Correctly using the numpy's convolve with an image - python

I was watching Andrew Ng's videos on CNN and wanted to to convolve a 6 x 6 image with a 3 x 3 filter. The way I approached this with numpy is as follows:
image = np.ones((6,6))
filter = np.ones((3,3))
convolved = np.convolve(image, filter)
Running this gives an error saying:
ValueError: object too deep for desired array
I could comprehend from the numpy documentation of convolve on how to correctly use the convolve method.
Also, is there a way I could do a strided convolutions with numpy?


np.convolve function, unfortunately, only works for 1-D convolution. That's why you get an error; you need a function that allows you to perform 2-D convolution.
However, even if it did work, you actually have the wrong operation. What is called convolution in machine learning is more properly termed cross-correlation in mathematics. They're actually almost the same; convolution involves flipping the filter matrix followed by performing cross-correlation.
To solve your problem, you can look at scipy.signal.correlate (also, don't use filter as a name, as you'll shadow the inbuilt function):
from scipy.signal import correlate
image = np.ones((6, 6))
f = np.ones((3, 3))
correlate(image, f)
Output:
array([[1., 2., 3., 3., 3., 3., 2., 1.],
[2., 4., 6., 6., 6., 6., 4., 2.],
[3., 6., 9., 9., 9., 9., 6., 3.],
[3., 6., 9., 9., 9., 9., 6., 3.],
[3., 6., 9., 9., 9., 9., 6., 3.],
[3., 6., 9., 9., 9., 9., 6., 3.],
[2., 4., 6., 6., 6., 6., 4., 2.],
[1., 2., 3., 3., 3., 3., 2., 1.]])
This is the standard setting of full cross-correlation. If you want to remove elements which would rely on the zero-padding, pass mode='valid':
from scipy.signal import correlate
image = np.ones((6, 6))
f = np.ones((3, 3))
correlate(image, f, mode='valid')
Output:
array([[9., 9., 9., 9.],
[9., 9., 9., 9.],
[9., 9., 9., 9.],
[9., 9., 9., 9.]])

Related

combining 2 numpy arrays

I have 2 numpy arrays:
one of shape (753,8,1) denoting 8 sequential actions of a customer
and other of shape (753,10) denoting 10 features of a training sample.
How can I combine these two such that:
all 10 features are appended to each of the 8 sequential actions of a training sample , that is, the combined final array should have shape of (753,8,11).

Maybe something like this:
import numpy as np
# create dummy arrays
a = np.zeros((753, 8, 1))
b = np.arange(753*10).reshape(753, 10)
# make a new axis for b and repeat the values along axis 1
c = np.repeat(b[:, np.newaxis, :], 8, axis=1)
c.shape
>>> (753, 8, 10)
# now the first two axes of a and c have the same shape
# append the values in c to a along the last axis
result = np.append(a, c, axis=2)
result.shape
>>> (753, 8, 11)
result[0]
>>> array([[0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.],
[0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.],
[0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.],
[0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.],
[0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.],
[0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.],
[0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.],
[0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.]])
# values from b (0-9) have been appended to a (0)

Python - Concatenate or stack more than two arrays with different shape

I would like to get an array of size 11x11 with different subarrays, for example the array M composed by the following arrays (shape in parenthesis):
CC(3x3) CA(3x4) CB(3x4)
AC(4x3) AA(4x4) AB(4x4)
BC(4x3) BA(4x4) BB(4x4)
I could use concatenate but it is not optimal. I also tried the stack function, but arrays must have the same shape. Do you have any ideas to do it?
Thanks a lot!

You want np.block(). It creates an array out of 'blocks', like what you have. For e.g.
>>> CC = 1*np.ones((3, 3))
>>> CA = 2*np.ones((3, 4))
>>> CB = 3*np.ones((3, 4))
>>> AC = 4*np.ones((4, 3))
>>> AA = 5*np.ones((4, 4))
>>> AB = 6*np.ones((4, 4))
>>> BC = 7*np.ones((4, 3))
>>> BA = 8*np.ones((4, 4))
>>> BB = 9*np.ones((4, 4))
>>> M = np.block([[CC, CA, CB],
[AC, AA, AB],
[BC, BA, BB]])
>>> M
array([[ 1., 1., 1., 2., 2., 2., 2., 3., 3., 3., 3.],
[ 1., 1., 1., 2., 2., 2., 2., 3., 3., 3., 3.],
[ 1., 1., 1., 2., 2., 2., 2., 3., 3., 3., 3.],
[ 4., 4., 4., 5., 5., 5., 5., 6., 6., 6., 6.],
[ 4., 4., 4., 5., 5., 5., 5., 6., 6., 6., 6.],
[ 4., 4., 4., 5., 5., 5., 5., 6., 6., 6., 6.],
[ 4., 4., 4., 5., 5., 5., 5., 6., 6., 6., 6.],
[ 7., 7., 7., 8., 8., 8., 8., 9., 9., 9., 9.],
[ 7., 7., 7., 8., 8., 8., 8., 9., 9., 9., 9.],
[ 7., 7., 7., 8., 8., 8., 8., 9., 9., 9., 9.],
[ 7., 7., 7., 8., 8., 8., 8., 9., 9., 9., 9.]])

Relabeling overlapping segments located in adjacent numpy 2-d blocks (without for-loops)

I have a numpy 2-d array which I divided in several numpy 2-d blocks. All blocks have the same shape. On these blocks I performed K-means segementation using the scikit-learn module. The edges of each block are overlapping (each block has one row/column overlap with the adjacent block). What I want is to give the overlapping segments in two adjacent blocks the same value. My current code can be downloaded here.
Image of the blocks and their position in the original image:
Blocks in python code
blockNW=np.array([[ 0., 0., 0., 0., 5.],
[ 0., 0., 4., 5., 5.],
[ 0., 4., 4., 5., 2.],
[ 0., 4., 5., 5., 2.],
[ 5., 5., 2., 2., 2.]])
blockNE=np.array([[ 1., 18., 18., 18., 6.],
[ 1., 18., 7., 6., 6.],
[ 3., 7., 7., 7., 6.],
[ 3., 3., 3., 7., 7.],
[ 3., 3., 7., 7., 7.]])
blockSW=np.array([[ 8., 8., 8., 10., 10.],
[ 8., 8., 9., 10., 10.],
[ 8., 8., 9., 9., 10.],
[ 8., 8., 8., 9., 10.],
[ 8., 8., 9., 9., 11.]])
blockSE=np.array([[ 12., 12., 12., 12., 12.],
[ 12., 12., 12., 12., 13.],
[ 12., 12., 12., 13., 13.],
[ 12., 12., 13., 13., 13.],
[ 12., 13., 13., 13., 13.]])
blocksStacked=np.array([blockNW,blockNE,blockSW,blockSE])
What I want is to connect the overlapping segments. For this I would like to use as few for-loops as possible, because they are slowing down the code. My current steps are:
import math
import numpy as np
from scipy import ndimage,stats
n_blocks,blocksize = np.shape(blocksStacked)[0],np.shape(blocksStacked)[1]
# shape of original image
out_shp = (8,8)
# horizontal and vertical blocks
horizontal_blocks=math.ceil(out_shp[1]/float(blocksize))
vertical_blocks=math.ceil(out_shp[0]/float(blocksize))
# numpy 2_d array in the shape of the image with an unique ID for each block
blockindex=np.arange(horizontal_blocks*vertical_blocks).reshape(-1,horizontal_blocks)
Block index
def find_neighbours(values,neighbourslist):
'''function to find the index of neighbouring blocks'''
mode=stats.mode(values)
if mode.count>1:
values=np.delete(values,np.where(values==mode[0]))
else:
values=np.delete(values,np.where(values==np.median(values)))
neighbourslist.append(values)
return 0
#Locate overlapping rows and columns per block
neighbourlist=[]
kernel=np.array([[0,1,0],[1,1,1],[0,1,0]],dtype='uint8')
_ =ndimage.generic_filter(blockindex, find_neighbours, footprint=kernel,extra_arguments=(neighbourlist,))
#output (block 0 has neighbours 1 and 2, etc.):
>>> neighbourlist
[array([ 1., 2.]), array([ 0., 3.]), array([ 0., 3.]), array([ 1., 2.])]
Now the next step could be is to loop through all blocks and neighbors and select the overlapping rows or columns (If possible I would also like to remove these loops).
# First I create masks to select overlapping rows or columns:
upmask=np.ones((blocksize,blocksize),dtype=bool)
upmask[1:,:]=0
downmask=np.ones((blocksize,blocksize),dtype=bool)
downmask[:-1,:]=0
rightmask=np.ones((blocksize,blocksize),dtype=bool)
rightmask[:,:-1]=0
leftmask=np.ones((blocksize,blocksize),dtype=bool)
leftmask[:,1:]=0
# Now loop through all blocks and neighbours and select the overlapping rows/columsn
for i in range(n_blocks):
n_neighbours = len(neighbourlist[i])
block=blocksStacked[i,:,:]
for j in range(n_neighbours):
neighborindex=neighbourlist[i][j]
block_neighbour=blocksStacked[neighborindex,:,:]
if i+1==neighborindex:
blockvals=block[rightmask]
neighbourvals=block_neighbour[leftmask]
elif i-1==neighborindex:
blockvals=block[leftmask]
neighbourvals=block_neighbour[rightmask]
elif i+horizontal_blocks==neighborindex:
blockvals=block[downmask]
neighbourvals=block_neighbour[upmask]
elif i-horizontal_blocks==neighborindex:
blockvals=block[upmask]
neighbourvals=block_neighbour[downmask]
In each loop I end up with two numpy 1d arrays representing the overlapping columns or rows. For the first loop I will end up with:
>>> blockvals
array([5., 5., 2., 2., 2.])
>>> neighbourvals
array([1., 1., 3., 3., 3.])
I want to relabel the values of the overlapping segments to the values of the segments in the block which is not a neighbour:
blockNW=np.array([[ 0., 0., 0., 0., 5.],
[ 0., 0., 4., 5., 5.],
[ 0., 4., 4., 5., 2.],
[ 0., 4., 5., 5., 2.],
[ 5., 5., 2., 2., 2.]])
blockNE=np.array([[ 5., 18., 18., 18., 6.],
[ 5., 18., 7., 6., 6.],
[ 2., 7., 7., 7., 6.],
[ 2., 2., 2., 7., 7.],
[ 2., 2., 7., 7., 7.]])
Any idea on how to detect and relabel these overlapping segments?
Also my code looks a bit too cumbersome, any ideas on how to improve my code?
A few remarks:
Some segments will not overlap for 100%, so it should be possible to set a threshold. For example is segments are overlapping for more than 70% they should be relabeled
The output shape of the function should be similar to the shape of the stacked blocks
The desired output will look like this:
EDIT
With for-loops the code to solve the question would look something like this:
from scipy.stats import itemfreq
# Locate and re-label overlapping segments
for k in range(len(np.unique(blockvals))):
#Iterate over each value in the overlapping row/column of the block
blockval=np.unique(blockvals)[k]
#count of blockval
block_val_count=len(blockvals[np.where(blockvals==blockval)])
#Select values in neighbour on the same location
overlap=neighbourvals[np.where(blockvals==blockval)]
overlapfreq=itemfreq(overlap)
#select neighboring value which overlaps the most
neighval_overlap_count= np.max(overlapfreq[:,1])
neighval=overlapfreq[np.where(overlapfreq[:,1]==neighval_overlap_count),0][0]
# count occurence of selected neighboring value
neigh_val_count=len(neighbourvals[np.where(neighbourvals==neighval)])
#If overlap is more than 70% relabel the neigboring value to the value in the block
thresh=0.7
if (neighval_overlap_count/float(neigh_val_count)>=thresh) and (neighval_overlap_count/float(block_val_count)>=thresh):
blocksStacked[neighborindex,:,:,][np.where(blocksStacked[neighborindex,:,:]==neighval)]=blockval
#output
>>> blocksStacked
array([[[ 0., 0., 0., 0., 5.],
[ 0., 0., 4., 5., 5.],
[ 0., 4., 4., 5., 2.],
[ 0., 4., 5., 5., 2.],
[ 5., 5., 2., 2., 2.]],
[[ 5., 18., 18., 18., 6.],
[ 5., 18., 7., 6., 6.],
[ 2., 7., 7., 7., 6.],
[ 2., 2., 2., 7., 7.],
[ 2., 2., 7., 7., 7.]],
[[ 8., 8., 8., 10., 10.],
[ 8., 8., 9., 10., 10.],
[ 8., 8., 9., 9., 10.],
[ 8., 8., 8., 9., 10.],
[ 8., 8., 9., 9., 11.]],
[[ 10., 10., 10., 10., 10.],
[ 10., 10., 10., 10., 13.],
[ 10., 10., 10., 13., 13.],
[ 10., 10., 13., 13., 13.],
[ 10., 13., 13., 13., 13.]]])

Adding a 1-D Array to a 3-D array in Numpy

I am attempting to add two arrays.
np.zeros((6,9,20)) + np.array([1,2,3,4,5,6,7,8,9])
I want to get something out that is like
array([[[ 1., 1., 1., ..., 1., 1., 1.],
[ 2., 2., 2., ..., 2., 2., 2.],
[ 3., 3., 3., ..., 3., 3., 3.],
...,
[ 7., 7., 7., ..., 7., 7., 7.],
[ 8., 8., 8., ..., 8., 8., 8.],
[ 9., 9., 9., ..., 9., 9., 9.]],
[[ 1., 1., 1., ..., 1., 1., 1.],
[ 2., 2., 2., ..., 2., 2., 2.],
[ 3., 3., 3., ..., 3., 3., 3.],
...,
[ 7., 7., 7., ..., 7., 7., 7.],
[ 8., 8., 8., ..., 8., 8., 8.],
[ 9., 9., 9., ..., 9., 9., 9.]],
So adding entries to each of the matrices at the corresponding column. I know I can code it in a loop of some sort, but I am trying to use a more elegant / faster solution.

You can bring broadcasting into play after extending the dimensions of the second array with None or np.newaxis, like so -
np.zeros((6,9,20))+np.array([1,2,3,4,5,6,7,8,9])[None,:,None]

If I understand you correctly, the best thing to use is NumPy's Broadcasting. You can get what you want with the following:
np.zeros((6,9,20))+np.array([1,2,3,4,5,6,7,8,9]).reshape((1,9,1))
I prefer using the reshape method to using slice notation for the indices the way Divakar shows, because I've done a fair bit of work manipulating shapes as variables, and it's a bit easier to pass around tuples in variables than slices. You can also do things like this:
array1.reshape(array2.shape)
By the way, if you're really looking for something as simple as an array that runs from 0 to N-1 along an axis, check out mgrid. You can get your above output with just
np.mgrid[0:6,1:10,0:20][1]

You could use tile (but you would also need swapaxes to get the correct shape).
A = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
B = np.tile(A, (6, 20, 1))
C = np.swapaxes(B, 1, 2)

Are there alternative way to manage value assignment of n-dim array/matrix/list in Python?

In python we do some thing like this for example:
n = 30
A = numpy.zeros(shape=(n,n))
for i in range(0, n):
for j in range(0, n):
A[i, j] = i+j
#i+j just example of assignment
To manage a 2-dim array. It's so simple. just use nest loop to walk around rows and columns.
But my friend told me why it's so complicated. Could you give me the another way to manage it?
He told me in Mathematica have some way more easier to manage n-dim array (I'm not sure. I've never use Mathematica)
Can you give me the alternative way to manage value assignment on n-dim matrix/array(in Numpy) or list(ordinary one in Python)?

You are looking for numpy.fromfunction:
>>> numpy.fromfunction(lambda x, y: x + y, (5, 5))
array([[ 0., 1., 2., 3., 4.],
[ 1., 2., 3., 4., 5.],
[ 2., 3., 4., 5., 6.],
[ 3., 4., 5., 6., 7.],
[ 4., 5., 6., 7., 8.]])
You can simplify slightly using operator:
>>> from operator import add
>>> numpy.fromfunction(add, (5, 5))
array([[ 0., 1., 2., 3., 4.],
[ 1., 2., 3., 4., 5.],
[ 2., 3., 4., 5., 6.],
[ 3., 4., 5., 6., 7.],
[ 4., 5., 6., 7., 8.]])

You can use the mathematical rules for matrixes and vectors:
n = 30
w = numpy.arange(n).reshape(1,-1)
A = w+w.T

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