_labels-1, bin_radial_index)
         radial_values = coo_matrix((pixel_data[bin_mask],
                                     labels_and_radii),
                                    (nobjects, 8)).toarray()
         pixel_count = coo_matrix((np.ones(bin_pixels), labels_and_radii),
                                  (nobjects, 8)).toarray()
         mask = pixel_count==0
         radial_means = masked_array(radial_values / pixel_count, mask)
         radial_cv = np.std(radial_means,1) / np.mean(radial_means, 1)
         radial_cv[np.sum(~mask,1)==0] = 0
         for measurement, feature in ((fraction_at_distance[:,bin], MF_FRAC_AT_D),
                                      (mean_pixel_fraction[:,bin], MF_MEAN_FRAC),
                                      (np.array(radial_cv), MF_RADIAL_CV)):
                                      
             measurements.add_measurement(object_name,
                                          feature % 
                                          (image_name, bin+1, bin_count),
                                          measurement)
         radial_cv.mask = np.sum(~mask,1)==0
         statistics += [(image_name, object_name, str(bin+1), str(bin_count),
                         round(np.mean(masked_fraction_at_distance[:,bin]),4),
                         round(np.mean(masked_mean_pixel_fraction[:, bin]),4),
                         round(np.mean(radial_cv),4))]
     return statistics