After my previous question on finding toes within each paw, I started loading up other measurements to see how it would hold up. Unfortunately, I quickly ran into a problem with one of the preceding steps: recognizing the paws.
You see, my proof of concept basically took the maximal pressure of each sensor over time and would start looking for the sum of each row, until it finds on that != 0.0. Then it does the same for the columns and as soon as it finds more than 2 rows with that are zero again. It stores the minimal and maximal row and column values to some index.
As you can see in the figure, this works quite well in most cases. However, there are a lot of downsides to this approach (other than being very primitive):
Humans can have 'hollow feet' which means there are several empty rows within the footprint itself. Since I feared this could happen with (large) dogs too, I waited for at least 2 or 3 empty rows before cutting off the paw.
This creates a problem if another contact made in a different column before it reaches several empty rows, thus expanding the area. I figure I could compare the columns and see if they exceed a certain value, they must be separate paws.
The problem gets worse when the dog is very small or walks at a higher pace. What happens is that the front paw's toes are still making contact, while the hind paw's toes just start to make contact within the same area as the front paw!
With my simple script, it won't be able to split these two, because it would have to determine which frames of that area belong to which paw, while currently I would only have to look at the maximal values over all frames.
Examples of where it starts going wrong:
So now I'm looking for a better way of recognizing and separating the paws (after which I'll get to the problem of deciding which paw it is!).
Update:
I've been tinkering to get Joe's (awesome!) answer implemented, but I'm having difficulties extracting the actual paw data from my files.
The coded_paws shows me all the different paws, when applied to the maximal pressure image (see above). However, the solution goes over each frame (to separate overlapping paws) and sets the four Rectangle attributes, such as coordinates or height/width.
I can't figure out how to take these attributes and store them in some variable that I can apply to the measurement data. Since I need to know for each paw, what its location is during which frames and couple this to which paw it is (front/hind, left/right).
So how can I use the Rectangles attributes to extract these values for each paw?
I have the measurements I used in the question setup in my public Dropbox folder (example 1, example 2, example 3). For anyone interested I also set up a blog to keep you up to date :-)
If you're just wanting (semi) contiguous regions, there's already an easy implementation in Python: SciPy's ndimage.morphology module. This is a fairly common image morphology operation.
Basically, you have 5 steps:
def find_paws(data, smooth_radius=5, threshold=0.0001):
data = sp.ndimage.uniform_filter(data, smooth_radius)
thresh = data > threshold
filled = sp.ndimage.morphology.binary_fill_holes(thresh)
coded_paws, num_paws = sp.ndimage.label(filled)
data_slices = sp.ndimage.find_objects(coded_paws)
return object_slices
Blur the input data a bit to make sure the paws have a continuous footprint. (It would be more efficient to just use a larger kernel (the structure kwarg to the various scipy.ndimage.morphology functions) but this isn't quite working properly for some reason...)
Threshold the array so that you have a boolean array of places where the pressure is over some threshold value (i.e. thresh = data > value)
Fill any internal holes, so that you have cleaner regions (filled = sp.ndimage.morphology.binary_fill_holes(thresh))
Find the separate contiguous regions (coded_paws, num_paws = sp.ndimage.label(filled)). This returns an array with the regions coded by number (each region is a contiguous area of a unique integer (1 up to the number of paws) with zeros everywhere else)).
Isolate the contiguous regions using data_slices = sp.ndimage.find_objects(coded_paws). This returns a list of tuples of slice objects, so you could get the region of the data for each paw with [data[x] for x in data_slices]. Instead, we'll draw a rectangle based on these slices, which takes slightly more work.
The two animations below show your "Overlapping Paws" and "Grouped Paws" example data. This method seems to be working perfectly. (And for whatever it's worth, this runs much more smoothly than the GIF images below on my machine, so the paw detection algorithm is fairly fast...)
Here's a full example (now with much more detailed explanations). The vast majority of this is reading the input and making an animation. The actual paw detection is only 5 lines of code.
import numpy as np
import scipy as sp
import scipy.ndimage
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
def animate(input_filename):
"""Detects paws and animates the position and raw data of each frame
in the input file"""
# With matplotlib, it's much, much faster to just update the properties
# of a display object than it is to create a new one, so we'll just update
# the data and position of the same objects throughout this animation...
infile = paw_file(input_filename)
# Since we're making an animation with matplotlib, we need
# ion() instead of show()...
plt.ion()
fig = plt.figure()
ax = fig.add_subplot(111)
fig.suptitle(input_filename)
# Make an image based on the first frame that we'll update later
# (The first frame is never actually displayed)
im = ax.imshow(infile.next()[1])
# Make 4 rectangles that we can later move to the position of each paw
rects = [Rectangle((0,0), 1,1, fc='none', ec='red') for i in range(4)]
[ax.add_patch(rect) for rect in rects]
title = ax.set_title('Time 0.0 ms')
# Process and display each frame
for time, frame in infile:
paw_slices = find_paws(frame)
# Hide any rectangles that might be visible
[rect.set_visible(False) for rect in rects]
# Set the position and size of a rectangle for each paw and display it
for slice, rect in zip(paw_slices, rects):
dy, dx = slice
rect.set_xy((dx.start, dy.start))
rect.set_width(dx.stop - dx.start + 1)
rect.set_height(dy.stop - dy.start + 1)
rect.set_visible(True)
# Update the image data and title of the plot
title.set_text('Time %0.2f ms' % time)
im.set_data(frame)
im.set_clim([frame.min(), frame.max()])
fig.canvas.draw()
def find_paws(data, smooth_radius=5, threshold=0.0001):
"""Detects and isolates contiguous regions in the input array"""
# Blur the input data a bit so the paws have a continous footprint
data = sp.ndimage.uniform_filter(data, smooth_radius)
# Threshold the blurred data (this needs to be a bit > 0 due to the blur)
thresh = data > threshold
# Fill any interior holes in the paws to get cleaner regions...
filled = sp.ndimage.morphology.binary_fill_holes(thresh)
# Label each contiguous paw
coded_paws, num_paws = sp.ndimage.label(filled)
# Isolate the extent of each paw
data_slices = sp.ndimage.find_objects(coded_paws)
return data_slices
def paw_file(filename):
"""Returns a iterator that yields the time and data in each frame
The infile is an ascii file of timesteps formatted similar to this:
Frame 0 (0.00 ms)
0.0 0.0 0.0
0.0 0.0 0.0
Frame 1 (0.53 ms)
0.0 0.0 0.0
0.0 0.0 0.0
...
"""
with open(filename) as infile:
while True:
try:
time, data = read_frame(infile)
yield time, data
except StopIteration:
break
def read_frame(infile):
"""Reads a frame from the infile."""
frame_header = infile.next().strip().split()
time = float(frame_header[-2][1:])
data = []
while True:
line = infile.next().strip().split()
if line == []:
break
data.append(line)
return time, np.array(data, dtype=np.float)
if __name__ == '__main__':
animate('Overlapping paws.bin')
animate('Grouped up paws.bin')
animate('Normal measurement.bin')
Update: As far as identifying which paw is in contact with the sensor at what times, the simplest solution is to just do the same analysis, but use all of the data at once. (i.e. stack the input into a 3D array, and work with it, instead of the individual time frames.) Because SciPy's ndimage functions are meant to work with n-dimensional arrays, we don't have to modify the original paw-finding function at all.
# This uses functions (and imports) in the previous code example!!
def paw_regions(infile):
# Read in and stack all data together into a 3D array
data, time = [], []
for t, frame in paw_file(infile):
time.append(t)
data.append(frame)
data = np.dstack(data)
time = np.asarray(time)
# Find and label the paw impacts
data_slices, coded_paws = find_paws(data, smooth_radius=4)
# Sort by time of initial paw impact... This way we can determine which
# paws are which relative to the first paw with a simple modulo 4.
# (Assuming a 4-legged dog, where all 4 paws contacted the sensor)
data_slices.sort(key=lambda dat_slice: dat_slice[2].start)
# Plot up a simple analysis
fig = plt.figure()
ax1 = fig.add_subplot(2,1,1)
annotate_paw_prints(time, data, data_slices, ax=ax1)
ax2 = fig.add_subplot(2,1,2)
plot_paw_impacts(time, data_slices, ax=ax2)
fig.suptitle(infile)
def plot_paw_impacts(time, data_slices, ax=None):
if ax is None:
ax = plt.gca()
# Group impacts by paw...
for i, dat_slice in enumerate(data_slices):
dx, dy, dt = dat_slice
paw = i%4 + 1
# Draw a bar over the time interval where each paw is in contact
ax.barh(bottom=paw, width=time[dt].ptp(), height=0.2,
left=time[dt].min(), align='center', color='red')
ax.set_yticks(range(1, 5))
ax.set_yticklabels(['Paw 1', 'Paw 2', 'Paw 3', 'Paw 4'])
ax.set_xlabel('Time (ms) Since Beginning of Experiment')
ax.yaxis.grid(True)
ax.set_title('Periods of Paw Contact')
def annotate_paw_prints(time, data, data_slices, ax=None):
if ax is None:
ax = plt.gca()
# Display all paw impacts (sum over time)
ax.imshow(data.sum(axis=2).T)
# Annotate each impact with which paw it is
# (Relative to the first paw to hit the sensor)
x, y = [], []
for i, region in enumerate(data_slices):
dx, dy, dz = region
# Get x,y center of slice...
x0 = 0.5 * (dx.start + dx.stop)
y0 = 0.5 * (dy.start + dy.stop)
x.append(x0); y.append(y0)
# Annotate the paw impacts
ax.annotate('Paw %i' % (i%4 +1), (x0, y0),
color='red', ha='center', va='bottom')
# Plot line connecting paw impacts
ax.plot(x,y, '-wo')
ax.axis('image')
ax.set_title('Order of Steps')
I'm no expert in image detection, and I don't know Python, but I'll give it a whack...
To detect individual paws, you should first only select everything with a pressure greater than some small threshold, very close to no pressure at all. Every pixel/point that is above this should be "marked." Then, every pixel adjacent to all "marked" pixels becomes marked, and this process is repeated a few times. Masses that are totally connected would be formed, so you have distinct objects. Then, each "object" has a minimum and maximum x and y value, so bounding boxes can be packed neatly around them.
Pseudocode:
(MARK) ALL PIXELS ABOVE (0.5)
(MARK) ALL PIXELS (ADJACENT) TO (MARK) PIXELS
REPEAT (STEP 2) (5) TIMES
SEPARATE EACH TOTALLY CONNECTED MASS INTO A SINGLE OBJECT
MARK THE EDGES OF EACH OBJECT, AND CUT APART TO FORM SLICES.
That should about do it.
Note: I say pixel, but this could be regions using an average of the pixels. Optimization is another issue...
Sounds like you need to analyze a function (pressure over time) for each pixel and determine where the function turns (when it changes > X in the other direction it is considered a turn to counter errors).
If you know at what frames it turns, you will know the frame where the pressure was the most hard and you will know where it was the least hard between the two paws. In theory, you then would know the two frames where the paws pressed the most hard and can calculate an average of those intervals.
after which I'll get to the problem of deciding which paw it is!
This is the same tour as before, knowing when each paw applies the most pressure helps you decide.
Related
I have a square 2D array data that I would like to add to a larger 2D array frame at some given set of non-integer coordinates coords. The idea is that data will be interpolated onto frame with it's center at the new coordinates.
Some toy data:
# A gaussian to add to the frame
x, y = np.meshgrid(np.linspace(-1,1,10), np.linspace(-1,1,10))
data = 50*np.exp(-np.sqrt(x**2+y**2)**2)
# The frame to add the gaussian to
frame = np.random.normal(size=(100,50))
# The desired (x,y) location of the gaussian center on the new frame
coords = 23.4, 22.6
Here's the idea. I want to add this:
to this:
to get this:
If the coordinates were integers (indexes), of course I could simply add them like this:
frame[23:33,22:32] += data
But I want to be able to specify non-integer coordinates so that data is regridded and added to frame.
I've looked into PIL.Image methods but my use case is just for 2D data, not images. Is there a way to do this with just scipy? Can this be done with interp2d or a similar function? Any guidance would be greatly appreciated!
Scipy's shift function from scipy.ndimage.interpolation is what you are looking for, as long as the grid spacings between data and frame overlap. If not, look to the other answer. The shift function can take floating point numbers as input and will do a spline interpolation. First, I put the data into an array as large as frame, then shift it, and then add it. Make sure to reverse the coordinate list, as x is the rightmost dimension in numpy arrays. One of the nice features of shift is that it sets to zero those values that go out of bounds.
import numpy as np
import matplotlib.pyplot as plt
from scipy.ndimage.interpolation import shift
# A gaussian to add to the frame.
x, y = np.meshgrid(np.linspace(-1,1,10), np.linspace(-1,1,10))
data = 50*np.exp(-np.sqrt(x**2+y**2)**2)
# The frame to add the gaussian to
frame = np.random.normal(size=(100,50))
x_frame = np.arange(50)
y_frame = np.arange(100)
# The desired (x,y) location of the gaussian center on the new frame.
coords = np.array([23.4, 22.6])
# First, create a frame as large as the frame.
data_large = np.zeros(frame.shape)
data_large[:data.shape[0], :data.shape[1]] = data[:,:]
# Subtract half the distance as the bottom left is at 0,0 instead of the center.
# The shift of 4.5 is because data is 10 points wide.
# Reverse the coords array as x is the last coordinate.
coords_shift = -4.5
data_large = shift(data_large, coords[::-1] + coords_shift)
frame += data_large
# Plot the result and add lines to indicate to coordinates
plt.figure()
plt.pcolormesh(x_frame, y_frame, frame, cmap=plt.cm.jet)
plt.axhline(coords[1], color='w')
plt.axvline(coords[0], color='w')
plt.colorbar()
plt.gca().invert_yaxis()
plt.show()
The script gives you the following figure, which has the desired coordinates indicated with white dotted lines.
One possible solution is to use scipy.interpolate.RectBivariateSpline. In the code below, x_0 and y_0 are the coordinates of a feature from data (i.e., the position of the center of the Gaussian in your example) that need to be mapped to the coordinates given by coords. There are a couple of advantages to this approach:
If you need to "place" the same object into multiple locations in the output frame, the spline needs to be computed only once (but evaluated multiple times).
In case you actually need to compute integrated flux of the model over a pixel, you can use the integral method of scipy.interpolate.RectBivariateSpline.
Resample using spline interpolation:
from scipy.interpolate import RectBivariateSpline
x = np.arange(data.shape[1], dtype=np.float)
y = np.arange(data.shape[0], dtype=np.float)
kx = 3; ky = 3; # spline degree
spline = RectBivariateSpline(
x, y, data.T, kx=kx, ky=ky, s=0
)
# Define coordinates of a feature in the data array.
# This can be the center of the Gaussian:
x_0 = (data.shape[1] - 1.0) / 2.0
y_0 = (data.shape[0] - 1.0) / 2.0
# create output grid, shifted as necessary:
yg, xg = np.indices(frame.shape, dtype=np.float64)
xg += x_0 - coords[0] # see below how to account for pixel scale change
yg += y_0 - coords[1] # see below how to account for pixel scale change
# resample and fill extrapolated points with 0:
resampled_data = spline.ev(xg, yg)
extrapol = (((xg < -0.5) | (xg >= data.shape[1] - 0.5)) |
((yg < -0.5) | (yg >= data.shape[0] - 0.5)))
resampled_data[extrapol] = 0
Now plot the frame and resampled data:
plt.figure(figsize=(14, 14));
plt.imshow(frame+resampled_data, cmap=plt.cm.jet,
origin='upper', interpolation='none', aspect='equal')
plt.show()
If you also want to allow for scale changes, then replace code for computing xg and yg above with:
coords = 20, 80 # change coords to easily identifiable (in plot) values
zoom_x = 2 # example scale change along X axis
zoom_y = 3 # example scale change along Y axis
yg, xg = np.indices(frame.shape, dtype=np.float64)
xg = (xg - coords[0]) / zoom_x + x_0
yg = (yg - coords[1]) / zoom_y + y_0
Most likely this is what you actually want based on your example. Specifically, the coordinates of pixels in data are "spaced" by 0.222(2) distance units. Therefore it actually seems that for your particular example (whether accidental or intentional), you have a zoom factor of 0.222(2). In that case your data image would shrink to almost 2 pixels in the output frame.
Comparison to #Chiel answer
In the image below, I compare the results from my method (left), #Chiel's method (center) and difference (right panel):
Fundamentally, the two methods are quite similar and possibly even use the same algorithm (I did not look at the code for shift but based on the description - it also uses splines). From comparison image it is visible that the biggest differences are at the edges and, for unknown to me reasons, shift seems to truncate the shifted image slightly too soon.
I think the biggest difference is that my method allows for pixel scale changes and it also allows re-use of the same interpolator to place the original image at different locations in the output frame. #Chiel's method is somewhat simpler but (what I did not like about it is that) it requires creation of a larger array (data_large) into which the original image is placed in the corner.
While the other answers have gone into detail, but here's my lazy solution:
xc,yc = 23.4, 22.6
x, y = np.meshgrid(np.linspace(-1,1,10)-xc%1, np.linspace(-1,1,10)-yc%1)
data = 50*np.exp(-np.sqrt(x**2+y**2)**2)
frame = np.random.normal(size=(100,50))
frame[23:33,22:32] += data
And it's the way you liked it. As you mentioned, the coordinates of both are the same, so the origin of data is somewhere between the indices. Now just simply shift it by the amount you want it to be off a grid point (remainder to one) in the second line and you're good to go (you might need to flip the sign, but I think this is correct).
I have quite a few sensors in the field that measure water pressure. In the past the height of these sensors have been changed quite a few times creating jumps in the timeseries. Since these timeseries are continuous and I have a manual measurement I should technically be able to remove the jumps (by hand this is easy, but there are too many measurements so I need to do it in python).
I've tried removing the jumps using a median filter but this doesn't really work.
My code:
# filter out noise in signal (peaks)
minimumPeak = 0.03 # filter peaks larger than 0.03m
filtered_value = np.array(im.median_filter(data['value'], 5))
noise = np.array((filtered_value-data['value']).abs() > minimumPeak)
data.loc[noise, 'value'] = filtered_value[noise]
data is pandas dataframe containing two columns: 'datetime' and 'value'.
I've also tried to do this manually and got it working in a simple case, but not well in any other. Any idea how I would filter out the jumps?
An example is shown in the picture below (yellow indicating the jumps, red the measurement by hand (it is very well possible that this measurement is not in the beginning as it is in this example))
You have sharp peaks and steps in your data. I guess you want to
remove the peaks and replace by some averaged values
remove the steps by cumulative changing the offset of the remaining data values
That's in line with what you said in your last comment. Please note, that this will alter (shift) big parts of your data!
It's important to recognize that the width of both, peaks and steps, is one pixel in your data. Also you can handle both effects pretty much independently.
I suggest to first remove the peaks, then remove the steps.
Remove peaks by calculating the absolute difference to the previous and to the next data value, then take the minimum of both, i.e. if your data series is y(i) compute p(i)=min(abs(y(i)-y(i-1)), abs(y(i+1)-y(i))). All values above a threshold are peaks. Take them and replace the data values with the mean of the previous and the next pixel like.
Now remove the steps, again by looking for absolute differences of consecutive values (as suggested in the comment by AreTor), s(i)=abs(y(i)-y(i-1)) and look for values above a certain threshold. The positions are the step positions. Create an zero-valued offset array of the same size, then insert the differences of the data points (without the absolute value), then form the cumulative sum and subtract the result from the original data to remove the steps.
Please note that this removes peaks and steps which go up as well as down. If you want to remove only one kind, just don't take the absolute value.
You can try it like this:
import numpy as np
import matplotlib.pyplot as plt
import h5py
%matplotlib inline
# I'm not sure that you need all of this packedges
filepath = 'measurment.hdf5'
with h5py.File(filepath, 'r') as hdf:
data_y = hdf['y'][:]
data_x = hdf['x'][:]
data = data_y
delta_max = 1 # maximum difference in y between two points
delta = 0 # running correction value
data_cor = [] # corrected array
data_cor.append(data[0:1]) # we append two first points
for i in range(len(data_x)-2): # two first points are allready appended
i += 2
delta_i = data[i] - data[i-1]
if np.abs(delta_i) > delta_max:
delta += (delta_i - (data_cor[i-1] - data_cor[i-2]))
data_cor.append(data[i]-delta)
else:
data_cor.append(data[i]-delta)
plt.plot(data_x, data_cor)
I am creating a simulation of diffusion in a complex system taking arbitrary images as a substrate and allowing arbitrary creation of diffusion fronts and allowing both surface reactions as well as deposition of new material on the starting substrates. The results I'm quite proud of so far, and you can check out the movies I made with it here for CVD and SFD deposition on particles.
CVD Movie
SFD Movie
Unfortunately I cannot generate more than 50 or so frames because it runs out of memory. I have tried clearing things as much as possible throughout the simulation, but I think I must be missing something. To summarize:
I start out by creating an empty list
ims = []
Then, each time my "simulation" runs, if frame number % frame "rate" == 0, it generates a frame which is:
displayed using plt.ion() through plt.draw() and
uses ims.append() to add the rendered plot to an array of animated frames.
Before each frame render, I run plt.clf() to prevent the plot from just having increasing numbers of overlaid plots.
Without the ims.append() step, the code consumes between 140 and 170MB of RAM. With that step, 50 frames consumes nearly 1.4GB of RAM. Obviously, this is very limiting. 50 frames is nice, but I'd really like at least 350. That may be impossible with this route, but this suggests a memory usage purely by the ims array of roughly 24MB per frame.
A workaround is to create the frame and render it to an .svg or .png file inside the loop and save it to disk. I find that this rendering process is very CPU intensive so doing that often makes the code quite slow. Additionally, creating 350 PNG files and then converting them manually into a video is pretty messy, so I'd love to somehow get it all inside of the program itself.
Does anyone have an idea for how to decrease the memory usage of this example code without resorting to rendering and writing each frame to disk?
In this toy code, I just used a random number generator to populate the two datasets as described in the comments to speed things up.
The code:
import matplotlib.pyplot as plt
import matplotlib.animation as anim
from numpy import *
from matplotlib import *
import time
# Defines the number of frames of animation to render.
outputframes = 50
# Defines the size of the canned simulation.
nx = 800
ny = 800
# Defines the number of actual simulation timesteps
nt = 100
# This gets the number of timesteps between outputframes.
framestep = 2
# For reporting.
framenum = 0
# Creates two steps, one for the stepped simulated step,
# and one for the prior state. There are two independently
# changing materials, each of which will have half the simulation
# space containing random values here, plus 10% overlap in the
# middle.
p1 = zeros((nx, ny, 2))
p1[360:800,:,0] = random.rand(440, ny)
p2 = zeros((nx, ny, 2))
p2[0:440,:,0] = random.rand(440, ny)
# Animation colormap setup
norm = colors.Normalize(vmin=0, vmax = 1)
# And sets up two corresponding colormaps, one blue and one
# red for p1 and p2 respectively (goal is overlaid).
cmap1 = cm.Blues
cmap2 = cm.Reds
# Sets up an empty array to hold animation frames.
ims = []
# Sets up and uses ion to draw the figure without blocking.
plt.ion()
fig = plt.figure()
plt.draw()
# Run the simulation.
for t in range(nt):
# This looks to see how far we are, and if we're at a point
# where t is an even multiple of framestep, we should render
# a new frame.
if (t%framestep == 0):
print('Frame ' + str(framenum))
framenum = framenum + 1
plt.clf()
# In here I did a bunch of stuff to get special colors in
# the colormap to get substrates and surfaces and other
# features clearly identified. I am creating a new frame1
# and frame2 object because in reality I will be doing a
# log plot math to convert to the graphic frame.
frame1 = p1[:,:,0]
# This part is necessary in my real program because
# I manually modify the colormap after it's created
# to include the above mentioned special colors.
frame1_colors = cmap1(norm(frame1))
# This is my (not quite right) attempt to do overlaid plots.
plt.imshow(frame1_colors, alpha = 0.5)
# Do the same for the second set of data.
frame2 = p2[:,:,0]
frame2_colors = cmap2(norm(frame2))
# The goal here was to take the combined output and make
# it into an animation frame to append to ims, the image
# array.
# This is where I start to run into problems. Without the
# ims.append, the program has constant memory usage. With
# it, I am using 1340MB by the 50th frame. This is the
# biggest issue. Even throwing away all other simulation
# data, this image array for animation is *enormous*.
# With the ims.append line replaced with the plt.imshow
# line alone, memory usage is much smaller, ranging from
# 140-170MB depending on execution point, but relatively
# constant.
ims.append([plt.imshow(frame2_colors, alpha = 0.5)])
# plt.imshow(frame2_colors, alpha = 0.5)
# Then try to draw updating animation to show progress
# using draw(). As best I can tell, this basically works,
# in that the plot is displaying with all components.
plt.draw()
# I'll put in a timer so that this doesn't go too fast, since
# the actual calculation is very complex.
time.sleep(0.01)
# Proxy for the actual calculation. Just overwrite with new
# random data in the overlapping ranges to show some change
# visually.
p1[360:800,:,1] = random.rand(440, ny)
p2[0:440,:,1] = random.rand(440, ny)
# In this version, it is trivial, but in the real simulation
# p1[:,:,1] does not end up equal to p1[:,:,0], so the following
# resets the simulation for the next timestep, overwriting the
# old values to avoid memory overflow from the p1 and p2 arrays
# being enormous.
# Copy new values into old values.
p1[:,:,0] = p1[:,:,1]
p2[:,:,0] = p2[:,:,1]
# This is just a repeat for the final frame.
plt.clf()
frame1 = p1[:,:,0]
frame1_colors = cmap1(norm(frame1))
plt.imshow(frame1_colors, alpha = 0.5)
frame2 = p2[:,:,0]
frame2_colors = cmap2(norm(frame2))
# As above, the ims.append uses tons of memory, the imshow alone works well.
ims.append([plt.imshow(frame2_colors, alpha = 0.5)])
# plt.imshow(frame2_colors, alpha = 0.5)
plt.draw()
anim = anim.ArtistAnimation(fig, ims, blit=True)
anim.save('test.mp4', fps=10, writer='avconv')
In the end, I decided the only reasonable way to do this was by rendering each frame I needed to disk as a .png and then generating a movie from the images afterwards with avconv.
Thanks for all the suggestions, but it looks like this is just a limitation due to the RAM usage of uncompressed images.
I have two 2D numpy arrays (of the same dimensions) that I am plotting using matplotlib. The first array I've plotted as a color map in gray-scale. The second one represents an aperture, but it is an irregular shape (some of the pixels get outlined, and it is a set of horizontal and vertical lines that form the outline). I am not sure how to ask it to plot this second array. The array is composed of three numbers (0, 1, and 3), and I only need the pixels of one value (3) to be outlined, but I need the outline to encompass the region of these pixels, not the pixels individually. I need the interior of all the pixels to remain transparent so that I can see the gray-scale color map through it.
Does anyone know how to accomplish this?
That is an interesting question, if I understood it correctly. In order to make sure what you mean, you would like to draw a line with some color around all contiguous areas where the pixel value is 3.
I do not think there is a ready-made function for that, but let's not let that stop us. We will need to create our own function.
We can start by creating a boolean map of the area which needs to be outlined:
import numpy as np
import matplotlib.pyplot as plt
# our image with the numbers 1-3 is in array maskimg
# create a boolean image map which has trues only where maskimg[x,y] == 3
mapimg = (maskimg == 3)
# a vertical line segment is needed, when the pixels next to each other horizontally
# belong to diffferent groups (one is part of the mask, the other isn't)
# after this ver_seg has two arrays, one for row coordinates, the other for column coordinates
ver_seg = np.where(mapimg[:,1:] != mapimg[:,:-1])
# the same is repeated for horizontal segments
hor_seg = np.where(mapimg[1:,:] != mapimg[:-1,:])
# if we have a horizontal segment at 7,2, it means that it must be drawn between pixels
# (2,7) and (2,8), i.e. from (2,8)..(3,8)
# in order to draw a discountinuous line, we add Nones in between segments
l = []
for p in zip(*hor_seg):
l.append((p[1], p[0]+1))
l.append((p[1]+1, p[0]+1))
l.append((np.nan,np.nan))
# and the same for vertical segments
for p in zip(*ver_seg):
l.append((p[1]+1, p[0]))
l.append((p[1]+1, p[0]+1))
l.append((np.nan, np.nan))
# now we transform the list into a numpy array of Nx2 shape
segments = np.array(l)
# now we need to know something about the image which is shown
# at this point let's assume it has extents (x0, y0)..(x1,y1) on the axis
# drawn with origin='lower'
# with this information we can rescale our points
segments[:,0] = x0 + (x1-x0) * segments[:,0] / mapimg.shape[1]
segments[:,1] = y0 + (y1-y0) * segments[:,1] / mapimg.shape[0]
# and now there isn't anything else to do than plot it
plt.plot(segments[:,0], segments[:,1], color=(1,0,0,.5), linewidth=3)
Let us test this by generating some data and showing it:
image = np.cumsum(np.random.random((20,20))-.5, axis=1)
maskimg = np.zeros(image.shape, dtype='int')
maskimg[image > 0] = 3
x0 = -1.5
x1 = 1.5
y0 = 2.3
y1 = 3.8
plt.figure()
plt.imshow(maskimg, origin='lower', extent=[x0,x1,y0,y1], cmap=plt.cm.gray, interpolation='nearest')
plt.axis('tight')
After that we run the procedure on the top, and get:
The code can be made much denser, if needed, but now comments take a lot of space. With large images it might be wise to optimize the image segment creation by finding continuous paths. That will reduce the number of points to plot by a factor of up to three. However, doing that requires a bit different code, which is not as clear as this one. (If there will appear comments asking for that and an appropriate number of upvotes, I'll add it :)
I'm trying to get python to return, as close as possible, the center of the most obvious clustering in an image like the one below:
In my previous question I asked how to get the global maximum and the local maximums of a 2d array, and the answers given worked perfectly. The issue is that the center estimation I can get by averaging the global maximum obtained with different bin sizes is always slightly off than the one I would set by eye, because I'm only accounting for the biggest bin instead of a group of biggest bins (like one does by eye).
I tried adapting the answer to this question to my problem, but it turns out my image is too noisy for that algorithm to work. Here's my code implementing that answer:
import numpy as np
from scipy.ndimage.filters import maximum_filter
from scipy.ndimage.morphology import generate_binary_structure, binary_erosion
import matplotlib.pyplot as pp
from os import getcwd
from os.path import join, realpath, dirname
# Save path to dir where this code exists.
mypath = realpath(join(getcwd(), dirname(__file__)))
myfile = 'data_file.dat'
x, y = np.loadtxt(join(mypath,myfile), usecols=(1, 2), unpack=True)
xmin, xmax = min(x), max(x)
ymin, ymax = min(y), max(y)
rang = [[xmin, xmax], [ymin, ymax]]
paws = []
for d_b in range(25, 110, 25):
# Number of bins in x,y given the bin width 'd_b'
binsxy = [int((xmax - xmin) / d_b), int((ymax - ymin) / d_b)]
H, xedges, yedges = np.histogram2d(x, y, range=rang, bins=binsxy)
paws.append(H)
def detect_peaks(image):
"""
Takes an image and detect the peaks usingthe local maximum filter.
Returns a boolean mask of the peaks (i.e. 1 when
the pixel's value is the neighborhood maximum, 0 otherwise)
"""
# define an 8-connected neighborhood
neighborhood = generate_binary_structure(2,2)
#apply the local maximum filter; all pixel of maximal value
#in their neighborhood are set to 1
local_max = maximum_filter(image, footprint=neighborhood)==image
#local_max is a mask that contains the peaks we are
#looking for, but also the background.
#In order to isolate the peaks we must remove the background from the mask.
#we create the mask of the background
background = (image==0)
#a little technicality: we must erode the background in order to
#successfully subtract it form local_max, otherwise a line will
#appear along the background border (artifact of the local maximum filter)
eroded_background = binary_erosion(background, structure=neighborhood, border_value=1)
#we obtain the final mask, containing only peaks,
#by removing the background from the local_max mask
detected_peaks = local_max - eroded_background
return detected_peaks
#applying the detection and plotting results
for i, paw in enumerate(paws):
detected_peaks = detect_peaks(paw)
pp.subplot(4,2,(2*i+1))
pp.imshow(paw)
pp.subplot(4,2,(2*i+2) )
pp.imshow(detected_peaks)
pp.show()
and here's the result of that (varying the bin size):
Clearly my background is too noisy for that algorithm to work, so the question is: how can I make that algorithm less sensitive? If an alternative solution exists then please let me know.
EDIT
Following Bi Rico advise I attempted smoothing my 2d array before passing it on to the local maximum finder, like so:
H, xedges, yedges = np.histogram2d(x, y, range=rang, bins=binsxy)
H1 = gaussian_filter(H, 2, mode='nearest')
paws.append(H1)
These were the results with a sigma of 2, 4 and 8:
EDIT 2
A mode ='constant' seems to work much better than nearest. It converges to the right center with a sigma=2 for the largest bin size:
So, how do I get the coordinates of the maximum that shows in the last image?
Answering the last part of your question, always you have points in an image, you can find their coordinates by searching, in some order, the local maximums of the image. In case your data is not a point source, you can apply a mask to each peak in order to avoid the peak neighborhood from being a maximum while performing a future search. I propose the following code:
import matplotlib.image as mpimg
import matplotlib.pyplot as plt
import numpy as np
import copy
def get_std(image):
return np.std(image)
def get_max(image,sigma,alpha=20,size=10):
i_out = []
j_out = []
image_temp = copy.deepcopy(image)
while True:
k = np.argmax(image_temp)
j,i = np.unravel_index(k, image_temp.shape)
if(image_temp[j,i] >= alpha*sigma):
i_out.append(i)
j_out.append(j)
x = np.arange(i-size, i+size)
y = np.arange(j-size, j+size)
xv,yv = np.meshgrid(x,y)
image_temp[yv.clip(0,image_temp.shape[0]-1),
xv.clip(0,image_temp.shape[1]-1) ] = 0
print xv
else:
break
return i_out,j_out
#reading the image
image = mpimg.imread('ggd4.jpg')
#computing the standard deviation of the image
sigma = get_std(image)
#getting the peaks
i,j = get_max(image[:,:,0],sigma, alpha=10, size=10)
#let's see the results
plt.imshow(image, origin='lower')
plt.plot(i,j,'ro', markersize=10, alpha=0.5)
plt.show()
The image ggd4 for the test can be downloaded from:
http://www.ipac.caltech.edu/2mass/gallery/spr99/ggd4.jpg
The first part is to get some information about the noise in the image. I did it by computing the standard deviation of the full image (actually is better to select an small rectangle without signal). This is telling us how much noise is present in the image.
The idea to get the peaks is to ask for successive maximums, which are above of certain threshold (let's say, 3, 4, 5, 10, or 20 times the noise). This is what the function get_max is actually doing. It performs the search of maximums until one of them is below the threshold imposed by the noise. In order to avoid finding the same maximum many times it is necessary to remove the peaks from the image. In the general way, the shape of the mask to do so depends strongly on the problem that one want to solve. for the case of stars, it should be good to remove the star by using a Gaussian function, or something similar. I have chosen for simplicity a square function, and the size of the function (in pixels) is the variable "size".
I think that from this example, anybody can improve the code by adding more general things.
EDIT:
The original image looks like:
While the image after identifying the luminous points looks like this:
Too much of a n00b on Stack Overflow to comment on Alejandro's answer elsewhere here. I would refine his code a bit to use a preallocated numpy array for output:
def get_max(image,sigma,alpha=3,size=10):
from copy import deepcopy
import numpy as np
# preallocate a lot of peak storage
k_arr = np.zeros((10000,2))
image_temp = deepcopy(image)
peak_ct=0
while True:
k = np.argmax(image_temp)
j,i = np.unravel_index(k, image_temp.shape)
if(image_temp[j,i] >= alpha*sigma):
k_arr[peak_ct]=[j,i]
# this is the part that masks already-found peaks.
x = np.arange(i-size, i+size)
y = np.arange(j-size, j+size)
xv,yv = np.meshgrid(x,y)
# the clip here handles edge cases where the peak is near the
# image edge
image_temp[yv.clip(0,image_temp.shape[0]-1),
xv.clip(0,image_temp.shape[1]-1) ] = 0
peak_ct+=1
else:
break
# trim the output for only what we've actually found
return k_arr[:peak_ct]
In profiling this and Alejandro's code using his example image, this code about 33% faster (0.03 sec for Alejandro's code, 0.02 sec for mine.) I expect on images with larger numbers of peaks, it would be even faster - appending the output to a list will get slower and slower for more peaks.
I think the first step needed here is to express the values in H in terms of the standard deviation of the field:
import numpy as np
H = H / np.std(H)
Now you can put a threshold on the values of this H. If the noise is assumed to be Gaussian, picking a threshold of 3 you can be quite sure (99.7%) that this pixel can be associated with a real peak and not noise. See here.
Now the further selection can start. It is not exactly clear to me what exactly you want to find. Do you want the exact location of peak values? Or do you want one location for a cluster of peaks which is in the middle of this cluster?
Anyway, starting from this point with all pixel values expressed in standard deviations of the field, you should be able to get what you want. If you want to find clusters you could perform a nearest neighbour search on the >3-sigma gridpoints and put a threshold on the distance. I.e. only connect them when they are close enough to each other. If several gridpoints are connected you can define this as a group/cluster and calculate some (sigma-weighted?) center of the cluster.
Hope my first contribution on Stackoverflow is useful for you!
The way I would do it:
1) normalize H between 0 and 1.
2) pick a threshold value, as tcaswell suggests. It could be between .9 and .99 for example
3) use masked arrays to keep only the x,y coordinates with H above threshold:
import numpy.ma as ma
x_masked=ma.masked_array(x, mask= H < thresold)
y_masked=ma.masked_array(y, mask= H < thresold)
4) now you can weight-average on the masked coordinates, with weight something like (H-threshold)^2, or any other power greater or equal to one, depending on your taste/tests.
Comment:
1) This is not robust with respect to the type of peaks you have, since you may have to adapt the thresold. This is the minor problem;
2) This DOES NOT work with two peaks as it is, and will give wrong results if the 2nd peak is above threshold.
Nonetheless, it will always give you an answer without crashing (with pros and cons of the thing..)
I'm adding this answer because it's the solution I ended up using. It's a combination of Bi Rico's comment here (May 30 at 18:54) and the answer given in this question: Find peak of 2d histogram.
As it turns out using the peak detection algorithm from this question Peak detection in a 2D array only complicates matters. After applying the Gaussian filter to the image all that needs to be done is to ask for the maximum bin (as Bi Rico pointed out) and then obtain the maximum in coordinates.
So instead of using the detect-peaks function as I did above, I simply add the following code after the Gaussian 2D histogram is obtained:
# Get 2D histogram.
H, xedges, yedges = np.histogram2d(x, y, range=rang, bins=binsxy)
# Get Gaussian filtered 2D histogram.
H1 = gaussian_filter(H, 2, mode='nearest')
# Get center of maximum in bin coordinates.
x_cent_bin, y_cent_bin = np.unravel_index(H1.argmax(), H1.shape)
# Get center in x,y coordinates.
x_cent_coor , y_cent_coord = np.average(xedges[x_cent_bin:x_cent_bin + 2]), np.average(yedges[y_cent_g:y_cent_g + 2])