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I am trying to find the main 200 components of a datasets of 846 images (2048x2048x3 RGB) with sklearn.decomposition.IncrementalPCA.
Data are read by cv2 and reshaped into a 2d np array ([846,2048x2048x3] size, float16)
To ensure a smaller memory cost, I used partial_fit() and divide the original data into smaller chunks (batches) in both partial_fit() and transform() steps.
just like the way in this problem's solution:
Python PCA on Matrix too large to fit into memory
Now my code works well for relative smaller size computations, like computing 20 components for 200 images in the datasets. It outputs right outcomes.
However, the tasks demands me to compute 200 components, which leads to the limit that my batch's size should be larger or at least equal to 200. (according to sklearn's document and the information in the terminal when running the code)
https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.IncrementalPCA.html
With such big chunk size,I can finish the IPCA model set, but always face MemoryError when doing partial_fit()
What's more, another problem is:
I need to use inverse_transform later, I am not sure if I can use chunk-style compute in this step or not. (In the code below I did not use it.)
What can I do to avoid this MemoryError? Or should I replace IncrementalPCA with some other method instead ? (these alternatives should have some method like inverse_transform())
The all memory I can access to is 131661572 kB(~127GB)
My code:
from sklearn.decomposition import PCA, IncrementalPCA
import numpy as np
import cv2
import os
folder_path = "./output_img"
input=[]
for i in range(1, 847):
if i%10 == 0: print("loading",i,"th image")
# if i == 60: continue #special case, should be skipped
image_path = folder_path+f"/{i}neutral.jpg"
img = cv2.imread(image_path)
input.append(img.reshape(-1))
print("Loaded all",i,"images")
# change into numpy matrix
all_image = np.stack(input,axis=0)
# trans to 0-1 format float64
all_image = (all_image.astype(np.float16))
### shape: #_of_imag x image_pixel_num (50331648 for img_normals case)
# print(all_image)
# print(all_image.shape)
# PCA, keeps 200 features
COM_NUM=200
pca=IncrementalPCA(n_components = COM_NUM)
print("finished IPCA model set")
saving_path = "./principle847"
element_num = all_image.shape[0] # how many elements(rows) we have in the dataset
chunk_size = 220 # how many elements we feed to IPCA at a time
for i in range(0, element_num//chunk_size):
pca.partial_fit(all_image[i*chunk_size : (i+1)*chunk_size])
print("finished PCA fit:",i*chunk_size,"to",(i+1)*chunk_size)
pca.partial_fit(all_image[(i+1)*chunk_size : element_num]) #tail
print("finished PCA fit:",(i+1)*chunk_size,"to",element_num)
for i in range(0, element_num//chunk_size):
if i==0:
result = pca.transform(all_image[i*chunk_size : (i+1)*chunk_size])
else:
tmp = pca.transform(all_image[i*chunk_size : (i+1)*chunk_size])
result = np.concatenate((result, tmp), axis=0)
print("finished PCA transform:",i*chunk_size,"to",(i+1)*chunk_size)
tmp = pca.transform(all_image[(i+1)*chunk_size : element_num]) #tail
result = np.concatenate((result, tmp), axis=0)
print("finished PCA transform:",(i+1)*chunk_size,"to",element_num)
result = pca.inverse_transform(result)
print("PCA mean:",pca.mean_)
mean_img = pca.mean_
mean_img = mean_img.reshape(2048,2048,3)
mean_img = mean_img.astype(np.uint8)
cv2.imwrite(os.path.join(saving_path,("mean.png")),mean_img)
result=result.reshape(-1,2048,2048,3)
# result shape: #_of_componets * 2048 * 2048 * 3
dst = result
# dst=result/np.linalg.norm(result,axis=(3),keepdims=True)
for j in range(0,COM_NUM):
reconImage = (dst)[j]
# reconImage = reconImage.reshape(4096,4096,3)
reconImage = np.clip(reconImage,0,255)
reconImage = reconImage.astype(np.uint8)
cv2.imwrite(os.path.join(saving_path,("p"+str(j)+".png")),reconImage)
print("Saved",j+1,"principle imgs")
The error goes like:
File "model_generate.py", line 36, in <module>
pca.partial_fit(all_image[i*chunk_size : (i+1)*chunk_size])
File "/root/anaconda3/envs/PCA/lib/python3.8/site-packages/sklearn/decomposition/_incremental_pca.py", line 299, in partial_fit
U, V = svd_flip(U, V, u_based_decision=False)
File "/root/anaconda3/envs/PCA/lib/python3.8/site-packages/sklearn/utils/extmath.py", line 538, in svd_flip
max_abs_rows = np.argmax(np.abs(v), axis=1)
File "/root/anaconda3/envs/PCA/lib/python3.8/site-packages/numpy/core/fromnumeric.py", line 1103, in argmax
return _wrapfunc(a, 'argmax', axis=axis, out=out)
File "/root/anaconda3/envs/PCA/lib/python3.8/site-packages/numpy/core/fromnumeric.py", line 56, in _wrapfunc
return getattr(obj, method)(*args, **kwds)
MemoryError
I have a pan-tilt-zoom camera (changing focal length over time). There is no idea about its base focal length (e.g. focal length in time point 0). However, It is possible to track the change in focal length between frame and another based on some known constraints and assumptions (Doing a SLAM).
If I assume a random focal length (in pixel unit), for example, 1000 pixel. Then, the new focal lengths are tracked frame by frame. Would I get correct results relatively? Would the results (focal lengths) in each frame be correct up to scale to the ground truth focal length?
For pan and tilt, assuming 0 at start would be valid. Although it is not correct, The estimated values of new tili-pan will be correct up to an offset. However, I suspect the estimated focal length will not be even correct up to scale or offset.. Is it correct or not?
For a quick short answer - if pan-tilt-zoom camera is approximated as a thin lens, then this is the relation between distance (z) and focal length (f):
This is just an approximation. Not fully correct. For more precise calculations, see the camera matrix. Focal length is an intrinsic parameter in the camera matrix. Even if not known, it can be calculated using some camera calibration method such as DLT, Zhang's Method and RANSAC. Once you have the camera matrix, focal length is just a small part of it. You get many more useful things along with it.
OpenCV has an inbuilt implementation of Zhang's method. (Look at this documentation for explanations, but code is old and unusable. New up-to-date code below.) You need to take some pictures of a chess board through your camera. Here is some helper code:
import cv2
from matplotlib import pyplot as plt
import numpy as np
from glob import glob
from scipy import linalg
x,y = np.meshgrid(range(6),range(8))
world_points=np.hstack((x.reshape(48,1),y.reshape(48,1),np.zeros((48,1)))).astype(np.float32)
_3d_points=[]
_2d_points=[]
img_paths=glob('./*.JPG') #get paths of all checkerboard images
for path in img_paths:
im=cv2.imread(path)
ret, corners = cv2.findChessboardCorners(im, (6,8))
if ret: #add points only if checkerboard was correctly detected:
_2d_points.append(corners) #append current 2D points
_3d_points.append(world_points) #3D points are always the same
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(_3d_points, _2d_points, (im.shape[1],im.shape[0]), None, None)
print ("Ret:\n",ret)
print ("Mtx:\n",mtx)
print ("Dist:\n",dist)
You might want Undistortion: Correcting for Radial Distortion
# termination criteria
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
# prepare object points, like (0,0,0), (1,0,0), (2,0,0) ....,(6,5,0)
objp = np.zeros((6*8,3), np.float32)
objp[:,:2] = np.mgrid[0:6,0:8].T.reshape(-1,2)
# Arrays to store object points and image points from all the images.
objpoints = [] # 3d point in real world space
imgpoints = [] # 2d points in image plane.
for fname in img_paths:
img = cv2.imread(fname)
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
# Find the chess board corners
ret, corners = cv2.findChessboardCorners(gray, (6,8),None)
# If found, add object points, image points (after refining them)
if ret == True:
objpoints.append(objp)
cv2.cornerSubPix(gray,corners,(11,11),(-1,-1),criteria)
imgpoints.append(corners)
if 'IMG_5456.JPG' in fname:
plt.figure(figsize=(20,10))
img_vis=img.copy()
cv2.drawChessboardCorners(img_vis, (6,8), corners, ret)
plt.imshow(img_vis)
plt.show()
#Calibration
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1],None,None)
# Reprojection Error
tot_error = 0
for i in range(len(objpoints)):
imgpoints2, _ = cv2.projectPoints(objpoints[i], rvecs[i], tvecs[i], mtx, dist)
error = cv2.norm(imgpoints[i],imgpoints2, cv2.NORM_L2)/len(imgpoints2)
tot_error += error
print ("Mean Reprojection error: ", tot_error/len(objpoints))
# undistort
mapx,mapy = cv2.initUndistortRectifyMap(mtx,dist,None,newcameramtx,(w,h),5)
dst = cv2.remap(img,mapx,mapy,cv2.INTER_LINEAR)
# crop the image
x,y,w,h = roi
dst = dst[y:y+h, x:x+w]
plt.figure(figsize=(20,10))
#cv2.drawChessboardCorners(dst, (6,8), corners, ret)
plt.imshow(dst)
plt.show()
# Reprojection Error
tot_error = 0
for i in range(len(objpoints)):
imgpoints2, _ = cv2.projectPoints(objpoints[i], rvecs[i], tvecs[i], mtx, dist)
error = cv2.norm(imgpoints[i],imgpoints2, cv2.NORM_L2)/len(imgpoints2)
tot_error += error
print ("Mean Reprojection error: ", tot_error/len(objpoints))
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.
I've implemented the Bayesian Probabilistic Matrix Factorization algorithm using pymc3 in Python. I also implemented it's precursor, Probabilistic Matrix Factorization (PMF). See my previous question for a reference to the data used here.
I'm having trouble drawing MCMC samples using the NUTS sampler. I initialize the model parameters using the MAP from PMF, and the hyperparameters using Gaussian random draws sprinkled around 0. However, I get a PositiveDefiniteError when setting up the step object for the sampler. I've verified that the MAP estimate from PMF is reasonable, so I expect it has something to do with the way the hyperparameters are being initialized. Here is the PMF model:
import pymc3 as pm
import numpy as np
import pandas as pd
import theano
import scipy as sp
data = pd.read_csv('jester-dense-subset-100x20.csv')
n, m = data.shape
test_size = m / 10
train_size = m - test_size
train = data.copy()
train.ix[:,train_size:] = np.nan # remove test set data
train[train.isnull()] = train.mean().mean() # mean value imputation
train = train.values
test = data.copy()
test.ix[:,:train_size] = np.nan # remove train set data
test = test.values
# Low precision reflects uncertainty; prevents overfitting
alpha_u = alpha_v = 1/np.var(train)
alpha = np.ones((n,m)) * 2 # fixed precision for likelihood function
dim = 10 # dimensionality
# Specify the model.
with pm.Model() as pmf:
pmf_U = pm.MvNormal('U', mu=0, tau=alpha_u * np.eye(dim),
shape=(n, dim), testval=np.random.randn(n, dim)*.01)
pmf_V = pm.MvNormal('V', mu=0, tau=alpha_v * np.eye(dim),
shape=(m, dim), testval=np.random.randn(m, dim)*.01)
pmf_R = pm.Normal('R', mu=theano.tensor.dot(pmf_U, pmf_V.T),
tau=alpha, observed=train)
# Find mode of posterior using optimization
start = pm.find_MAP(fmin=sp.optimize.fmin_powell)
And here is BPMF:
n, m = data.shape
dim = 10 # dimensionality
beta_0 = 1 # scaling factor for lambdas; unclear on its use
alpha = np.ones((n,m)) * 2 # fixed precision for likelihood function
logging.info('building the BPMF model')
std = .05 # how much noise to use for model initialization
with pm.Model() as bpmf:
# Specify user feature matrix
lambda_u = pm.Wishart(
'lambda_u', n=dim, V=np.eye(dim), shape=(dim, dim),
testval=np.random.randn(dim, dim) * std)
mu_u = pm.Normal(
'mu_u', mu=0, tau=beta_0 * lambda_u, shape=dim,
testval=np.random.randn(dim) * std)
U = pm.MvNormal(
'U', mu=mu_u, tau=lambda_u, shape=(n, dim),
testval=np.random.randn(n, dim) * std)
# Specify item feature matrix
lambda_v = pm.Wishart(
'lambda_v', n=dim, V=np.eye(dim), shape=(dim, dim),
testval=np.random.randn(dim, dim) * std)
mu_v = pm.Normal(
'mu_v', mu=0, tau=beta_0 * lambda_v, shape=dim,
testval=np.random.randn(dim) * std)
V = pm.MvNormal(
'V', mu=mu_v, tau=lambda_v, shape=(m, dim),
testval=np.random.randn(m, dim) * std)
# Specify rating likelihood function
R = pm.Normal(
'R', mu=theano.tensor.dot(U, V.T), tau=alpha,
observed=train)
# `start` is the start dictionary obtained from running find_MAP for PMF.
for key in bpmf.test_point:
if key not in start:
start[key] = bpmf.test_point[key]
with bpmf:
step = pm.NUTS(scaling=start)
At the last line, I get the following error:
PositiveDefiniteError: Scaling is not positive definite. Simple check failed. Diagonal contains negatives. Check indexes [ 0 2 ... 2206 2207 ]
As I understand it, I can't use find_MAP with models that have hyperpriors like BPMF. This is why I'm attempting to initialize with the MAP values from PMF, which uses point estimates for the parameters on U and V rather than parameterized hyperpriors.
Unfortunately the Wishart distribution is non-functional. I recently added a warning here: https://github.com/pymc-devs/pymc3/commit/642f63973ec9f807fb6e55a0fc4b31bdfa1f261e
See here for more discussions on this tricky distribution: https://github.com/pymc-devs/pymc3/issues/538
You could confirm that that's the source by fixing the covariance matrix. If that's the case, I'd try using the JKL prior distribution: https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/LKJ_correlation.py
For those that want to export a simple 3D numpy array (along with axes) to a .vtk (or .vtr) file for post-processing and display in Paraview or Mayavi there's a little module called PyEVTK that does exactly that. The module supports structured and unstructured data etc..
Unfortunately, even though the code works fine in unix-based systems I couldn't make it work (keeps crashing) on any windows installation which simply makes things complicated. Ive contacted the developer but his suggestions did not work
Therefore my question is:
How can one use the from vtk.util import numpy_support function to export a 3D array (the function itself doesn't support 3D arrays) to a .vtk file? Is there a simple way to do it without creating vtkDatasets etc etc?
Thanks a lot!
It's been forever and I had entirely forgotten asking this question but I ended up figuring it out. I've written a post about it in my blog (PyScience) providing a tutorial on how to convert between NumPy and VTK. Do take a look if interested:
pyscience.wordpress.com/2014/09/06/numpy-to-vtk-converting-your-numpy-arrays-to-vtk-arrays-and-files/
It's not a direct answer to your question, but if you have tvtk (if you have mayavi, you should have it), you can use it to write your data to vtk format. (See: http://code.enthought.com/projects/files/ETS3_API/enthought.tvtk.misc.html )
It doesn't use PyEVTK, and it supports a broad range of data sources (more than just structured and unstructured grids), so it will probably work where other things aren't.
As a quick example (Mayavi's mlab interface can make this much less verbose, especially if you're already using it.):
import numpy as np
from enthought.tvtk.api import tvtk, write_data
data = np.random.random((10,10,10))
grid = tvtk.ImageData(spacing=(10, 5, -10), origin=(100, 350, 200),
dimensions=data.shape)
grid.point_data.scalars = np.ravel(order='F')
grid.point_data.scalars.name = 'Test Data'
# Writes legacy ".vtk" format if filename ends with "vtk", otherwise
# this will write data using the newer xml-based format.
write_data(grid, 'test.vtk')
And a portion of the output file:
# vtk DataFile Version 3.0
vtk output
ASCII
DATASET STRUCTURED_POINTS
DIMENSIONS 10 10 10
SPACING 10 5 -10
ORIGIN 100 350 200
POINT_DATA 1000
SCALARS Test%20Data double
LOOKUP_TABLE default
0.598189 0.228948 0.346975 0.948916 0.0109774 0.30281 0.643976 0.17398 0.374673
0.295613 0.664072 0.307974 0.802966 0.836823 0.827732 0.895217 0.104437 0.292796
0.604939 0.96141 0.0837524 0.498616 0.608173 0.446545 0.364019 0.222914 0.514992
...
...
TVTK of Mayavi has a beautiful way of writing vtk files. Here is a test example I have written for myself following #Joe and tvtk documentation. The advantage it has over evtk, is the support for both ascii and html.Hope it will help other people.
from tvtk.api import tvtk, write_data
import numpy as np
#data = np.random.random((3, 3, 3))
#
#i = tvtk.ImageData(spacing=(1, 1, 1), origin=(0, 0, 0))
#i.point_data.scalars = data.ravel()
#i.point_data.scalars.name = 'scalars'
#i.dimensions = data.shape
#
#w = tvtk.XMLImageDataWriter(input=i, file_name='spoints3d.vti')
#w.write()
points = np.array([[0,0,0], [1,0,0], [1,1,0], [0,1,0]], 'f')
(n1, n2) = points.shape
poly_edge = np.array([[0,1,2,3]])
print n1, n2
## Scalar Data
#temperature = np.array([10., 20., 30., 40.])
#pressure = np.random.rand(n1)
#
## Vector Data
#velocity = np.random.rand(n1,n2)
#force = np.random.rand(n1,n2)
#
##Tensor Data with
comp = 5
stress = np.random.rand(n1,comp)
#
#print stress.shape
## The TVTK dataset.
mesh = tvtk.PolyData(points=points, polys=poly_edge)
#
## Data 0 # scalar data
#mesh.point_data.scalars = temperature
#mesh.point_data.scalars.name = 'Temperature'
#
## Data 1 # additional scalar data
#mesh.point_data.add_array(pressure)
#mesh.point_data.get_array(1).name = 'Pressure'
#mesh.update()
#
## Data 2 # Vector data
#mesh.point_data.vectors = velocity
#mesh.point_data.vectors.name = 'Velocity'
#mesh.update()
#
## Data 3 additional vector data
#mesh.point_data.add_array( force)
#mesh.point_data.get_array(3).name = 'Force'
#mesh.update()
mesh.point_data.tensors = stress
mesh.point_data.tensors.name = 'Stress'
# Data 4 additional tensor Data
#mesh.point_data.add_array(stress)
#mesh.point_data.get_array(4).name = 'Stress'
#mesh.update()
write_data(mesh, 'polydata.vtk')
# XML format
# Method 1
#write_data(mesh, 'polydata')
# Method 2
#w = tvtk.XMLPolyDataWriter(input=mesh, file_name='polydata.vtk')
#w.write()
I know it is a bit late and I do love your tutorials #somada141. This should work too.
def numpy2VTK(img, spacing=[1.0, 1.0, 1.0]):
# evolved from code from Stou S.,
# on http://www.siafoo.net/snippet/314
# This function, as the name suggests, converts numpy array to VTK
importer = vtk.vtkImageImport()
img_data = img.astype('uint8')
img_string = img_data.tostring() # type short
dim = img.shape
importer.CopyImportVoidPointer(img_string, len(img_string))
importer.SetDataScalarType(VTK_UNSIGNED_CHAR)
importer.SetNumberOfScalarComponents(1)
extent = importer.GetDataExtent()
importer.SetDataExtent(extent[0], extent[0] + dim[2] - 1,
extent[2], extent[2] + dim[1] - 1,
extent[4], extent[4] + dim[0] - 1)
importer.SetWholeExtent(extent[0], extent[0] + dim[2] - 1,
extent[2], extent[2] + dim[1] - 1,
extent[4], extent[4] + dim[0] - 1)
importer.SetDataSpacing(spacing[0], spacing[1], spacing[2])
importer.SetDataOrigin(0, 0, 0)
return importer
Hope it helps!
Here's a SimpleITK version with the function load_itk taken from here:
import SimpleITK as sitk
import numpy as np
if len(sys.argv)<3:
print('Wrong number of arguments.', file=sys.stderr)
print('Usage: ' + __file__ + ' input_sitk_file' + ' output_sitk_file', file=sys.stderr)
sys.exit(1)
def quick_read(filename):
# Read image information without reading the bulk data.
file_reader = sitk.ImageFileReader()
file_reader.SetFileName(filename)
file_reader.ReadImageInformation()
print('image size: {0}\nimage spacing: {1}'.format(file_reader.GetSize(), file_reader.GetSpacing()))
# Some files have a rich meta-data dictionary (e.g. DICOM)
for key in file_reader.GetMetaDataKeys():
print(key + ': ' + file_reader.GetMetaData(key))
def load_itk(filename):
# Reads the image using SimpleITK
itkimage = sitk.ReadImage(filename)
# Convert the image to a numpy array first and then shuffle the dimensions to get axis in the order z,y,x
data = sitk.GetArrayFromImage(itkimage)
# Read the origin of the ct_scan, will be used to convert the coordinates from world to voxel and vice versa.
origin = np.array(list(reversed(itkimage.GetOrigin())))
# Read the spacing along each dimension
spacing = np.array(list(reversed(itkimage.GetSpacing())))
return data, origin, spacing
def convert(data, output_filename):
image = sitk.GetImageFromArray(data)
writer = sitk.ImageFileWriter()
writer.SetFileName(output_filename)
writer.Execute(image)
def wait():
print('Press Enter to load & convert or exit using Ctrl+C')
input()
quick_read(sys.argv[1])
print('-'*20)
wait()
data, origin, spacing = load_itk(sys.argv[1])
convert(sys.argv[2])