"""Contains class for calculating the statistics of grains - 2d raster images"""
import logging
from pathlib import Path
from random import randint
from typing import Union, List, Tuple, Dict
import numpy as np
import skimage.measure as skimage_measure
import skimage.morphology as skimage_morphology
import skimage.feature as skimage_feature
import scipy.ndimage
import matplotlib.pyplot as plt
import pandas as pd
from topostats.logs.logs import LOGGER_NAME
from topostats.utils import create_empty_dataframe
# pylint: disable=too-many-lines
# pylint: disable=too-many-instance-attributes
# pylint: disable=too-many-arguments
# pylint: disable=too-many-branches
# pylint: disable=line-too-long
# pylint: disable=fixme
# FIXME : The calculate_stats() and calculate_aspect_ratio() raise this error when linting, could consider putting
# variables into dictionar, see example of breaking code out to staticmethod extremes() and returning a
# dictionary of x_min/x_max/y_min/y_max
# pylint: disable=too-many-locals
# FIXME : calculate_aspect_ratio raises this error when linting it has 65 statements, recommended not to exceed 50.
# Could break some out to small functions such as the lines that calculate the samllest bounding rectangle
# pylint: disable=too-many-statements
LOGGER = logging.getLogger(LOGGER_NAME)
GRAIN_STATS_COLUMNS = [
"molecule_number",
"centre_x",
"centre_y",
"radius_min",
"radius_max",
"radius_mean",
"radius_median",
"height_min",
"height_max",
"height_median",
"height_mean",
"volume",
"area",
"area_cartesian_bbox",
"smallest_bounding_width",
"smallest_bounding_length",
"smallest_bounding_area",
"aspect_ratio",
]
[docs]
class GrainStats:
"""Class for calculating grain stats."""
def __init__(
self,
data: np.ndarray,
labelled_data: np.ndarray,
pixel_to_nanometre_scaling: float,
direction: str,
base_output_dir: Union[str, Path],
image_name: str = None,
edge_detection_method: str = "binary_erosion",
cropped_size: float = -1,
plot_opts: dict = None,
metre_scaling_factor: float = 1e-9,
):
"""Initialise the class.
Parameters
----------
data : np.ndarray
2D Numpy array containing the flattened afm image. Data in this 2D array is floating point.
labelled_data : np.ndarray
2D Numpy array containing all the grain masks in the image. Data in this 2D array is boolean.
pixel_to_nanometre_scaling : float
Floating point value that defines the scaling factor between nanometres and pixels.
direction: str
Direction for which grains have been detected ("above" or "below").
base_output_dir : Path
Path to the folder that will store the grain stats output images and data.
image_name : str
The name of the file being processed.
edge_detection_method : str
Method used for detecting the edges of grain masks before calculating statistics on them.
Do not change unless you know exactly what this is doing. Options: "binary_erosion", "canny".
cropped_size : float
Length of square side (in nm) to crop grains to.
plot_opts : dict
Plotting options dictionary for the cropped grains
metre_scaling_factor : float
Multiplier to convert the current length scale to metres. Default: 1e-9 for the
usual AFM length scale of nanometres.
"""
self.data = data
self.labelled_data = labelled_data
self.pixel_to_nanometre_scaling = pixel_to_nanometre_scaling
self.direction = direction
self.base_output_dir = Path(base_output_dir)
self.start_point = None
self.image_name = image_name
self.edge_detection_method = edge_detection_method
self.cropped_size = cropped_size
self.plot_opts = plot_opts
self.metre_scaling_factor = metre_scaling_factor
[docs]
@staticmethod
def get_angle(point_1: tuple, point_2: tuple) -> float:
"""Function that calculates the angle in radians between two points.
Parameters
----------
point1: tuple
Coordinate vectors for the first point to find the angle between.
point2: tuple
Coordinate vectors for the second point to find the angle between.
Returns
-------
angle : float
The angle in radians between the two input vectors.
"""
return np.arctan2(point_1[1] - point_2[1], point_1[0] - point_2[0])
[docs]
@staticmethod
def is_clockwise(p_1: tuple, p_2: tuple, p_3: tuple) -> bool:
"""Function to determine if three points make a clockwise or counter-clockwise turn.
Parameters
----------
p_1: tuple
First point to be used to calculate turn.
p_2: tuple
Second point to be used to calculate turn.
p_3: tuple
Third point to be used to calculate turn.
Returns
-------
boolean
Indicator of whether turn is clockwise.
"""
# Determine if three points form a clockwise or counter-clockwise turn.
# I use the method of calculating the determinant of the following rotation matrix here. If the determinant
# is > 0 then the rotation is counter-clockwise.
rotation_matrix = np.array(((p_1[0], p_1[1], 1), (p_2[0], p_2[1], 1), (p_3[0], p_3[1], 1)))
return not np.linalg.det(rotation_matrix) > 0
[docs]
def calculate_stats(self) -> Dict:
"""Calculate the stats of grains in the labelled image.
Returns
-------
grainstats: pd.DataFrame
A DataFrame containing all the grain stats that have been calculated for the labelled image.
grains_plot_data:
A list of dictionaries containing grain data to be plotted.
"""
grains_plot_data = []
if self.labelled_data is None:
LOGGER.info(
f"[{self.image_name}] : No labelled regions for this image, grain statistics can not be calculated."
)
return pd.DataFrame(columns=GRAIN_STATS_COLUMNS), grains_plot_data
# Calculate region properties
region_properties = skimage_measure.regionprops(self.labelled_data)
# Iterate over all the grains in the image
stats_array = []
# List to hold all the plot data for all the grains. Each entry is a dictionary of plotting data.
# There are multiple entries for each grain.
for index, region in enumerate(region_properties):
LOGGER.info(f"[{self.image_name}] : Processing grain: {index}")
# Skip grain if too small to calculate stats for
LOGGER.debug(f"[{self.image_name}] : Grain size: {region.image.size}")
if min(region.image.shape) < 5:
LOGGER.info(
f"[{self.image_name}] : Skipping grain due to being too small (size: {region.image.shape}) to calculate stats for."
)
continue
# Create directory for each grain's plots
output_grain = self.base_output_dir / self.direction
# Obtain cropped grain mask and image
minr, minc, maxr, maxc = region.bbox
grain_mask = np.array(region.image)
grain_image = self.data[minr:maxr, minc:maxc]
grain_mask_image = np.ma.masked_array(grain_image, mask=np.invert(grain_mask), fill_value=np.nan).filled()
if self.cropped_size == -1:
for name, image in {
"grain_image": grain_image,
"grain_mask": grain_mask,
"grain_mask_image": grain_mask_image,
}.items():
grains_plot_data.append(
{
"image": image,
"output_grain": output_grain,
"filename": f"{self.image_name}_{name}_{index}",
"plot_opts": self.plot_opts[name],
}
)
else:
# Get cropped image and mask
grain_centre = int((minr + maxr) / 2), int((minc + maxc) / 2)
length = int(self.cropped_size / (2 * self.pixel_to_nanometre_scaling))
solo_mask = self.labelled_data.copy()
solo_mask[solo_mask != index + 1] = 0
solo_mask[solo_mask == index + 1] = 1
cropped_grain_image = self.get_cropped_region(self.data, length, np.asarray(grain_centre))
cropped_grain_mask = self.get_cropped_region(solo_mask, length, np.asarray(grain_centre)).astype(bool)
cropped_grain_mask_image = np.ma.masked_array(
grain_image, mask=np.invert(grain_mask), fill_value=np.nan
).filled()
for name, image in {
"grain_image": cropped_grain_image,
"grain_mask": cropped_grain_mask,
"grain_mask_image": cropped_grain_mask_image,
}.items():
grains_plot_data.append(
{
"data": image,
"output_dir": output_grain,
"filename": f"{self.image_name}_{name}_{index}",
"name": name,
}
)
points = self.calculate_points(grain_mask)
edges = self.calculate_edges(grain_mask, edge_detection_method=self.edge_detection_method)
radius_stats = self.calculate_radius_stats(edges, points)
# hull, hull_indices, hull_simplexes = self.convex_hull(edges, output_grain)
_, _, hull_simplexes = self.convex_hull(edges, output_grain)
centroid = self._calculate_centroid(points)
# Centroids for the grains (minc and minr added because centroid returns values local to the cropped grain images)
centre_x = centroid[0] + minc
centre_y = centroid[1] + minr
(
smallest_bounding_width,
smallest_bounding_length,
aspect_ratio,
) = self.calculate_aspect_ratio(
edges=edges,
hull_simplices=hull_simplexes,
path=output_grain,
)
# Calculate minimum and maximum feret diameters
min_feret, max_feret = self.get_max_min_ferets(edge_points=edges)
# Save the stats to dictionary. Note that many of the stats are multiplied by a scaling factor to convert
# from pixel units to nanometres.
# Removed formatting, better to keep accurate until the end, including in CSV, then shorten display
length_scaling_factor = self.pixel_to_nanometre_scaling * self.metre_scaling_factor
area_scaling_factor = length_scaling_factor**2
stats = {
"centre_x": centre_x * length_scaling_factor,
"centre_y": centre_y * length_scaling_factor,
"radius_min": radius_stats["min"] * length_scaling_factor,
"radius_max": radius_stats["max"] * length_scaling_factor,
"radius_mean": radius_stats["mean"] * length_scaling_factor,
"radius_median": radius_stats["median"] * length_scaling_factor,
"height_min": np.nanmin(grain_mask_image) * self.metre_scaling_factor,
"height_max": np.nanmax(grain_mask_image) * self.metre_scaling_factor,
"height_median": np.nanmedian(grain_mask_image) * self.metre_scaling_factor,
"height_mean": np.nanmean(grain_mask_image) * self.metre_scaling_factor,
# [volume] = [pixel] * [pixel] * [height] = px * px * nm.
# To turn into m^3, multiply by pixel_to_nanometre_scaling^2 and metre_scaling_factor^3.
"volume": np.nansum(grain_mask_image)
* self.pixel_to_nanometre_scaling**2
* (self.metre_scaling_factor**3),
"area": region.area * area_scaling_factor,
"area_cartesian_bbox": region.area_bbox * area_scaling_factor,
"smallest_bounding_width": smallest_bounding_width * length_scaling_factor,
"smallest_bounding_length": smallest_bounding_length * length_scaling_factor,
"smallest_bounding_area": smallest_bounding_length * smallest_bounding_width * area_scaling_factor,
"aspect_ratio": aspect_ratio,
"threshold": self.direction,
"max_feret": max_feret * length_scaling_factor,
"min_feret": min_feret * length_scaling_factor,
}
stats_array.append(stats)
if len(stats_array) > 0:
grainstats_df = pd.DataFrame(data=stats_array)
else:
grainstats_df = create_empty_dataframe()
grainstats_df.index.name = "molecule_number"
grainstats_df["image"] = self.image_name
return grainstats_df, grains_plot_data
[docs]
@staticmethod
def calculate_points(grain_mask: np.ndarray):
"""Class method that takes a 2D boolean numpy array image of a grain and returns a list containing the
co-ordinates of the points in the grain.
Parameters
----------
grain_mask : np.ndarray
A 2D numpy array image of a grain. Data in the array must be boolean.
Returns
-------
points : list
A python list containing the coordinates of the pixels in the grain."""
nonzero_coordinates = grain_mask.nonzero()
points = []
for point in np.transpose(nonzero_coordinates):
points.append(list(point))
return points
[docs]
@staticmethod
def calculate_edges(grain_mask: np.ndarray, edge_detection_method: str):
"""Class method that takes a 2D boolean numpy array image of a grain and returns a python list of the
coordinates of the edges of the grain.
Parameters
----------
grain_mask : np.ndarray
A 2D numpy array image of a grain. Data in the array must be boolean.
edge_detection_method : str
Method used for detecting the edges of grain masks before calculating statistics on them.
Do not change unless you know exactly what this is doing. Options: "binary_erosion", "canny".
Returns
-------
edges : list
List containing the coordinates of the edges of the grain.
"""
# Fill any holes
filled_grain_mask = scipy.ndimage.binary_fill_holes(grain_mask)
if edge_detection_method == "binary_erosion":
# Add padding (needed for erosion)
padded = np.pad(filled_grain_mask, 1)
# Erode by 1 pixel
eroded = skimage_morphology.binary_erosion(padded)
# Remove padding
eroded = eroded[1:-1, 1:-1]
# Edges is equal to the difference between the
# original image and the eroded image.
edges = filled_grain_mask.astype(int) - eroded.astype(int)
else:
# Get outer edge using canny filtering
edges = skimage_feature.canny(filled_grain_mask, sigma=3)
nonzero_coordinates = edges.nonzero()
# Get vector representation of the points
# FIXME : Switched to list comprehension but should be unnecessary to create this as a list as we can use
# np.stack() to combine the arrays and use that...
# return np.stack(nonzero_coordinates, axis=1)
# edges = []
# for vector in np.transpose(nonzero_coordinates):
# edges.append(list(vector))
# return edges
return [list(vector) for vector in np.transpose(nonzero_coordinates)]
[docs]
def calculate_radius_stats(self, edges: list, points: list) -> Tuple:
"""Class method that calculates the statistics relating to the radius. The radius in this context
is the distance from the centroid to points on the edge of the grain.
Parameters
----------
edges: list
A 2D python list containing the coordinates of the edges of a grain.
points: list
A 2D python list containing the coordinates of the points in a grain.
Returns
-------
Tuple[float]
A tuple of the minimum, maximum, mean and median radius of the grain
"""
# Calculate the centroid of the grain
centroid = self._calculate_centroid(points)
# Calculate the displacement
displacements = self._calculate_displacement(edges, centroid)
# Calculate the radius of each point
radii = self._calculate_radius(displacements)
return {
"min": np.min(radii),
"max": np.max(radii),
"mean": np.mean(radii),
"median": np.median(radii),
}
[docs]
@staticmethod
def _calculate_centroid(points: np.array) -> tuple:
"""Calculate the centroid of a bounding box.
Parameters
----------
points: list
A 2D python list containing the co-ordinates of the points in a grain.
Returns
-------
tuple
The co-ordinates of the centroid.
"""
# FIXME : Remove once we have a numpy array returned by calculate_edges
points = np.array(points)
return (np.mean(points[:, 0]), np.mean(points[:, 1]))
[docs]
@staticmethod
def _calculate_displacement(edges: np.array, centroid: tuple) -> np.array:
"""Calculate the displacement between the centroid and edges"""
# FIXME : Remove once we have a numpy array returned by calculate_edges
return np.array(edges) - centroid
[docs]
@staticmethod
def _calculate_radius(displacements) -> np.array:
"""Calculate the radius of each point from the centroid
Parameters
----------
displacements: List[list]
Retrurns
--------
np.array
"""
return np.array([np.sqrt(radius[0] ** 2 + radius[1] ** 2) for radius in displacements])
[docs]
def convex_hull(self, edges: list, base_output_dir: Path, debug: bool = False):
"""Class method that takes a grain mask and the edges of the grain and returns the grain's convex hull. Based
off of the Graham Scan algorithm and should ideally scale in time with O(nlog(n)).
Parameters
----------
edges : list
A python list contianing the coordinates of the edges of the grain.
base_output_dir : Union[str, Path]
Directory to save output to.
debug : bool
Default false. If true, debug information will be displayed to the terminal and plots for the convex hulls and edges will be saved.
Returns
-------
hull : list
Coordinates of the points in the hull.
hull_indices : list
The hull points indices inside the edges list. In other words, this provides a way to find the points from the hull inside the edges list that was passed.
simplices : list
List of tuples, each tuple representing a simplex of the convex hull. These simplices are sorted such that they follow each other in counterclockwise order.
"""
hull, hull_indices, simplexes = self.graham_scan(edges)
# Debug information
if debug:
base_output_dir.mkdir(parents=True, exist_ok=True)
self.plot(edges, hull, base_output_dir / "_points_hull.png")
LOGGER.info(f"points: {edges}")
LOGGER.info(f"hull: {hull}")
LOGGER.info(f"hull indexes: {hull_indices}")
LOGGER.info(f"simplexes: {simplexes}")
return hull, hull_indices, simplexes
[docs]
def calculate_squared_distance(self, point_2: tuple, point_1: tuple = None) -> float:
"""Function that calculates the distance squared between two points. Used for distance sorting purposes and
therefore does not perform a square root in the interests of efficiency.
Parameters
----------
point_2 : tuple
The point to find the squared distance to.
point_1 : tuple
Optional - defaults to the starting point defined in the graham_scan() function. The point to find the
squared distance from.
Returns
-------
distance_squared : float
The squared distance between the two points.
"""
# Get the distance squared between two points. If the second point is not provided, use the starting point.
point_1 = self.start_point if point_1 is None else point_1
delta_x = point_2[0] - point_1[0]
delta_y = point_2[1] - point_1[1]
# Don't need the sqrt since just sorting for dist
return float(delta_x**2 + delta_y**2)
[docs]
def sort_points(self, points: List) -> List:
# def sort_points(self, points: np.array) -> List:
"""Function to sort points in counter-clockwise order of angle made with the starting point.
Parameters
----------
points: list
A python list of the coordinates to sort.
Returns
-------
sorted_points : list
A python list of sorted points.
"""
# Return if the list is length 1 or 0 (i.e. a single point).
if len(points) <= 1:
return points
# Lists that allow sorting of points relative to a current comparision point
smaller, equal, larger = [], [], []
# Get a random point in the array to calculate the pivot angle from. This sorts the points relative to this point.
pivot_angle = self.get_angle(points[randint(0, len(points) - 1)], self.start_point)
for point in points:
point_angle = self.get_angle(point, self.start_point)
# If the
if point_angle < pivot_angle:
smaller.append(point)
elif point_angle == pivot_angle:
equal.append(point)
else:
larger.append(point)
# Lets take a different approach and use arrays, we have a start point lets work out the angle of each point
# relative to that and _then_ sort it.
# pivot_angles = self.get_angle(points, self.start_point)
# Recursively sort the arrays until each point is sorted
sorted_points = (
self.sort_points(smaller) + sorted(equal, key=self.calculate_squared_distance) + self.sort_points(larger)
)
# Return sorted array where equal angle points are sorted by distance
return sorted_points
[docs]
def get_start_point(self, edges) -> int:
"""Determine the index of the bottom most point of the hull when sorted by x-position.
Parameters
----------
edges: np.array
Returns
-------
"""
min_y_index = np.argmin(edges[:, 1])
self.start_point = edges[min_y_index]
[docs]
def graham_scan(self, edges: list):
"""A function based on the Graham Scan algorithm that constructs a convex hull from points in 2D cartesian
space. Ideally this algorithm will take O( n * log(n) ) time.
Parameters
----------
edges : list
A python list of coordinates that make up the edges of the grain.
Returns
-------
hull : list
A list containing coordinates of the points in the hull.
hull_indices : list
A list containing the hull points indices inside the edges list. In other words, this provides a way to find
the points from the hull inside the edges list that was passed.
simplices : list
A list of tuples, each tuple representing a simplex of the convex hull. These simplices are sorted such
that they follow each other in counterclockwise order.
"""
# FIXME : Make this an isolated method
# Find a point guaranteed to be on the hull. I find the bottom most point(s) and sort by x-position.
min_y_index = None
for index, point in enumerate(edges):
if min_y_index is None or point[1] < edges[min_y_index][1]:
min_y_index = index
if point[1] == edges[min_y_index][1] and point[0] < edges[min_y_index][0]:
min_y_index = index
self.start_point = edges[min_y_index]
# This does the same thing, but as a separate method and with Numpy Array rather than a lsit
# self.get_start_point(edges)
# Sort the points
points_sorted_by_angle = self.sort_points(edges)
# Remove starting point from the list so it's not added more than once to the hull
start_point_index = points_sorted_by_angle.index(self.start_point)
del points_sorted_by_angle[start_point_index]
# Add start point and the first point sorted by angle. Both of these points will always be on the hull.
hull = [self.start_point, points_sorted_by_angle[0]]
# Iterate through each point, checking if this point would cause a clockwise rotation if added to the hull, and
# if so, backtracking.
for index, point in enumerate(points_sorted_by_angle[1:]):
# Determine if the proposed point demands a clockwise rotation
while self.is_clockwise(hull[-2], hull[-1], point) is True:
# Delete the failed point
del hull[-1]
if len(hull) < 2:
break
# The point does not immediately cause a clockwise rotation.
hull.append(point)
# Get hull indices from original points array
hull_indices = []
for point in hull:
hull_indices.append(edges.index(point))
# Create simplices from the hull points
simplices = []
for index, value in enumerate(hull_indices):
simplices.append((hull_indices[index - 1], value))
return hull, hull_indices, simplices
[docs]
@staticmethod
def plot(edges: list, convex_hull: list = None, file_path: Path = None):
"""A function that plots and saves the coordinates of the edges in the grain and optionally the hull. The
plot is saved as the file name that is provided.
Parameters
----------
coordinates : list
A list of points to be plotted.
convex_hull : list
Optional argument. A list of points that form the convex hull. Will be plotted with the coordinates if
provided.
file_path : Path
Path of the file to save the plot as.
"""
_, ax = plt.subplots(1, 1, figsize=(8, 8))
x_s, y_s = zip(*edges)
ax.scatter(x_s, y_s)
if convex_hull is not None:
for index in range(1, len(convex_hull) + 1):
# Loop on the final simplex of the hull to join the last and first points together.
if len(convex_hull) == index:
index = 0
point2 = convex_hull[index]
point1 = convex_hull[index - 1]
# Plot a line between the two points
plt.plot((point1[0], point2[0]), (point1[1], point2[1]), "#994400")
plt.savefig(file_path)
plt.close()
[docs]
def calculate_aspect_ratio(self, edges: list, hull_simplices: np.ndarray, path: Path, debug: bool = False) -> tuple:
"""Class method that takes a list of edge points for a grain, and convex hull simplices and returns the width,
length and aspect ratio of the smallest bounding rectangle for the grain.
Parameters
----------
edges : list
A python list of coordinates of the edge of the grain.
hull_simplices : np.ndarray
A 2D numpy array of simplices that the hull is comprised of.
path : Path
Path to the save folder for the grain.
debug : bool
If true, various plots will be saved for diagnostic purposes.
Returns
-------
smallest_bounding_width : float
The width in pixels (not nanometres), of the smallest bounding rectangle for the grain.
smallest_bounding_length : float
The length in pixels (not nanometres), of the smallest bounding rectangle for the grain.
aspect_ratio : float
The width divided by the length of the smallest bounding rectangle for the grain. It will always be greater
or equal to 1.
"""
# Ensure the edges are in the form of a numpy array.
edges = np.array(edges)
# Create a variable to store the smallest area in - this is to be able to compare whilst iterating
smallest_bounding_area = None
# FIXME : pylint complains that this is unused which looks like a false positive to me as it is used.
# Probably does not need initiating here though (and code runs fine when doing so)
# smallest_bounding_rectangle = None
# Iterate through the simplices
for simplex_index, simplex in enumerate(hull_simplices):
p_1 = edges[simplex[0]]
p_2 = edges[simplex[1]]
delta = p_1 - p_2
angle = np.arctan2(delta[0], delta[1])
# Find the centroid of the points
centroid = (sum(edges[:, 0]) / len(edges), sum(edges[:, 1] / len(edges)))
# Map the coordinates such that the centroid is now centered on the origin. This is needed for the
# matrix rotation step coming up.
remapped_points = edges - centroid
# Rotate the coordinates using a rotation matrix
rotated_coordinates = np.array(((np.cos(angle), -np.sin(angle)), (np.sin(angle), np.cos(angle))))
# For each point in the set, rotate it using the above rotation matrix.
rotated_points = []
for _, point in enumerate(remapped_points):
newpoint = rotated_coordinates @ point
# FIXME : Can probably use np.append() here to append arrays directly, something like
# np.append(rotated_points, newpoint, axis=0) but doing so requires other areas to be modified
rotated_points.append(newpoint)
rotated_points = np.array(rotated_points)
# Find the cartesian extremities
extremes = self.find_cartesian_extremes(rotated_points)
if debug:
# Ensure directory is there
path.mkdir(parents=True, exist_ok=True)
# Create plot
# FIXME : Make this a method
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
# Draw the points and the current simplex that is being tested
plt.scatter(x=remapped_points[:, 0], y=remapped_points[:, 1])
plt.plot(
remapped_points[simplex, 0],
remapped_points[simplex, 1],
"#444444",
linewidth=4,
)
plt.scatter(x=rotated_points[:, 0], y=rotated_points[:, 1])
plt.plot(
rotated_points[simplex, 0],
rotated_points[simplex, 1],
"k-",
linewidth=5,
)
LOGGER.info(rotated_points[simplex, 0], rotated_points[simplex, 1])
# Draw the convex hulls
for _simplex in hull_simplices:
plt.plot(
remapped_points[_simplex, 0],
remapped_points[_simplex, 1],
"#888888",
)
plt.plot(
rotated_points[_simplex, 0],
rotated_points[_simplex, 1],
"#555555",
)
# Draw bounding box
plt.plot(
[
extremes["x_min"],
extremes["x_min"],
extremes["x_max"],
extremes["x_max"],
extremes["x_min"],
],
[
extremes["y_min"],
extremes["y_max"],
extremes["y_max"],
extremes["y_min"],
extremes["y_min"],
],
"#994400",
)
plt.savefig(path / ("bounding_rectangle_construction_simplex_" + str(simplex_index) + ".png"))
# Calculate the area of the proposed bounding rectangle
bounding_area = (extremes["x_max"] - extremes["x_min"]) * (extremes["y_max"] - extremes["y_min"])
# If current bounding rectangle is the smallest so far
if smallest_bounding_area is None or bounding_area < smallest_bounding_area:
smallest_bounding_area = bounding_area
# smallest_bounding_rectangle = (
# extremes["x_min"],
# extremes["x_max"],
# extremes["y_min"],
# extremes["y_max"],
# )
aspect_ratio = (extremes["x_max"] - extremes["x_min"]) / (extremes["y_max"] - extremes["y_min"])
smallest_bounding_width = min(
(extremes["x_max"] - extremes["x_min"]),
(extremes["y_max"] - extremes["y_min"]),
)
smallest_bounding_length = max(
(extremes["x_max"] - extremes["x_min"]),
(extremes["y_max"] - extremes["y_min"]),
)
# Enforce >= 1 aspect ratio
if aspect_ratio < 1.0:
aspect_ratio = 1 / aspect_ratio
# Unrotate the bounding box vertices
r_inverse = rotated_coordinates.T
translated_rotated_bounding_rectangle_vertices = np.array(
(
[extremes["x_min"], extremes["y_min"]],
[extremes["x_max"], extremes["y_min"]],
[extremes["x_max"], extremes["y_max"]],
[extremes["x_min"], extremes["y_max"]],
)
)
translated_bounding_rectangle_vertices = []
for _, point in enumerate(translated_rotated_bounding_rectangle_vertices):
newpoint = r_inverse @ point
# FIXME : As above can likely use np.append(, axis=0) here
translated_bounding_rectangle_vertices.append(newpoint)
translated_bounding_rectangle_vertices = np.array(translated_bounding_rectangle_vertices)
if debug:
# Create plot
# FIXME : Make this a private method
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
plt.scatter(x=edges[:, 0], y=edges[:, 1])
ax.plot(
np.append(
translated_rotated_bounding_rectangle_vertices[:, 0],
translated_rotated_bounding_rectangle_vertices[0, 0],
),
np.append(
translated_rotated_bounding_rectangle_vertices[:, 1],
translated_rotated_bounding_rectangle_vertices[0, 1],
),
"#994400",
label="rotated",
)
ax.plot(
np.append(
translated_bounding_rectangle_vertices[:, 0],
translated_bounding_rectangle_vertices[0, 0],
),
np.append(
translated_bounding_rectangle_vertices[:, 1],
translated_bounding_rectangle_vertices[0, 1],
),
"#004499",
label="unrotated",
)
ax.scatter(
x=remapped_points[:, 0],
y=remapped_points[:, 1],
color="#004499",
label="translated",
)
ax.scatter(x=rotated_points[:, 0], y=rotated_points[:, 1], label="rotated")
ax.legend()
plt.savefig(path / "hull_bounding_rectangle_extra")
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
bounding_rectangle_vertices = translated_bounding_rectangle_vertices + centroid
ax.plot(
np.append(bounding_rectangle_vertices[:, 0], bounding_rectangle_vertices[0, 0]),
np.append(bounding_rectangle_vertices[:, 1], bounding_rectangle_vertices[0, 1]),
"#994400",
label="unrotated",
)
ax.scatter(x=edges[:, 0], y=edges[:, 1], label="original points")
ax.set_aspect(1)
ax.legend()
plt.xlabel("Grain Length (nm)")
plt.ylabel("Grain Width (nm)")
# plt.savefig(path / "minimum_bbox.png")
plt.close()
return smallest_bounding_width, smallest_bounding_length, aspect_ratio
[docs]
@staticmethod
def find_cartesian_extremes(rotated_points: np.ndarray) -> Dict:
"""Find the limits of x and y of rotated points.
Parameters
----------
rotated_points: np.ndarray
2-D array of rotated points.
Returns
-------
Dict
Dictionary of the x and y min and max.__annotations__
"""
extremes = {}
extremes["x_min"] = np.min(rotated_points[:, 0])
extremes["x_max"] = np.max(rotated_points[:, 0])
extremes["y_min"] = np.min(rotated_points[:, 1])
extremes["y_max"] = np.max(rotated_points[:, 1])
return extremes
[docs]
@staticmethod
def get_shift(coords: np.ndarray, shape: np.ndarray) -> int:
"""Obtains the coordinate shift to reflect the cropped image box for molecules near the edges of the image.
Parameters
----------
coords: np.ndarray
Value representing integer coordinates which may be outside of the image.
shape: np.ndarray
Array of the shape of an image.
Returns
-------
np.int64
Max value of the shift to reflect the croped region so it stays within the image.
"""
shift = shape - coords[np.where(coords > shape)]
shift = np.hstack((shift, -coords[np.where(coords < 0)]))
if len(shift) == 0:
return 0
max_index = np.argmax(abs(shift))
return shift[max_index]
[docs]
def get_cropped_region(self, image: np.ndarray, length: int, centre: np.ndarray) -> np.ndarray:
"""Crops the image with respect to a given pixel length around the centre coordinates.
Parameters
----------
image: np.ndarray
The image array.
length: int
The length (in pixels) of the resultant cropped image.
centre: np.ndarray
The centre of the object to crop.
Returns
-------
np.ndarray
Cropped array of the image.
"""
shape = image.shape
xy1 = shape - (centre + length + 1)
xy2 = shape - (centre - length)
xy = np.stack((xy1, xy2))
shiftx = self.get_shift(xy[:, 0], shape[0])
shifty = self.get_shift(xy[:, 1], shape[1])
return image.copy()[
centre[0] - length - shiftx : centre[0] + length + 1 - shiftx, # noqa: E203
centre[1] - length - shifty : centre[1] + length + 1 - shifty, # noqa: E203
]
[docs]
@staticmethod
def get_triangle_height(base_point_1: np.array, base_point_2: np.array, top_point: np.array) -> float:
"""Returns the height of a triangle defined by the input point vectors.
Parameters
----------
base_point_1: np.ndarray
a base point of the triangle, eg: [5, 3].
base_point_2: np.ndarray
a base point of the triangle, eg: [8, 3].
top_point: np.ndarray
the top point of the triangle, defining the height from the line between the two base points, eg: [6,10].
Returns
-------
Float
The height of the triangle - ie the shortest distance between the top point and the line between the two
base points.
"""
# Height of triangle = A/b = ||AB X AC|| / ||AB||
a_b = base_point_1 - base_point_2
a_c = base_point_1 - top_point
return np.linalg.norm(np.cross(a_b, a_c)) / np.linalg.norm(a_b)
[docs]
@staticmethod
def get_max_min_ferets(edge_points: list):
"""Returns the minimum and maximum feret diameters for a grain.
These are defined as the smallest and greatest distances between
a pair of callipers that are rotating around a 2d object, maintaining
contact at all times.
Parameters
----------
edge_points: list
a list of the vector positions of the pixels comprising the edge of the
grain. Eg: [[0, 0], [1, 0], [2, 1]]
Returns
-------
min_feret: float
the minimum feret diameter of the grain
max_feret: float
the maximum feret diameter of the grain
Notes
-----
The method starts out by calculating the upper and lower convex hulls using
an algorithm based on the Graham Scan Algorithm [1]. Using these upper and
lower hulls, the callipers are simulated as rotating clockwise around the grain.
We determine the order in which vertices are encountered by comparing the
gradients of the slopes between vertices. An array of pairs of points that
are in contact with either calliper at a given time is created in order to
be able to calculate the maximum feret diameter. The minimum diameter is a
little tricky, since it won't simply be the shortest distance between two
contact points, but it will occur somewhere during the rotation around a
pair of contact points. It turns out that the point will always be such
that two points are in contact with one calliper while the other calliper
is in contact with another point. We can use this fact to be sure of finding
the smallest feret diameter, simply by testing each triangle of 3 contact points
as we iterate, finding the height of the triangle that is formed between the
three aforementioned points, as this will be the perpendicular distance between
the callipers.
References
----------
[1] Graham, R.L. (1972).
"An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set".
Information Processing Letters. 1 (4): 132-133.
doi:10.1016/0020-0190(72)90045-2.
"""
# Sort the vectors by their x coordinate and then by their y coordinate.
# The conversion between list and numpy array can be removed, though it would be harder
# to read.
edge_points.sort()
edge_points = np.array(edge_points)
# Construct upper and lower hulls for the edge points. Sadly we can't just use the standard hull
# that graham_scan() returns, since we need to separate the upper and lower hulls. I might streamline
# these two into one method later.
upper_hull = []
lower_hull = []
for point in edge_points:
while len(lower_hull) > 1 and GrainStats.is_clockwise(lower_hull[-2], lower_hull[-1], point):
lower_hull.pop()
lower_hull.append(point)
while len(upper_hull) > 1 and not GrainStats.is_clockwise(upper_hull[-2], upper_hull[-1], point):
upper_hull.pop()
upper_hull.append(point)
upper_hull = np.array(upper_hull)
lower_hull = np.array(lower_hull)
# Create list of contact vertices for calipers on the antipodal hulls
contact_points = []
upper_index = 0
lower_index = len(lower_hull) - 1
min_feret = None
while upper_index < len(upper_hull) - 1 or lower_index > 0:
contact_points.append([lower_hull[lower_index, :], upper_hull[upper_index, :]])
# If we have reached the end of the upper hull, continute iterating over the lower hull
if upper_index == len(upper_hull) - 1:
lower_index -= 1
small_feret = GrainStats.get_triangle_height(
np.array(lower_hull[lower_index + 1, :]),
np.array(lower_hull[lower_index, :]),
np.array(upper_hull[upper_index, :]),
)
if min_feret is None or small_feret < min_feret:
min_feret = small_feret
# If we have reached the end of the lower hull, continue iterating over the upper hull
elif lower_index == 0:
upper_index += 1
small_feret = GrainStats.get_triangle_height(
np.array(upper_hull[upper_index - 1, :]),
np.array(upper_hull[upper_index, :]),
np.array(lower_hull[lower_index, :]),
)
if min_feret is None or small_feret < min_feret:
min_feret = small_feret
# Check if the gradient of the last point and the proposed next point in the upper hull is greater than the gradient
# of the two corresponding points in the lower hull, if so, this means that the next point in the upper hull
# will be encountered before the next point in the lower hull and vice versa.
# Note that the calculation here for gradients is the simple delta upper_y / delta upper_x > delta lower_y / delta lower_x
# however I have multiplied through the denominators such that there are no instances of division by zero. The
# inequality still holds and provides what is needed.
elif (upper_hull[upper_index + 1, 1] - upper_hull[upper_index, 1]) * (
lower_hull[lower_index, 0] - lower_hull[lower_index - 1, 0]
) > (lower_hull[lower_index, 1] - lower_hull[lower_index - 1, 1]) * (
upper_hull[upper_index + 1, 0] - upper_hull[upper_index, 0]
):
# If the upper hull is encoutnered first, increment the iteration index for the upper hull
# Also consider the triangle that is made as the two upper hull vertices are colinear with the caliper
upper_index += 1
small_feret = GrainStats.get_triangle_height(
np.array(upper_hull[upper_index - 1, :]),
np.array(upper_hull[upper_index, :]),
np.array(lower_hull[lower_index, :]),
)
if min_feret is None or small_feret < min_feret:
min_feret = small_feret
else:
# The next point in the lower hull will be encountered first, so increment the lower hull iteration index.
lower_index -= 1
small_feret = GrainStats.get_triangle_height(
np.array(lower_hull[lower_index + 1, :]),
np.array(lower_hull[lower_index, :]),
np.array(upper_hull[upper_index, :]),
)
if min_feret is None or small_feret < min_feret:
min_feret = small_feret
contact_points = np.array(contact_points)
# Find the minimum and maximum distance in the contact points
max_feret = None
for point_pair in contact_points:
dist = np.sqrt((point_pair[0, 0] - point_pair[1, 0]) ** 2 + (point_pair[0, 1] - point_pair[1, 1]) ** 2)
if max_feret is None or max_feret < dist:
max_feret = dist
return min_feret, max_feret