I'm using image-segmentation on some images, and sometimes it would be nice to be able to plot the borders of the segments.
I have a 2D NumPy array that I plot with Matplotlib, and the closest I've gotten, is using contour-plotting.
This makes corners in the array, but is otherwise perfect.
Can Matplotlib's contour-function be made to only plot vertical/horizontal lines, or is there some other way to do this?
An example can be seen here:
import matplotlib.pyplot as plt
import numpy as np
array = np.zeros((20, 20))
array[4:7, 3:8] = 1
array[4:7, 12:15] = 1
array[7:15, 7:15] = 1
array[12:14, 13:14] = 0
plt.imshow(array, cmap='binary')
plt.contour(array, levels=[0.5], colors='g')
plt.show()
I wrote some functions to achieve this some time ago, but I would be glad to figure out how it can be done quicker.
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
def get_all_edges(bool_img):
"""
Get a list of all edges (where the value changes from True to False) in the 2D boolean image.
The returned array edges has he dimension (n, 2, 2).
Edge i connects the pixels edges[i, 0, :] and edges[i, 1, :].
Note that the indices of a pixel also denote the coordinates of its lower left corner.
"""
edges = []
ii, jj = np.nonzero(bool_img)
for i, j in zip(ii, jj):
# North
if j == bool_img.shape[1]-1 or not bool_img[i, j+1]:
edges.append(np.array([[i, j+1],
[i+1, j+1]]))
# East
if i == bool_img.shape[0]-1 or not bool_img[i+1, j]:
edges.append(np.array([[i+1, j],
[i+1, j+1]]))
# South
if j == 0 or not bool_img[i, j-1]:
edges.append(np.array([[i, j],
[i+1, j]]))
# West
if i == 0 or not bool_img[i-1, j]:
edges.append(np.array([[i, j],
[i, j+1]]))
if not edges:
return np.zeros((0, 2, 2))
else:
return np.array(edges)
def close_loop_edges(edges):
"""
Combine thee edges defined by 'get_all_edges' to closed loops around objects.
If there are multiple disconnected objects a list of closed loops is returned.
Note that it's expected that all the edges are part of exactly one loop (but not necessarily the same one).
"""
loop_list = []
while edges.size != 0:
loop = [edges[0, 0], edges[0, 1]] # Start with first edge
edges = np.delete(edges, 0, axis=0)
while edges.size != 0:
# Get next edge (=edge with common node)
ij = np.nonzero((edges == loop[-1]).all(axis=2))
if ij[0].size > 0:
i = ij[0][0]
j = ij[1][0]
else:
loop.append(loop[0])
# Uncomment to to make the start of the loop invisible when plotting
# loop.append(loop[1])
break
loop.append(edges[i, (j + 1) % 2, :])
edges = np.delete(edges, i, axis=0)
loop_list.append(np.array(loop))
return loop_list
def plot_outlines(bool_img, ax=None, **kwargs):
if ax is None:
ax = plt.gca()
edges = get_all_edges(bool_img=bool_img)
edges = edges - 0.5 # convert indices to coordinates; TODO adjust according to image extent
outlines = close_loop_edges(edges=edges)
cl = LineCollection(outlines, **kwargs)
ax.add_collection(cl)
array = np.zeros((20, 20))
array[4:7, 3:8] = 1
array[4:7, 12:15] = 1
array[7:15, 7:15] = 1
array[12:14, 13:14] = 0
plt.figure()
plt.imshow(array, cmap='binary')
plot_outlines(array.T, lw=5, color='r')
Related
I have code that shows the label for each point in a matplotlib scatterplot using mplcursors, similar to this example. I want to know how to, form a list of values, make a certain point stand out, as in if I have a graph of points y=-x^2. When I go near the peak, it shouldn't show 0.001, but 0 instead, without the trouble needing to find the exact mouse placement of the top. I can't solve for each point in the graph, as I don't have a specific function.
Supposing the points in the scatter plot are ordered, we can investigate whether an extreme in a nearby window is also an extreme in a somewhat larger window. If, so we can report that extreme with its x and y coordinates.
The code below only shows the annotation when we're close to a local maximum or minimum. It also temporarily shows a horizontal and vertical line to indicate the exact spot. The code can be a starting point for many variations.
import matplotlib.pyplot as plt
import mplcursors
import numpy as np
near_window = 10 # the width of the nearby window
far_window = 20 # the width of the far window
def show_annotation(sel):
ind = sel.target.index
near_start_index = max(0, ind - near_window)
y_near = y[near_start_index: min(N, ind + near_window)]
y_far = y[max(0, ind - far_window): min(N, ind + far_window)]
near_max = y_near.max()
far_max = y_far.max()
annotation_str = ''
if near_max == far_max:
near_argmax = y_near.argmax()
annotation_str = f'local max:\nx:{x[near_start_index + near_argmax]:.3f}\ny:{near_max:.3f}'
maxline = plt.axhline(near_max, color='crimson', ls=':')
maxline_x = plt.axvline(x[near_start_index+near_argmax], color='grey', ls=':')
sel.extras.append(maxline)
sel.extras.append(maxline_x)
else:
near_min = y_near.min()
far_min = y_far.min()
if near_min == far_min:
near_argmin = y_near.argmin()
annotation_str = f'local min:\nx:{x[near_start_index+near_argmin]:.3f}\ny:{near_min:.3f}'
minline = plt.axhline(near_min, color='limegreen', ls=':')
minline_x = plt.axvline(x[near_start_index + near_argmin], color='grey', ls=':')
sel.extras.append(minline)
sel.extras.append(minline_x)
if len(annotation_str) > 0:
sel.annotation.set_text(annotation_str)
else:
sel.annotation.set_visible(False) # hide the annotation
# sel.annotation.set_text(f'x:{sel.target[0]:.3f}\n y:{sel.target[1]:.3f}')
N = 500
x = np.linspace(0, 100, 500)
y = np.cumsum(np.random.normal(0, 0.1, N))
box = np.ones(20) / 20
y = np.convolve(y, box, mode='same')
scat = plt.scatter(x, y, s=1)
cursor = mplcursors.cursor(scat, hover=True)
cursor.connect('add', show_annotation)
plt.show()
I looked at this code:
import numpy as np
from matplotlib import pyplot as plt
def dipole(m, r, r0):
"""
Calculation of field B in point r. B is created by a dipole moment m located in r0.
"""
# R = r - r0 - subtraction of elements of vectors r and r0, transposition of array
R = np.subtract(np.transpose(r), r0).T
# Spatial components of r are the outermost axis
norm_R = np.sqrt(np.einsum("i...,i...", R, R)) # einsum - Einsteinova sumace
# Dot product of R and m
m_dot_R = np.tensordot(m, R, axes=1)
# Computation of B
B = 3 * m_dot_R * R / norm_R**5 - np.tensordot(m, 1 / norm_R**3, axes=0)
B *= 1e-7 # abbreviation for B = B * 1e-7, multiplication B of 1e-7, permeability of vacuum: 4\pi * 10^(-7)
# The result is the magnetic field B
return B
X = np.linspace(-1, 1)
Y = np.linspace(-1, 1)
Bx, By = dipole(m=[0, 1], r=np.meshgrid(X, Y), r0=[-0.2,0.8])
plt.figure(figsize=(8, 8))
plt.streamplot(X, Y, Bx, By)
plt.margins(0, 0)
plt.show()
It shows the following figure:
Is it possible to get coordinates of one line of force? I don't understand how it is plotted.
The streamplot returns a container object 'StreamplotSet' with two parts:
lines: a LineCollection of the streamlines
arrows: a PatchCollection containing FancyArrowPatch objects (these are the triangular arrows)
c.lines.get_paths() gives all the segments. Iterating through these segments, their vertices can be examined. When a segment starts where the previous ended, both belong to the same curve. Note that each segment is a short straight line; many segments are used together to form a streamline curve.
The code below demonstrates iterating through the segments. To show what's happening, each segment is converted to an array of 2D points suitable for plt.plot. Default, plt.plot colors each curve with a new color (repeating every 10). The dots show where each of the short straight segments are located.
To find one particular curve, you could hover with the mouse over the starting point, and note the x coordinate of that point. And then test for that coordinate in the code. As an example, the curve that starts near x=0.48 is drawn in a special way.
import numpy as np
from matplotlib import pyplot as plt
from matplotlib import patches
def dipole(m, r, r0):
R = np.subtract(np.transpose(r), r0).T
norm_R = np.sqrt(np.einsum("i...,i...", R, R))
m_dot_R = np.tensordot(m, R, axes=1)
B = 3 * m_dot_R * R / norm_R**5 - np.tensordot(m, 1 / norm_R**3, axes=0)
B *= 1e-7
return B
X = np.linspace(-1, 1)
Y = np.linspace(-1, 1)
Bx, By = dipole(m=[0, 1], r=np.meshgrid(X, Y), r0=[-0.2,0.8])
plt.figure(figsize=(8, 8))
c = plt.streamplot(X, Y, Bx, By)
c.lines.set_visible(False)
paths = c.lines.get_paths()
prev_end = None
start_indices = []
for index, segment in enumerate(paths):
if not np.array_equal(prev_end, segment.vertices[0]): # new segment
start_indices.append(index)
prev_end = segment.vertices[-1]
for i0, i1 in zip(start_indices, start_indices[1:] + [len(paths)]):
# get all the points of the curve that starts at index i0
curve = np.array([paths[i].vertices[0] for i in range(i0, i1)] + [paths[i1 - 1].vertices[-1]])
special_x_coord = 0.48
for i0, i1 in zip(start_indices, start_indices[1:] + [len(paths)]):
# get all the points of the curve that starts at index i0
curve = np.array([paths[i].vertices[0] for i in range(i0, i1)] + [paths[i1 - 1].vertices[-1]])
if abs(curve[0,0] - special_x_coord) < 0.01: # draw one curve in a special way
plt.plot(curve[:, 0], curve[:, 1], '-', lw=10, alpha=0.3)
else:
plt.plot(curve[:, 0], curve[:, 1], '.', ls='-')
plt.margins(0, 0)
plt.show()
I've got the problem with repeating the animation. I want to use matplotlib in order to visualise each simulation on the matrix. Here is the code for simulation:
import numpy as np
from matplotlib import pyplot as plt
s = np.array([[1,1,1], [1,10,1], [1,1,1]], dtype=np.int8) #Matrix of wages
e = np.zeros((19,), dtype=np.int8) # Vector of rules
e[3]=1
e[12]=1
e[13]=1
mama = np.array([[1, 0, 1], [0, 1, 0], [0, 0, 1]], dtype=np.int8) #The matrix to be tested
def simulation(ma): #Simulation on a given matrix
n, m = ma.shape
p = np.zeros((n+2, m+2), dtype=np.int8) #Creates an extended matrix, avoiding conflicts at the edges of the initial matrix. Here I construct a torus
p[1:-1, 1:-1] = ma #middle
p[0, 1:-1] = ma[n-1] #the first row of p, the last of ma
p[-1, 1:-1] = ma[0] #the last row of p, the first of ma
p[1:-1, 0] = ma[0:, -1] #left col p, right of ma
p[1:-1, -1] = ma[0:, 0] #right col of p, left of ma
p[-1, 0] = ma[0, -1] #left bottom corner
p[-1, -1] = ma[0, 0] #right bottom corner
p[0, 0] = ma[-1, -1] #left upper corner
p[0, -1] = ma[-1, 0] #right upper corner
new = np.zeros(ma.shape, dtype=np.int8)
v, c = p.shape #verses and columns
for i in range(1, v):
for j in range(1, c):
if p[i-1:i+2, j-1:j+2].shape == (3, 3):
new[i-1, j-1] = e[np.sum(p[i-1:i+2,j-1:j+2]*s)]
return new
However, I want to run simulation over the specified number of repetitions and visualise each step of the simulation, so I have tried the code:
def rep(fun, mac, ti): #function, matrix, repetitions (time)
if ti == 1:
plt.imshow(fun(mac))
plt.title("Celllar automaton")
plt.show()
else:
f = fun(rep(fun, mac, ti-1))
plt.imshow(f)
plt.title("Cellular automaton")
plt.show()
I get an error:
n, m = ma.shape
AttributeError: 'NoneType' object has no attribute 'shape'
Please, could you help me? I got really tired of my unability to visualise my work.
ADDITIONALLY:
I have substituted with rep with:
def shoow(fig):
plt.imshow(fig)
plt.title("Cellular automaton")
plt.show()
def repet(fun, mac, ti):
c1 = mac
for i in range(ti):
f = fun(c1)
shoow(f)
c1 = f
However, it creates each time a new figure. How can I get a continuous simulation?
This is for a class and I would really appreciate your help! I made some changes based on a comment I received, but now I get another error..
I need to modify an existing function that implements the mean-shift algorithm, but instead of initializing all the points as the first set of centroids, the function creates a grid of centroids with the grid based on the radius. I also need to delete the centroids that don't contain any data points. My issue is that I don't understand how to fix the error I get!
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
<ipython-input-7-de18ffed728f> in <module>()
49 centroids = initialize_centroids(x)
50
---> 51 new_centroids = update_centroids(x, centroids, r = 1)
52
53 print(len(centroids))
<ipython-input-7-de18ffed728f> in update_centroids(data, centroids, r)
26 #print(len(centroids))
27 #print(range(len(centroids)))
---> 28 centroid = centroids[i]
29 for data_point in data:
30 if np.linalg.norm(data_point - centroid) < r:
IndexError: index 2 is out of bounds for axis 0 with size 2
I tried using the range of the input dataset as boundaries for a grid, with the points separated by the radius.
from sklearn import datasets
import numpy as np
import matplotlib.pyplot as plt
def initialize_centroids(data, r = 1):
'''Creates a grid of centroids with grid based on radius'''
data = np.array(data)
xi,yi = min(range(len(data))), max(range(len(data)))
mx = np.arange(xi,yi,r)
x,y = np.meshgrid(mx,mx)
centroids=np.vstack([x.ravel(), y.ravel()])
return centroids
#update centroids based on mean of points that fall within a specified radius of each centroid
def update_centroids(data, centroids, r = 1):
new_centroids = []
for i in centroids:
in_radius = []
centroid = centroids[i] #this is where the error occurs
for data_point in data:
if np.linalg.norm(data_point - centroid) < radius:
in_radius.append(data_point) #this list is appended by adding the new centroid to it if the above conition is satisfied.
new_centroid = np.mean(in_radius, axis=0)
#maybe another way to do the next part
new_centroids.append(tuple(new_centroid))
unique_centroids = sorted(list(set(new_centroids))) #for element in in_radius, if element in set skip else set.append(element(in_rad)). append does not work with set.
new_centroids = {i:np.array(unique_centroids[i]) for i in range(len(unique_centroids))}
return new_centroids
#test function on:
x, y = datasets.make_blobs(n_samples=300, n_features = 2, centers=[[0, 7], [0, -7], [5,7], [5, 0]])
centroids = initialize_centroids(x)
new_centroids = update_centroids(x, centroids, radius = 2)
print(len(centroids))
print()
print(len(new_centroids))
#code for plotting initially:
plt.scatter(x[:,0], x[:,1], color = 'k')
for i in range(len(new_centroids)):
plt.scatter(new_centroids[i][0], new_centroids[i][1], s=200, color = 'r', marker = "*")
#code for plotting updated centroids:
new_centroids = update_centroids(x, new_centroids, radius = 2)
plt.scatter(x[:,0], x[:,1], color = 'k')
for i in range(len(new_centroids)):
plt.scatter(new_centroids[i][0], new_centroids[i][1], s=200, color = 'r', marker = "*")
#code for iterations:
def iterate_to_conv(data, max_iter=100):
centroids = initialize_centroids(data)
iter_count = 0
while iter_count <= max_iter:
new_centroids = update_centroids(data, centroids, radius = 2)
centroids = new_centroids
iter_count += 1
return centroids
centroids = iterate_to_conv(x)
plt.scatter(x[:,0], x[:,1], color = 'k')
for i in range(len(centroids)):
plt.scatter(centroids[i][0], centroids[i][1], s=200, color = 'r', marker = "*")
The function needs to return the number of final centroids. I haven't gotten ahead far enough to know how the entire implementation of mean-shift would work with this function..
When you are running that loop: for i in centroids the i that is iterated through centroids isn't a number, it is a vector which is why an error is pops up. For example, the first i value might be equal to [0 1 2 0 1 2 0 1 2]. So to take an index of that doesn't make sense. What your code is saying to do is to take centroid = centroid[n1 n2 nk]. To fix it, you really need to change how your initialize centroid function works. Meshgrid also won't create an N dimensional grid, so your meshgrid might work for 2 dimensions but not N. I hope that helps.
I have been trying to get less boxes with MSER since I have too many boxes created on the same element repeatedly with very little pixel differences. My code is as below:
## Get mser, and set parameters
_delta = 10
_min_area = 250
_max_area = 800
_max_variation = 10.0
_min_diversity = 30.0
_max_evolution = 10
_area_threshold = 12.0
_min_margin = 2.9
_edge_blur_size = 3
mser = cv2.MSER_create(_delta,_min_area, _max_area, _max_variation,
_min_diversity,_max_evolution, _area_threshold, _min_margin, _edge_blur_size)
and then
## Do mser detection, get the coodinates and bboxes on the original image
gray = cv2.cvtColor(final, cv2.COLOR_BGR2GRAY)
coordinates, bboxes = mser.detectRegions(gray)
After this , I see there are 26K boxes created. Which amongst the parameters can be tuned for lesser number of regions(since they are overlapping a lot). Kindly help?
_delta is the most important parameter for reducing the number of boxes. Try raising it to 25. The higher the _delta the less blobs you will get.
_min_area - The smallest blob
_max_area - The largest blob
_min_diversity - Raise to reduce the number of overlapping blobs
_max_variation - Raise to reduce areas with high variance
For more information
After that I would checking the bboxes to filter out over lapping blobs
Code Example
import cv2
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
img = cv.imread('input_img.png')
iou_th = 0.95
mser = cv2.MSER_create(_delta=10, _min_area=1000, _max_area=int(0.1 * np.pi * (img.shape[0] /2)**2), _max_variation=0.1)
regions, bboxes = mser.detectRegions(img)
hulls = [cv2.convexHull(p.reshape(-1, 1, 2)) for p in regions]
# Debug plot
img_ = img.copy()
cv2.polylines(img_, hulls, 1, (255, 0, 0), thickness=1)
fig, ax = plt.subplots(figsize=(10, 6))
ax.imshow(img_)
ax.set_title('MSER with overlapping regions')
size_dict = {k: len(region) for k, region in enumerate(regions)}
# Cull overlapping blobs
graph = nx.Graph()
graph.add_nodes_from(range(len(hulls)))
for i, cnt in enumerate(hulls):
for j, cnt in enumerate(hulls):
if i >= j:
continue
box_i = bboxes[i]
box_j = bboxes[j]
tl_i = box_i[:2]
tl_j = box_j[:2]
br_i = tl_i + box_i[2:]
br_j = tl_j + box_j[2:]
tl = np.maximum(tl_i, tl_j)
br = np.minimum(br_i, br_j)
intersected_rect = br - tl
intersection = np.prod(intersected_rect) if intersected_rect[0] > 0 and intersected_rect[1] > 0 else 0
union = np.prod(box_i[2:]) + np.prod(box_j[2:]) - intersection
iou = intersection / union
if iou > iou_th:
graph.add_edge(i, j, iou=iou)
# make list of unique regions - pick the smallest region
trees = list(nx.connected_component_subgraphs(graph))
unique_blobs = []
for tree in trees:
# Choose the smallest region
smallest_idx = None
smallest_blob = np.inf
for node in tree.nodes():
if size_dict[node] < smallest_blob:
smallest_blob = size_dict[node]
smallest_idx = node
unique_blobs.append(smallest_idx)
unique_blobs = unique_blobs
hulls = [hulls[k] for k in unique_blobs]
regions = [regions[k] for k in unique_blobs]
bboxes = [bboxes[k] for k in unique_blobs]
size_dict = {k: len(region) for k, region in enumerate(regions)}
# debug plot
img_ = img.copy()
cv2.polylines(img_, hulls, 1, (255, 0, 0), thickness=1)
fig, ax = plt.subplots(figsize=(10, 6))
ax.imshow(img_)
ax.set_title('MSER with unique regions')