from cycler import cycler
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
import numpy as np
from PIL import Image
import pymc3 as pm
import theano
import theano.tensor as tt
from tqdm import tqdm
import scipy
def get_rainbow():
"""Creates a rainbow color cycle"""
return cycler('color', [
'#FF0000',
'#FF7F00',
'#FFFF00',
'#00FF00',
'#0000FF',
'#4B0082',
'#9400D3',
])
def load_image(image_file, mode=None):
"""Load filename into a numpy array, filling in transparency with 0's.
Parameters
----------
image_file : str
File to load. Usually works with .jpg and .png.
Returns
-------
numpy.ndarray of resulting image. Has shape (w, h), (w, h, 3), or (w, h, 4)
if black and white, color, or color with alpha channel, respectively.
"""
image = Image.open(image_file)
if mode is None:
mode = image.mode
alpha = image.convert('RGBA').split()[-1]
background = Image.new("RGBA", image.size, (255, 255, 255, 255,))
background.paste(image, mask=alpha)
img = np.flipud(np.asarray(background.convert(mode)))
img = img / 255
if mode == 'L': # I don't know how images work, but .png's are inverted
img = 1 - img
return img
class ImageLikelihood(theano.Op):
"""
Custom theano op for turning a 2d intensity matrix into a density
distribution.
"""
itypes = [tt.dvector]
otypes = [tt.dvector]
def __init__(self, img):
self.width, self.height = img.shape
self.density = scipy.interpolate.RectBivariateSpline(
x=np.arange(self.width),
y=np.arange(self.height),
z=img)
def perform(self, node, inputs, output_storage):
"""Evaluates the density of the image at the given point."""
x, y = inputs[0]
if x < 0 or x > self.width or y < 0 or y > self.height:
output_storage[0][0] = np.array([np.log(0)])
else:
output_storage[0][0] = np.log(self.density(x, y))[0]
def sample_grayscale(image, samples=5000, tune=100, nchains=4, threshold=0.2):
"""Run MCMC on a 1 color image. Works best on logos or text.
Parameters
----------
image : numpy.ndarray
Image array from `load_image`. Should have `image.ndims == 2`.
samples : int
Number of samples to draw from the image
tune : int
Number of tuning steps to take. Note that this adjusts the step size:
if you want smaller steps, make tune closer to 0.
nchains : int
Number of chains to sample with. This will later turn into the number
of colors in your plot. Note that you get `samples * nchains` of total
points in your final scatter.
threshold : float
Float between 0 and 1. It looks nicer when an image is binarized, and
this will do that. Use `None` to not binarize. In theory you should get
fewer samples from lighter areas, but your mileage may vary.
Returns
-------
pymc3.MultiTrace of samples from the image. Each sample is an (x, y) float
of indices that were sampled, with the variable name 'image'.
"""
# preprocess
image_copy = image.copy()
if threshold != -1:
image_copy[image < threshold] = 0
image_copy[image >= threshold] = 1
# need an active pixel to start on
active_pixels = np.array(list(zip(*np.where(image_copy == image_copy.max()))))
idx = np.random.randint(0, len(active_pixels), nchains)
start = active_pixels[idx]
with pm.Model():
pm.DensityDist('image', ImageLikelihood(image_copy), shape=2)
trace = pm.sample(samples,
tune=tune,
chains=nchains, step=pm.Metropolis(),
start=[{'image': x} for x in start],
)
return trace
def sample_color(image, samples=5000, tune=1000, nchains=4):
"""Run MCMC on a color image. EXPERIMENTAL!
Parameters
----------
image : numpy.ndarray
Image array from `load_image`. Should have `image.ndims == 2`.
samples : int
Number of samples to draw from the image
tune : int
All chains start at the same spot, so it is good to let them wander
apart a bit before beginning
Returns
-------
pymc3.MultiTrace of samples from the image. Each sample is an (x, y) float
of indices that were sampled, with three variables named 'red',
'green', 'blue'.
"""
with pm.Model():
pm.DensityDist('red', ImageLikelihood(image[:, :, 0]), shape=2)
pm.DensityDist('green', ImageLikelihood(image[:, :, 1]), shape=2)
pm.DensityDist('blue', ImageLikelihood(image[:, :, 2]), shape=2)
trace = pm.sample(samples, chains=nchains, tune=tune, step=pm.Metropolis())
return trace
def plot_multitrace(trace, image, max_size=10, colors=None, **plot_kwargs):
"""Plot an image of the grayscale trace.
Parameters
----------
trace : pymc3.MultiTrace
Get this from sample_grayscale
image : numpy.ndarray
Image array from `load_image`, used to produce the trace.
max_size : float
Used to set the figsize for the image, maintaining the aspect ratio.
In inches!
colors : iterable
You can set custom colors to cycle through! Default is the rainbow.
plot_kwargs :
Other keyword arguments passed to the trace plotting. Some useful
examples are marker='.' in case you sampled lots of points, alpha=0.3
to add transparency to the points, or linestyle='-', so you can see the
actual path the chains took.
Returns
-------
(figure, axis)
The matplotlib figure and axis with the plot
"""
default_kwargs = {'marker': 'o', 'linestyle': '', 'alpha': 0.4}
default_kwargs.update(plot_kwargs)
if colors is None:
colors = get_rainbow()
else:
colors = cycler('color', colors)
vals = [trace.get_values('image', chains=chain) for chain in trace.chains]
fig, ax = plt.subplots(figsize=get_figsize(image, max_size))
ax.set_prop_cycle(colors)
ax.set_xlim((0, image.shape[1]))
ax.set_ylim((0, image.shape[0]))
ax.axis('off')
for val in vals:
ax.plot(val[:, 1], val[:, 0], **default_kwargs)
return fig, ax
def make_gif(trace, image, steps=200, leading_point=True,
filename='output.gif', max_size=10, interval=30, dpi=20,
colors=None, **plot_kwargs):
"""Make a gif of the grayscale trace.
Parameters
----------
trace : pymc3.MultiTrace
Get this from sample_grayscale
image : numpy.ndarray
Image array from `load_image`, used to produce the trace.
steps : int
Number of frames in the resulting .gif
leading_point : bool
If true, adds a large point at the head of each chain, so you can
follow the path easier.
filename : str
Place to save the resulting .gif to
max_size : float
Used to set the figsize for the image, maintaining the aspect ratio.
In inches!
interval : int
How long each frame lasts. Pretty sure this is hundredths of seconds
dpi : int
Quality of the resulting .gif Seems like larger values make the gif
bigger too.
colors : iterable
You can set custom colors to cycle through! Default is the rainbow.
plot_kwargs :
Other keyword arguments passed to the trace plotting. Some useful
examples are marker='.' in case you sampled lots of points, alpha=0.3
to add transparency to the points, or linestyle='-', so you can see the
actual path the chains took.
Returns
-------
str
filename where the gif was saved
"""
default_kwargs = {'marker': 'o', 'linestyle': '', 'alpha': 0.4}
default_kwargs.update(plot_kwargs)
if colors is None:
colors = get_rainbow()
else:
colors = cycler('color', colors)
vals = [trace.get_values('image', chains=chain) for chain in trace.chains]
intervals = np.linspace(0, vals[0].shape[0] - 1, num=steps + 1, dtype=int)[1:] # noqa
fig, ax = plt.subplots(figsize=get_figsize(image, max_size))
ax.set_prop_cycle(colors)
ax.set_xlim((0, image.shape[1]))
ax.set_ylim((0, image.shape[0]))
ax.axis('off')
lines, points = [], []
for _ in vals:
lines.append(ax.plot([], [], **default_kwargs)[0])
if leading_point:
points.append(ax.plot([], [], 'o', c=lines[-1].get_color(), markersize=20)[0]) # noqa
else:
points.append(None)
def update(idx):
if idx < len(intervals):
for pts, lns, val in zip(points, lines, vals):
lns.set_data(val[:intervals[idx], 1], val[:intervals[idx], 0])
if leading_point:
pts.set_data(val[intervals[idx], 1], val[intervals[idx], 0])
elif idx == len(intervals) and leading_point:
for pts in points:
pts.set_data([], [])
return ax
anim = FuncAnimation(fig, update, frames=np.arange(steps + 20), interval=interval) # noqa
anim.save(filename, dpi=dpi, writer='imagemagick')
return filename
def get_figsize(image, max_size=10):
"""Helper to scale figures"""
scale = max_size / max(image.shape)
return (scale * image.shape[1], scale * image.shape[0])
def _process_image_trace(trace, image, blur):
"""Adds Gaussian blur"""
w, h = image.shape[:2]
colors = ('red', 'green', 'blue')
channels = [np.zeros((w, h)) for color in colors]
for color, channel in zip(colors, channels):
for idx in np.array(np.round(trace[color]), dtype=int):
x, y = idx
channel[min(x, w - 1), min(y, h - 1)] += 1
return [scipy.ndimage.filters.gaussian_filter(channel, blur) for channel in channels] # noqa
def plot_multitrace_color(trace, image, blur=8, channel_max=None):
"""Plot the trace from a color image
Does additive blending of the three channels using Pillow. Higher `blur`
make the colors look right, but the image look blurrier.
Parameters
----------
trace : pymc3.MultiTrace
Get this from sample_color
image : numpy.ndarray
Image array from `load_image`, used to produce the trace.
blur : float
Each point only colors in a single pixel, but a gaussian blur makes the
samples blend well. This typically must be tuned by eye.
channel_max : list or None
This is used internally to normalize channels for making a gif
Returns
-------
PIL.Image
RGB image of the samples
"""
smoothed = _process_image_trace(trace, image, blur)
if channel_max is None:
channel_max = [channel.max() for channel in smoothed]
pils = []
for channel, c_max in zip(smoothed, channel_max):
pils.append(Image.fromarray(np.uint8(255 * np.flipud(channel / c_max))))
return Image.merge('RGB', pils)
def make_color_gif(trace, image, blur=8, steps=200, max_size=10, filename='output.gif',
interval=30, dpi=20):
"""Make a gif of the color trace. SUPER EXPERIMENTAL!
Tries to grab portions of the trace from
Parameters
----------
trace : pymc3.MultiTrace
Get this from sample_grayscale
image : numpy.ndarray
Image array from `load_image`, used to produce the trace.
blur : float
Each point only colors in a single pixel, but a gaussian blur makes the
samples blend well. This typically must be tuned by eye.
steps : int
Number of frames in the resulting .gif
max_size : float
Used to set the figsize for the image, maintaining the aspect ratio. In
inches!
leading_point : bool
If true, adds a large point at the head of each chain, so you can
follow the path easier.
filename : str
Place to save the resulting .gif to
interval : int
How long each frame lasts. Pretty sure this is hundredths of seconds
dpi : int
Quality of the resulting .gif Seems like larger values make the gif
bigger too.
Returns
-------
str
filename where the gif was saved
"""
figsize = get_figsize(image, max_size=max_size)
intervals = np.linspace(0, len(trace) - 1, num=steps + 1, dtype=int)[1:]
fig, ax = plt.subplots(figsize=figsize)
ax.imshow(np.zeros_like(image))
ax.axis('off')
channel_max = [channel.max() for channel in _process_image_trace(trace, image, blur)] # noqa
with tqdm(total=steps) as pbar:
def update(idx):
color_image = plot_multitrace_color(trace[:intervals[idx]], image, blur=blur,
channel_max=channel_max)
ax.imshow(color_image)
pbar.update(1)
return ax
anim = FuncAnimation(fig, update, frames=np.arange(steps), interval=interval) # noqa
anim.save(filename, dpi=dpi, writer='imagemagick')
return filename
