NV12 to YUV444 speed up - numpy

I have a code that converts image from nv12 to yuv444
for h in range(self.img_shape[0]):
# centralize yuv 444 data for inference framework
for w in range(self.img_shape[1]):
yuv444_res[h][w][0] = (nv12_y_data[h * self.img_shape[1] +w]).astype(np.int8)
yuv444_res[h][w][1] = (nv12_u_data[int(h / 2) * int(self.img_shape[1] / 2) +int(w / 2)]).astype(np.int8)
yuv444_res[h][w][2] = (nv12_v_data[int(h / 2) * int(self.img_shape[1] / 2) +int(w / 2)]).astype(np.int8)
Since for loop is very slow in python, much slower than numpy. I was wondering if this conversion can be done in NumPy calculation.
Update on 06/15/2021:
I was able to get this piece of code with fancy indexing from this page External Link:
yuv444 = np.empty([self.height, self.width, 3], dtype=np.uint8)
yuv444[:, :, 0] = nv12_data[:self.width * self.height].reshape(
self.height, self.width)
u = nv12_data[self.width * self.height::2].reshape(
self.height // 2, self.width // 2)
yuv444[:, :, 1] = Image.fromarray(u).resize((self.width, self.height))
v = nv12_data[self.width * self.height + 1::2].reshape(
self.height // 2, self.width // 2)
yuv444[:, :, 2] = Image.fromarray(v).resize((self.width, self.height))
data[0] = yuv444.astype(np.int8)
If the PIL is used to replace the deprecated imresize, then the code match the old code 100%
Update on 06/19/2021:
After a closer look at the answer Rotem given, I realize that his way is quicker.
#nv12_data is reshaped to one dimension
y = nv12_data[:self.width * self.height].reshape(
self.height, self.width)
shrunk_u = nv12_data[self.width * self.height::2].reshape(
self.height // 2, self.width // 2)
shrunk_v = nv12_data[self.width * self.height + 1::2].reshape(
self.height // 2, self.width // 2)
u = cv2.resize(shrunk_u, (self.width, self.height),
interpolation=cv2.INTER_NEAREST)
v = cv2.resize(shrunk_v, (self.width, self.height),
interpolation=cv2.INTER_NEAREST)
yuv444 = np.dstack((y, u, v))
Also, I did a time comparison for processing 1000 pics. Turns out the cv reshape is quicker and guarantees the same result.
cv time: 4.417593002319336, pil time: 5.395732164382935
Update on 06/25/2021:
Pillow resize has different default resample param values in different versions.
5.1.0:
def resize(self, size, resample=NEAREST, box=None):
8.1.0:
def resize(self, size, resample=BICUBIC, box=None, reducing_gap=None):
It would be a good idea to specify the resample strategy used.

You may use the process described in my following post, in reverse order (without the RGB part).
Illustration:
Start by creating a synthetic sample image in NV12 format, using FFmpeg (command line tool).
The sample image is used for testing.
Executing from Python using subprocess module:
import subprocess as sp
import shlex
sp.run(shlex.split('ffmpeg -y -f lavfi -i testsrc=size=192x108:rate=1:duration=1 -vcodec rawvideo -pix_fmt nv12 nv12.yuv'))
sp.run(shlex.split('ffmpeg -y -f rawvideo -video_size 192x162 -pixel_format gray -i nv12.yuv -pix_fmt gray nv12_gray.png'))
Read the sample image, and executing the code from your post (used as reference):
import numpy as np
import cv2
nv12 = cv2.imread('nv12_gray.png', cv2.IMREAD_GRAYSCALE)
cols, rows = nv12.shape[1], nv12.shape[0]*2//3
# Reference implementation - using for-loops (the solution is in the part below):
################################################################################
nv12_y_data = nv12[0:rows, :].flatten()
nv12_u_data = nv12[rows:, 0::2].flatten()
nv12_v_data = nv12[rows:, 1::2].flatten()
yuv444_res = np.zeros((rows, cols, 3), np.uint8)
for h in range(rows):
# centralize yuv 444 data for inference framework
for w in range(cols):
yuv444_res[h][w][0] = (nv12_y_data[h * cols + w]).astype(np.int8)
yuv444_res[h][w][1] = (nv12_u_data[int(h / 2) * int(cols / 2) + int(w / 2)]).astype(np.int8)
yuv444_res[h][w][2] = (nv12_v_data[int(h / 2) * int(cols / 2) + int(w / 2)]).astype(np.int8)
################################################################################
My suggested solution applies the following stages:
Separate U and V into two "half size" matrices shrunk_u and shrunk_v.
Resize shrunk_u and shrunk_v to full image size matrices using cv2.resize.
In my code sample I used nearest neighbor interpolation for getting the same result as your result.
It is recommended to replace it with linear interpolation for better quality.
Use np.dstack for merging Y, U and V into YUV (3 color channels) image.
Here is the complete code sample:
import numpy as np
import subprocess as sp
import shlex
import cv2
sp.run(shlex.split('ffmpeg -y -f lavfi -i testsrc=size=192x108:rate=1:duration=1 -vcodec rawvideo -pix_fmt nv12 nv12.yuv'))
sp.run(shlex.split('ffmpeg -y -f rawvideo -video_size 192x162 -pixel_format gray -i nv12.yuv -pix_fmt gray nv12_gray.png'))
#sp.run(shlex.split('ffmpeg -y -f rawvideo -video_size 192x108 -pixel_format nv12 -i nv12.yuv -vcodec rawvideo -pix_fmt yuv444p yuv444.yuv'))
#sp.run(shlex.split('ffmpeg -y -f rawvideo -video_size 192x324 -pixel_format gray -i yuv444.yuv -pix_fmt gray yuv444_gray.png'))
#sp.run(shlex.split('ffmpeg -y -f rawvideo -video_size 192x108 -pixel_format yuv444p -i yuv444.yuv -pix_fmt rgb24 rgb.png'))
#sp.run(shlex.split('ffmpeg -y -f rawvideo -video_size 192x108 -pixel_format gbrp -i yuv444.yuv -filter_complex "extractplanes=g+b+r[g][b][r],[r][g][b]mergeplanes=0x001020:gbrp[v]" -map "[v]" -vcodec rawvideo -pix_fmt rgb24 yuvyuv.yuv'))
#sp.run(shlex.split('ffmpeg -y -f rawvideo -video#_size 576x108 -pixel_format gray -i yuvyuv.yuv -pix_fmt gray yuvyuv_gray.png'))
nv12 = cv2.imread('nv12_gray.png', cv2.IMREAD_GRAYSCALE)
cols, rows = nv12.shape[1], nv12.shape[0]*2//3
nv12_y_data = nv12[0:rows, :].flatten()
nv12_u_data = nv12[rows:, 0::2].flatten()
nv12_v_data = nv12[rows:, 1::2].flatten()
yuv444_res = np.zeros((rows, cols, 3), np.uint8)
for h in range(rows):
# centralize yuv 444 data for inference framework
for w in range(cols):
yuv444_res[h][w][0] = (nv12_y_data[h * cols + w]).astype(np.int8)
yuv444_res[h][w][1] = (nv12_u_data[int(h / 2) * int(cols / 2) + int(w / 2)]).astype(np.int8)
yuv444_res[h][w][2] = (nv12_v_data[int(h / 2) * int(cols / 2) + int(w / 2)]).astype(np.int8)
y = nv12[0:rows, :]
shrunk_u = nv12[rows:, 0::2].copy()
shrunk_v = nv12[rows:, 1::2].copy()
u = cv2.resize(shrunk_u, (cols, rows), interpolation=cv2.INTER_NEAREST) # Resize U channel (use NEAREST interpolation - fastest, but lowest quality).
v = cv2.resize(shrunk_v, (cols, rows), interpolation=cv2.INTER_NEAREST) # Resize V channel
yuv444 = np.dstack((y, u, v))
is_eqaul = np.all(yuv444 == yuv444_res)
print('is_eqaul = ' + str(is_eqaul)) # is_eqaul = True
# Convert to RGB for display
yvu = np.dstack((y, v, u)) # Use COLOR_YCrCb2BGR, because it's uses the corrected conversion coefficients.
rgb = cv2.cvtColor(yvu, cv2.COLOR_YCrCb2BGR)
# Show results:
cv2.imshow('nv12', nv12)
cv2.imshow('yuv444_res', yuv444_res)
cv2.imshow('yuv444', yuv444)
cv2.imshow('rgb', rgb)
cv2.waitKey()
cv2.destroyAllWindows()
Input (NV12 displayed as Grayscale):
Output (after converting to RGB):

Seems to be a prime case for fancy indexing (advanced indexing).
Something like this should do the trick, though I didn't verify it on an actual image. I've added a section to reconstruct the image in the beginning, because it is easier to work with the array as a whole than broken into parts. Likely, you can refactor this and avoid splitting it to begin with.
# reconstruct image array
y = nv12_y_data.reshape(self.image_shape[0], self.image_shape[1])
u = nv12_u_data.reshape(self.image_shape[0], self.image_shape[1])
v = nv12_v_data.reshape(self.image_shape[0], self.image_shape[1])
img = np.stack((y,u,v), axis=-1)
# take every index twice until half the range
idx_h = np.repeat(np.arange(img.shape[0] // 2), 2)[:, None]
idx_w = np.repeat(np.arange(img.shape[1] // 2), 2)[None, :]
# convert
yuv444 = np.empty_like(img, dtype=np.uint8)
yuv444[..., 0] = img[..., 0]
yuv444[..., 1] = img[idx_h, idx_w, 1]
yuv444[..., 2] = img[idx_h, idx_w, 2]
If this is along your critical path, and you want to tease out a little more performance, you could consider processing the image channel first, which will be faster on modern CPUs (but not GPUs).

This answer is just another way to do it, and is not the quickest way to get the job done, but definitely should be easy to understand. I have checked the generated files with yuvplayer application as well to confirm it works.
#height mentioned is height of nv12 file and so is the case with width
def convert_nv12toyuv444(filename= 'input.nv12',height=2358,width=2040):
nv12_data = np.fromfile(filename, dtype=np.uint8)
imageSize = (height, width)
npimg = nv12_data.reshape(imageSize)
y_height = npimg.shape[0] * (2/3)
y_wid = npimg.shape[1]
y_height = int(y_height)
y_wid = int(y_wid)
y_data= npimg[:y_height,:y_wid]
uv_data=npimg[y_height:,:y_wid]
shrunkU= uv_data[:, 0 : :2]
shrunkV= uv_data[:, 1 : :2]
u = cv2.resize(shrunkU, (y_wid, y_height),
interpolation=cv2.INTER_NEAREST)
v = cv2.resize(shrunkV, (y_wid, y_height),
interpolation=cv2.INTER_NEAREST)
yuv444 = np.dstack((y_data, u, v))

Related

networkx position (biggest) nodes in the middle of a graph

I've been creating graphs with the networkx package and everything works fine. I would like to make the graphs even better by placing the bigger nodes in the middle of the graph and the layout functions from networkx does not seem to do the job. The nodes represent the size of degree (the higher connected the node, the bigger).
Is there any way to program these graphs in such a way that the bigger nodes are positioned in the middle? It does not have to be automated, i could also manually choose the nodes and give them the middle position but i can also not find how to do this.
If this is not possible with networkx or something else; is there any way to do it with Gephi or cytoscape? I had trouble with Gephi that it does not import the graph the same way i see it in my jupyter notebook (the colors, the node- and edge-sizes do not import).
To summarize; i want to put bigger nodes in the middle of my graph but i dont mind how i get it done (with networkx, matplotlib or whatever).
Unfortunately i cannot provide my actual graphs but here is an example which can look like one of my graphs; it is a directed weighted graph.
G = nx.gnp_random_graph(15, 0.2, directed=True)
d = dict(G.degree(weight='weight'))
d = {k: v/10 for k, v in d.items()}
edge_size = [(float(i)/sum(weights))*100 for i in weights]
node_size = [(v*1000) for v in d.values()]
nx.draw(G,width=edge_size,node_size=node_size)
There are several options:
import networkx as nx
G = nx.gnp_random_graph(15, 0.2, directed=True)
node_degree = dict(G.degree(weight='weight'))
# A) Precompute node positions, and then manually over-ride some node positions.
node_positions = nx.spring_layout(G)
node_positions[0] = (0.5, 0.5) # by default, networkx plots on a canvas with the origin at (0, 0) and a width and height of 1; (0.5, 0.5) is hence the center
nx.draw(G, pos=node_positions, node_size=[100 * node_degree[node] for node in G])
plt.show()
# B) Use netgraph to draw the graph and then drag the nodes around with the mouse.
from netgraph import InteractiveGraph # pip install netgraph
plot_instance = InteractiveGraph(G, node_size=node_degree)
plt.show()
# C) Modify the Fruchterman-Reingold algorithm to include a gravitational force that pulls nodes with a large "mass" towards the center.
# This is left as an exercise to the interested reader (i.e. very non-trivial).
Edit: option C is non-trivial but also very do-able.
Here is my stab at it.
#!/usr/bin/env python
# coding: utf-8
"""
FR layout but with an additional gravitational pull towards a gravitational center.
The pull is proportional to the mass of the node.
"""
import numpy as np
import matplotlib.pyplot as plt
# pip install netgraph
from netgraph._main import BASE_SCALE
from netgraph._utils import (
_get_unique_nodes,
_edge_list_to_adjacency_matrix,
)
from netgraph._node_layout import (
_is_within_bbox,
_get_temperature_decay,
_get_fr_repulsion,
_get_fr_attraction,
_rescale_to_frame,
_handle_multiple_components,
_reduce_node_overlap,
)
DEBUG = False
#_handle_multiple_components
def get_fruchterman_reingold_newton_layout(edges,
edge_weights = None,
k = None,
g = 1.,
scale = None,
origin = None,
gravitational_center = None,
initial_temperature = 1.,
total_iterations = 50,
node_size = 0,
node_mass = 1,
node_positions = None,
fixed_nodes = None,
*args, **kwargs):
"""Modified Fruchterman-Reingold node layout.
Uses a modified Fruchterman-Reingold algorithm [Fruchterman1991]_ to compute node positions.
This algorithm simulates the graph as a physical system, in which nodes repell each other.
For connected nodes, this repulsion is counteracted by an attractive force exerted by the edges, which are simulated as springs.
Unlike the original algorithm, there is an additional attractive force pulling nodes towards a gravitational center, in proportion to their masses.
Parameters
----------
edges : list
The edges of the graph, with each edge being represented by a (source node ID, target node ID) tuple.
edge_weights : dict
Mapping of edges to edge weights.
k : float or None, default None
Expected mean edge length. If None, initialized to the sqrt(area / total nodes).
g : float or None, default 1.
Gravitational constant that sets the magnitude of the gravitational pull towards the center.
origin : tuple or None, default None
The (float x, float y) coordinates corresponding to the lower left hand corner of the bounding box specifying the extent of the canvas.
If None is given, the origin is placed at (0, 0).
scale : tuple or None, default None
The (float x, float y) dimensions representing the width and height of the bounding box specifying the extent of the canvas.
If None is given, the scale is set to (1, 1).
gravitational_center : tuple or None, default None
The (float x, float y) coordinates towards which nodes experience a gravitational pull.
If None, the gravitational center is placed at the center of the canvas defined by origin and scale.
total_iterations : int, default 50
Number of iterations.
initial_temperature: float, default 1.
Temperature controls the maximum node displacement on each iteration.
Temperature is decreased on each iteration to eventually force the algorithm into a particular solution.
The size of the initial temperature determines how quickly that happens.
Values should be much smaller than the values of `scale`.
node_size : scalar or dict, default 0.
Size (radius) of nodes.
Providing the correct node size minimises the overlap of nodes in the graph,
which can otherwise occur if there are many nodes, or if the nodes differ considerably in size.
node_mass : scalar or dict, default 1.
Mass of nodes.
Nodes with higher mass experience a larger gravitational pull towards the center.
node_positions : dict or None, default None
Mapping of nodes to their (initial) x,y positions. If None are given,
nodes are initially placed randomly within the bounding box defined by `origin` and `scale`.
If the graph has multiple components, explicit initial positions may result in a ValueError,
if the initial positions fall outside of the area allocated to that specific component.
fixed_nodes : list or None, default None
Nodes to keep fixed at their initial positions.
Returns
-------
node_positions : dict
Dictionary mapping each node ID to (float x, float y) tuple, the node position.
References
----------
.. [Fruchterman1991] Fruchterman, TMJ and Reingold, EM (1991) ‘Graph drawing by force‐directed placement’,
Software: Practice and Experience
"""
# This is just a wrapper around `_fruchterman_reingold`, which implements (the loop body of) the algorithm proper.
# This wrapper handles the initialization of variables to their defaults (if not explicitely provided),
# and checks inputs for self-consistency.
assert len(edges) > 0, "The list of edges has to be non-empty."
if origin is None:
if node_positions:
minima = np.min(list(node_positions.values()), axis=0)
origin = np.min(np.stack([minima, np.zeros_like(minima)], axis=0), axis=0)
else:
origin = np.zeros((2))
else:
# ensure that it is an array
origin = np.array(origin)
if scale is None:
if node_positions:
delta = np.array(list(node_positions.values())) - origin[np.newaxis, :]
maxima = np.max(delta, axis=0)
scale = np.max(np.stack([maxima, np.ones_like(maxima)], axis=0), axis=0)
else:
scale = np.ones((2))
else:
# ensure that it is an array
scale = np.array(scale)
assert len(origin) == len(scale), \
"Arguments `origin` (d={}) and `scale` (d={}) need to have the same number of dimensions!".format(len(origin), len(scale))
dimensionality = len(origin)
if gravitational_center is None:
gravitational_center = origin + 0.5 * scale
else:
# ensure that it is an array
gravitational_center = np.array(gravitational_center)
if fixed_nodes is None:
fixed_nodes = []
connected_nodes = _get_unique_nodes(edges)
if node_positions is None: # assign random starting positions to all nodes
node_positions_as_array = np.random.rand(len(connected_nodes), dimensionality) * scale + origin
unique_nodes = connected_nodes
else:
# 1) check input dimensionality
dimensionality_node_positions = np.array(list(node_positions.values())).shape[1]
assert dimensionality_node_positions == dimensionality, \
"The dimensionality of values of `node_positions` (d={}) must match the dimensionality of `origin`/ `scale` (d={})!".format(dimensionality_node_positions, dimensionality)
is_valid = _is_within_bbox(list(node_positions.values()), origin=origin, scale=scale)
if not np.all(is_valid):
error_message = "Some given node positions are not within the data range specified by `origin` and `scale`!"
error_message += "\n\tOrigin : {}, {}".format(*origin)
error_message += "\n\tScale : {}, {}".format(*scale)
error_message += "\nThe following nodes do not fall within this range:"
for ii, (node, position) in enumerate(node_positions.items()):
if not is_valid[ii]:
error_message += "\n\t{} : {}".format(node, position)
error_message += "\nThis error can occur if the graph contains multiple components but some or all node positions are initialised explicitly (i.e. node_positions != None)."
raise ValueError(error_message)
# 2) handle discrepancies in nodes listed in node_positions and nodes extracted from edges
if set(node_positions.keys()) == set(connected_nodes):
# all starting positions are given;
# no superfluous nodes in node_positions;
# nothing left to do
unique_nodes = connected_nodes
else:
# some node positions are provided, but not all
for node in connected_nodes:
if not (node in node_positions):
warnings.warn("Position of node {} not provided. Initializing to random position within frame.".format(node))
node_positions[node] = np.random.rand(2) * scale + origin
unconnected_nodes = []
for node in node_positions:
if not (node in connected_nodes):
unconnected_nodes.append(node)
fixed_nodes.append(node)
# warnings.warn("Node {} appears to be unconnected. The current node position will be kept.".format(node))
unique_nodes = connected_nodes + unconnected_nodes
node_positions_as_array = np.array([node_positions[node] for node in unique_nodes])
total_nodes = len(unique_nodes)
if isinstance(node_size, (int, float)):
node_size = node_size * np.ones((total_nodes))
elif isinstance(node_size, dict):
node_size = np.array([node_size[node] if node in node_size else 0. for node in unique_nodes])
if isinstance(node_mass, (int, float)):
node_mass = node_mass * np.ones((total_nodes))
elif isinstance(node_mass, dict):
node_mass = np.array([node_mass[node] if node in node_mass else 0. for node in unique_nodes])
adjacency = _edge_list_to_adjacency_matrix(
edges, edge_weights=edge_weights, unique_nodes=unique_nodes)
# Forces in FR are symmetric.
# Hence we need to ensure that the adjacency matrix is also symmetric.
adjacency = adjacency + adjacency.transpose()
if fixed_nodes:
is_mobile = np.array([False if node in fixed_nodes else True for node in unique_nodes], dtype=bool)
mobile_positions = node_positions_as_array[is_mobile]
fixed_positions = node_positions_as_array[~is_mobile]
mobile_node_sizes = node_size[is_mobile]
fixed_node_sizes = node_size[~is_mobile]
mobile_node_masses = node_mass[is_mobile]
fixed_node_masses = node_mass[~is_mobile]
# reorder adjacency
total_mobile = np.sum(is_mobile)
reordered = np.zeros((adjacency.shape[0], total_mobile))
reordered[:total_mobile, :total_mobile] = adjacency[is_mobile][:, is_mobile]
reordered[total_mobile:, :total_mobile] = adjacency[~is_mobile][:, is_mobile]
adjacency = reordered
else:
is_mobile = np.ones((total_nodes), dtype=bool)
mobile_positions = node_positions_as_array
fixed_positions = np.zeros((0, 2))
mobile_node_sizes = node_size
fixed_node_sizes = np.array([])
mobile_node_masses = node_mass
fixed_node_masses = np.array([])
if k is None:
area = np.product(scale)
k = np.sqrt(area / float(total_nodes))
temperatures = _get_temperature_decay(initial_temperature, total_iterations)
# --------------------------------------------------------------------------------
# main loop
for ii, temperature in enumerate(temperatures):
candidate_positions = _fruchterman_reingold_newton(mobile_positions, fixed_positions,
mobile_node_sizes, fixed_node_sizes,
adjacency, temperature, k,
mobile_node_masses, fixed_node_masses,
gravitational_center, g)
is_valid = _is_within_bbox(candidate_positions, origin=origin, scale=scale)
mobile_positions[is_valid] = candidate_positions[is_valid]
# --------------------------------------------------------------------------------
# format output
node_positions_as_array[is_mobile] = mobile_positions
if np.all(is_mobile):
node_positions_as_array = _rescale_to_frame(node_positions_as_array, origin, scale)
node_positions = dict(zip(unique_nodes, node_positions_as_array))
return node_positions
def _fruchterman_reingold_newton(mobile_positions, fixed_positions,
mobile_node_radii, fixed_node_radii,
adjacency, temperature, k,
mobile_node_masses, fixed_node_masses,
gravitational_center, g):
"""Inner loop of modified Fruchterman-Reingold layout algorithm."""
combined_positions = np.concatenate([mobile_positions, fixed_positions], axis=0)
combined_node_radii = np.concatenate([mobile_node_radii, fixed_node_radii])
delta = mobile_positions[np.newaxis, :, :] - combined_positions[:, np.newaxis, :]
distance = np.linalg.norm(delta, axis=-1)
# alternatively: (hack adapted from igraph)
if np.sum(distance==0) - np.trace(distance==0) > 0: # i.e. if off-diagonal entries in distance are zero
warnings.warn("Some nodes have the same position; repulsion between the nodes is undefined.")
rand_delta = np.random.rand(*delta.shape) * 1e-9
is_zero = distance <= 0
delta[is_zero] = rand_delta[is_zero]
distance = np.linalg.norm(delta, axis=-1)
# subtract node radii from distances to prevent nodes from overlapping
distance -= mobile_node_radii[np.newaxis, :] + combined_node_radii[:, np.newaxis]
# prevent distances from becoming less than zero due to overlap of nodes
distance[distance <= 0.] = 1e-6 # 1e-13 is numerical accuracy, and we will be taking the square shortly
with np.errstate(divide='ignore', invalid='ignore'):
direction = delta / distance[..., None] # i.e. the unit vector
# calculate forces
repulsion = _get_fr_repulsion(distance, direction, k)
attraction = _get_fr_attraction(distance, direction, adjacency, k)
gravity = _get_gravitational_pull(mobile_positions, mobile_node_masses, gravitational_center, g)
if DEBUG:
r = np.median(np.linalg.norm(repulsion, axis=-1))
a = np.median(np.linalg.norm(attraction, axis=-1))
g = np.median(np.linalg.norm(gravity, axis=-1))
print(r, a, g)
displacement = attraction + repulsion + gravity
# limit maximum displacement using temperature
displacement_length = np.linalg.norm(displacement, axis=-1)
displacement = displacement / displacement_length[:, None] * np.clip(displacement_length, None, temperature)[:, None]
mobile_positions = mobile_positions + displacement
return mobile_positions
def _get_gravitational_pull(mobile_positions, mobile_node_masses, gravitational_center, g):
delta = gravitational_center[np.newaxis, :] - mobile_positions
direction = delta / np.linalg.norm(delta, axis=-1)[:, np.newaxis]
magnitude = mobile_node_masses - np.mean(mobile_node_masses)
return g * magnitude[:, np.newaxis] * direction
if __name__ == '__main__':
import networkx as nx
from netgraph import Graph
G = nx.gnp_random_graph(15, 0.2, directed=True)
node_degree = dict(G.degree(weight='weight'))
node_positions = get_fruchterman_reingold_newton_layout(
list(G.edges()),
node_size={node : BASE_SCALE * degree for node, degree in node_degree.items()},
node_mass=node_degree, g=2
)
Graph(G, node_layout=node_positions, node_size=node_degree)
plt.show()

Why does histogram equalization on a 16-bit image show a strange result?

I have a 16-bit image which I want to rescale to 8-bit while achieving a high contrast. Now I tried histogram equalization as follows:
image_equ = cv.equalizeHist(cv_image.astype(np.uint8))
But the output is super strange:
What is happening? Is the rescaling to 8-bit first maybe the problem?
cv2.equalizeHist does not support uint16 input, and cv_image.astype(np.uint8) results overflows.
The solution is using different library, or implement the equalization using NumPy.
We can find the NumPy implementation of uint8 equalization in the OpenCV documentation:
Histograms - 2: Histogram Equalization
We can adjust the code (using NumPy) for uint16 input and output:
Replace 256 with 65536 (256 = 2^8 and 65536 = 2^16).
Replace 255 with 65535.
Replace uint8 with uint16.
Assuming the original code is correct, the following should work for uint16:
hist, bins = np.histogram(img.flatten(), 65536, [0, 65536]) # Collect 16 bits histogram (65536 = 2^16).
cdf = hist.cumsum()
cdf_m = np.ma.masked_equal(cdf, 0) # Find the minimum histogram value (excluding 0)
cdf_m = (cdf_m - cdf_m.min())*65535/(cdf_m.max()-cdf_m.min())
cdf = np.ma.filled(cdf_m,0).astype('uint16')
# Now we have the look-up table...
img2 = cdf[img]
Complete code sample (building sample 16 bits input):
import cv2
import numpy as np
# Build sample input for testing.
################################################################################
img = cv2.imread('chelsea.png', cv2.IMREAD_GRAYSCALE) # Read sample input image.
cv2.imshow('img', img) # Show input for testing.
img = img.astype(np.uint16) * 16 + 1000 # Make the image 16 bit, but the pixels range is going to be [1000, 5080] not full range (for example).
################################################################################
#equ = cv2.equalizeHist(img) # error: (-215:Assertion failed) _src.type() == CV_8UC1 in function 'cv::equalizeHist'
# https://docs.opencv.org/4.x/d5/daf/tutorial_py_histogram_equalization.html
hist, bins = np.histogram(img.flatten(), 65536, [0, 65536]) # Collect 16 bits histogram (65536 = 2^16).
cdf = hist.cumsum()
cdf_m = np.ma.masked_equal(cdf, 0) # Find the minimum histogram value (excluding 0)
cdf_m = (cdf_m - cdf_m.min())*65535/(cdf_m.max()-cdf_m.min())
cdf = np.ma.filled(cdf_m,0).astype('uint16')
# Now we have the look-up table...
equ = cdf[img]
# Show result for testing.
cv2.imshow('equ', equ)
cv2.waitKey()
cv2.destroyAllWindows()
Input (before scaling to 16 bits):
Output:

Slow computation on google colab while solving partial differential equation

I 'm using google colab to solve the homogeneous heat equation. I had made a program earlier with scipy using sparse matrices which worked upto N = 10(hyperparameter) but I need to run it for like N = 4... 1000 and thus it won't work on my pc. I therefore converted the code to tensorflow and here I 'm unable to use sparse matrices like I could in sympy but even the GPU/TPU computation is also slow and slower than my pc. Problems that I'm facing in the code and require solution for
1) tf.contrib is removed and thus I 've to use an older version of tensorflow for odeint function. Where is it in 2.0?
2)If the computation can be computed with sparse matrices it could be good since matrices are tridiagonal.I know about sparse_dense_mul() function but that returns dense tensor and it wouldn't do the job. The "func" function applies time independent boundary conditions and then requires matrix multiplication of (nxn) with (nX1) which gives (nX1) with multiple matrices.
Also the program was running faster without I created the class.
Also it's giving this
WARNING: Logging before flag parsing goes to stderr.
W0829 09:12:24.415445 139855355791232 lazy_loader.py:50]
The TensorFlow contrib module will not be included in TensorFlow 2.0.
For more information, please see:
* https://github.com/tensorflow/community/blob/master/rfcs/20180907-contrib-sunset.md
* https://github.com/tensorflow/addons
* https://github.com/tensorflow/io (for I/O related ops)
If you depend on functionality not listed there, please file an issue.
W0829 09:12:24.645356 139855355791232 deprecation.py:323] From /usr/local/lib/python3.6/dist-packages/tensorflow/contrib/integrate/python/ops/odes.py:233: div (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.
Instructions for updating:
Deprecated in favor of operator or tf.math.divide.
when I run code for loop in range(2, 10) and tqdm does not display and cell keeps running forever but it works fine for in (2, 5) and tqdm bar does appears.
#find a way to use sparse matrices
class Heat:
def __init__(self, N):
self.N = N
self.H = 1/N
self.A = ts.to_dense(ts.SparseTensor(indices=[[0, 0], [0, 1]] + \
[[i, i+j] for i in range(1, N) for j in [-1, 0, 1]] +[[N, N-1], [N, N]],
values=self.H*np.array([1/3, 1/6] + [1/6, 2/3, 1/6]*(N-1) + [1/6, 1/3], dtype=np.float32),
dense_shape=(N+1, N+1 )))
self.D = ts.to_dense(ts.SparseTensor(indices=[[0, 0], [0, 1]] + [[i, i+j] \
for i in range(1, N) for j in [-1, 0, 1]] +[[N, N-1], [N, N]],
values=N*np.array([1-(1), -1 -(-1)] + [-1, 2, -1]*(N-1) + [-1-(-1), 1-(1)], dtype=np.float32),
dense_shape=(N+1, N+1)))
self.domain = tf.linspace(0.0, 1.0, N+1)
def f(k):
if k == 0:
return (1 + math.pi**2)*(math.pi*self.H - math.sin(math.pi*self.H))/(math.pi**2*self.H)
elif k == N:
return -(1 + math.pi**2)*(-math.pi*self.H + math.sin(math.pi*self.H))/(math.pi**2*self.H)
else:
return -2*(1 + math.pi**2)*(math.cos(math.pi*self.H) - 1)*math.sin(math.pi*self.H*k)/(math.pi**2*self.H)
self.F = tf.constant([f(k) for k in range(N+1)], shape=(N+1,), dtype=tf.float32) #caution! shape changed caution caution 1, N+1(problem) is different from N+1,
self.exact = tm.scalar_mul(scalar=np.exp(1), x=tf.sin(math.pi*self.domain))
def error(self):
return np.linalg.norm(self.exact.numpy() - self.approx, 2)
def func (self, y, t):
y = tf.Variable(y)
y = y[0].assign(0.0)
y = y[self.N].assign(0.0)
if self.N**2> 100:
y_dash = tl.matvec(tf.linalg.inv(self.A), tl.matvec(a=tm.negative(self.D), b=y, a_is_sparse=True) + tm.scalar_mul(scalar=math.exp(t), x=self.F)) #caution! shape changed F is (1, N+1) others too
else:
y_dash = tl.matvec(tf.linalg.inv(self.A), tl.matvec(a=tm.negative(self.D), b=y) + tm.scalar_mul(scalar=math.exp(t), x=self.F)) #caution! shape changed F is (1, N+1) others too
y_dash = tf.Variable(y_dash) #!!y_dash performs Hadamard product like multiplication not matrix-like multiplication;returns 2-D
y_dash = y_dash[0].assign(0.0)
y_dash = y_dash[self.N].assign(0.0)
return y_dash
def algo_1(self):
self.approx = tf.contrib.integrate.odeint(
func=self.func,
y0=tf.sin(tm.scalar_mul(scalar=math.pi, x=self.domain)),
t=tf.constant([0.0, 1.0]),
rtol=1e-06,
atol=1e-12,
method='dopri5',
options={"max_num_steps":10**10},
full_output=False,
name=None
).numpy()[1]
def algo_2(self):
self.approx = tf.contrib.integrate.odeint_fixed(
func=self.func,
y0=tf.sin(tm.scalar_mul(scalar=math.pi, x=self.domain)),
t=tf.constant([0.0, 1.0]),
dt=tf.constant([self.H**2], dtype=tf.float32),
method='rk4',
name=None
).numpy()[1]
df = pd.DataFrame(columns=["NumBasis", "Errors"])
Ns = [2**r for r in range(2, 10)]
l =[]
for i in tqdm_notebook(Ns):
heateqn = Heat(i)
heateqn.algo_1()
l.append([i, heateqn.error()])
df.append({"NumBasis":i, "Errors":heateqn.error()}, ignore_index=True)
tf.keras.backend.clear_session()

RuntimeError: libpng signaled error while visualizing cnn layers

I am visualizing layers of cnn with keras. The visualization is on mnist test image.The model summary is here
The code for visualization is as follows:
layer_names = []
for layer in model.layers[:12]:
layer_names.append(layer.name) # Names of the layers, so you can have them as part of your plot
images_per_row = 16
for layer_name, layer_activation in zip(layer_names, activations): # Displays the feature maps
n_features = layer_activation.shape[-1] # Number of features in the feature map
size = layer_activation.shape[1] #The feature map has shape (1, size, size, n_features).
n_cols = n_features // images_per_row # Tiles the activation channels in this matrix
display_grid = np.zeros((size * n_cols, images_per_row * size))
for col in range(n_cols): # Tiles each filter into a big horizontal grid
for row in range(images_per_row):
channel_image = layer_activation[0,
:, :,
col * images_per_row + row]
channel_image -= channel_image.mean() # Post-processes the feature to make it visually palatable
channel_image /= channel_image.std()
channel_image *= 64
channel_image += 128
channel_image = np.clip(channel_image, 0, 255).astype('uint8')
display_grid[col * size : (col + 1) * size, # Displays the grid
row * size : (row + 1) * size] = channel_image
scale = 1. / size
plt.figure(figsize=(scale * display_grid.shape[1],
scale * display_grid.shape[0]))
plt.title(layer_name)
plt.grid(False)
plt.imshow(display_grid, aspect='auto', cmap='viridis')
This code visualize output of first two layers and show image with filters. But with the third layer it throws the error as follows:
RuntimeError: libpng signaled error
<Figure size 1152x0 with 1 Axes>
I have tried to uninstall and reinstall matplotlib but still it is not working.
It’s a logic error:
<Figure size 1152x0 with 1 Axes>
implies that scale * display_grid.shape[0] == 0 which can only happen if you set n_cols to zero in this line:
n_cols = n_features // images_per_row
caused by n_features being < images_per_row/2.
There should be a nicer error in future versions of matplotlib.

Is there any way to use bivariate colormaps in matplotlib?

In other words, I want to make a heatmap (or surface plot) where the color varies as a function of 2 variables. (Specifically, luminance = magnitude and hue = phase.) Is there any native way to do this?
Some examples of similar plots:
Several good examples of exactly(?) what I want to do.
More examples from astronomy, but with non-perceptual hue
Edit: This is what I did with it: https://github.com/endolith/complex_colormap
imshow can take an array of [r, g, b] entries. So you can convert the absolute values to intensities and phases - to hues.
I will use as an example complex numbers, because for it it makes the most sense. If needed, you can always add numpy arrays Z = X + 1j * Y.
So for your data Z you can use e.g.
imshow(complex_array_to_rgb(Z))
where (EDIT: made it quicker and nicer thanks to this suggestion)
def complex_array_to_rgb(X, theme='dark', rmax=None):
'''Takes an array of complex number and converts it to an array of [r, g, b],
where phase gives hue and saturaton/value are given by the absolute value.
Especially for use with imshow for complex plots.'''
absmax = rmax or np.abs(X).max()
Y = np.zeros(X.shape + (3,), dtype='float')
Y[..., 0] = np.angle(X) / (2 * pi) % 1
if theme == 'light':
Y[..., 1] = np.clip(np.abs(X) / absmax, 0, 1)
Y[..., 2] = 1
elif theme == 'dark':
Y[..., 1] = 1
Y[..., 2] = np.clip(np.abs(X) / absmax, 0, 1)
Y = matplotlib.colors.hsv_to_rgb(Y)
return Y
So, for example:
Z = np.array([[3*(x + 1j*y)**3 + 1/(x + 1j*y)**2
for x in arange(-1,1,0.05)] for y in arange(-1,1,0.05)])
imshow(complex_array_to_rgb(Z, rmax=5), extent=(-1,1,-1,1))
imshow(complex_array_to_rgb(Z, rmax=5, theme='light'), extent=(-1,1,-1,1))
imshow will take an NxMx3 (rbg) or NxMx4 (grba) array so you can do your color mapping 'by hand'.
You might be able to get a bit of traction by sub-classing Normalize to map your vector to a scaler and laying out a custom color map very cleverly (but I think this will end up having to bin one of your dimensions).
I have done something like this (pdf link, see figure on page 24), but the code is in MATLAB (and buried someplace in my archives).
I agree a bi-variate color map would be useful (primarily for representing very dense vector fields where your kinda up the creek no matter what you do).
I think the obvious extension is to let color maps take complex arguments. It would require specialized sub-classes of Normalize and Colormap and I am going back and forth on if I think it would be a lot of work to implement. I suspect if you get it working by hand it will just be a matter of api wrangling.
I created an easy to use 2D colormap class, that takes 2 NumPy arrays and maps them to an RGB image, based on a reference image.
I used #GjjvdBurg's answer as a starting point. With a bit of work, this could still be improved, and possibly turned into a proper Python module - if you want, feel free to do so, I grant you all credits.
TL;DR:
# read reference image
cmap_2d = ColorMap2D('const_chroma.jpeg', reverse_x=True) # , xclip=(0,0.9))
# map the data x and y to the RGB space, defined by the image
rgb = cmap_2d(data_x, data_y)
# generate a colorbar image
cbar_rgb = cmap_2d.generate_cbar()
The ColorMap2D class:
class ColorMap2D:
def __init__(self, filename: str, transpose=False, reverse_x=False, reverse_y=False, xclip=None, yclip=None):
"""
Maps two 2D array to an RGB color space based on a given reference image.
Args:
filename (str): reference image to read the x-y colors from
rotate (bool): if True, transpose the reference image (swap x and y axes)
reverse_x (bool): if True, reverse the x scale on the reference
reverse_y (bool): if True, reverse the y scale on the reference
xclip (tuple): clip the image to this portion on the x scale; (0,1) is the whole image
yclip (tuple): clip the image to this portion on the y scale; (0,1) is the whole image
"""
self._colormap_file = filename or COLORMAP_FILE
self._img = plt.imread(self._colormap_file)
if transpose:
self._img = self._img.transpose()
if reverse_x:
self._img = self._img[::-1,:,:]
if reverse_y:
self._img = self._img[:,::-1,:]
if xclip is not None:
imin, imax = map(lambda x: int(self._img.shape[0] * x), xclip)
self._img = self._img[imin:imax,:,:]
if yclip is not None:
imin, imax = map(lambda x: int(self._img.shape[1] * x), yclip)
self._img = self._img[:,imin:imax,:]
if issubclass(self._img.dtype.type, np.integer):
self._img = self._img / 255.0
self._width = len(self._img)
self._height = len(self._img[0])
self._range_x = (0, 1)
self._range_y = (0, 1)
#staticmethod
def _scale_to_range(u: np.ndarray, u_min: float, u_max: float) -> np.ndarray:
return (u - u_min) / (u_max - u_min)
def _map_to_x(self, val: np.ndarray) -> np.ndarray:
xmin, xmax = self._range_x
val = self._scale_to_range(val, xmin, xmax)
rescaled = (val * (self._width - 1))
return rescaled.astype(int)
def _map_to_y(self, val: np.ndarray) -> np.ndarray:
ymin, ymax = self._range_y
val = self._scale_to_range(val, ymin, ymax)
rescaled = (val * (self._height - 1))
return rescaled.astype(int)
def __call__(self, val_x, val_y):
"""
Take val_x and val_y, and associate the RGB values
from the reference picture to each item. val_x and val_y
must have the same shape.
"""
if val_x.shape != val_y.shape:
raise ValueError(f'x and y array must have the same shape, but have {val_x.shape} and {val_y.shape}.')
self._range_x = (np.amin(val_x), np.amax(val_x))
self._range_y = (np.amin(val_y), np.amax(val_y))
x_indices = self._map_to_x(val_x)
y_indices = self._map_to_y(val_y)
i_xy = np.stack((x_indices, y_indices), axis=-1)
rgb = np.zeros((*val_x.shape, 3))
for indices in np.ndindex(val_x.shape):
img_indices = tuple(i_xy[indices])
rgb[indices] = self._img[img_indices]
return rgb
def generate_cbar(self, nx=100, ny=100):
"generate an image that can be used as a 2D colorbar"
x = np.linspace(0, 1, nx)
y = np.linspace(0, 1, ny)
return self.__call__(*np.meshgrid(x, y))
Usage:
Full example, using the constant chroma reference taken from here as a screenshot:
# generate data
x = y = np.linspace(-2, 2, 300)
xx, yy = np.meshgrid(x, y)
ampl = np.exp(-(xx ** 2 + yy ** 2))
phase = (xx ** 2 - yy ** 2) * 6 * np.pi
data = ampl * np.exp(1j * phase)
data_x, data_y = np.abs(data), np.angle(data)
# Here is the 2D colormap part
cmap_2d = ColorMap2D('const_chroma.jpeg', reverse_x=True) # , xclip=(0,0.9))
rgb = cmap_2d(data_x, data_y)
cbar_rgb = cmap_2d.generate_cbar()
# plot the data
fig, plot_ax = plt.subplots(figsize=(8, 6))
plot_extent = (x.min(), x.max(), y.min(), y.max())
plot_ax.imshow(rgb, aspect='auto', extent=plot_extent, origin='lower')
plot_ax.set_xlabel('x')
plot_ax.set_ylabel('y')
plot_ax.set_title('data')
# create a 2D colorbar and make it fancy
plt.subplots_adjust(left=0.1, right=0.65)
bar_ax = fig.add_axes([0.68, 0.15, 0.15, 0.3])
cmap_extent = (data_x.min(), data_x.max(), data_y.min(), data_y.max())
bar_ax.imshow(cbar_rgb, extent=cmap_extent, aspect='auto', origin='lower',)
bar_ax.set_xlabel('amplitude')
bar_ax.set_ylabel('phase')
bar_ax.yaxis.tick_right()
bar_ax.yaxis.set_label_position('right')
for item in ([bar_ax.title, bar_ax.xaxis.label, bar_ax.yaxis.label] +
bar_ax.get_xticklabels() + bar_ax.get_yticklabels()):
item.set_fontsize(7)
plt.show()
I know this is an old post, but want to help out others that may arrive late. Below is a python function to implement complex_to_rgb from sage. Note: This implementation isn't optimal, but it is readable. See links: (examples)(source code)
Code:
import numpy as np
def complex_to_rgb(z_values):
width = z_values.shape[0]
height = z_values.shape[1]
rgb = np.zeros(shape=(width, height, 3))
for i in range(width):
row = z_values[i]
for j in range(height):
# define value, real(value), imag(value)
zz = row[j]
x = np.real(zz)
y = np.imag(zz)
# define magnitued and argument
magnitude = np.hypot(x, y)
arg = np.arctan2(y, x)
# define lighness
lightness = np.arctan(np.log(np.sqrt(magnitude) + 1)) * (4 / np.pi) - 1
if lightness < 0:
bot = 0
top = 1 + lightness
else:
bot = lightness
top = 1
# define hue
hue = 3 * arg / np.pi
if hue < 0:
hue += 6
# set ihue and use it to define rgb values based on cases
ihue = int(hue)
# case 1
if ihue == 0:
r = top
g = bot + hue * (top - bot)
b = bot
# case 2
elif ihue == 1:
r = bot + (2 - hue) * (top - bot)
g = top
b = bot
# case 3
elif ihue == 2:
r = bot
g = top
b = bot + (hue - 2) * (top - bot)
# case 4
elif ihue == 3:
r = bot
g = bot + (4 - hue) * (top - bot)
b = top
# case 5
elif ihue == 4:
r = bot + (hue - 4) * (top - bot)
g = bot
b = top
# case 6
else:
r = top
g = bot
b = bot + (6 - hue) * (top - bot)
# set rgb array values
rgb[i, j, 0] = r
rgb[i, j, 1] = g
rgb[i, j, 2] = b
return rgb