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# exercise 3.2.1
from __future__ import print_function
from pylab import *
from scipy.io import loadmat
from similarity import similarity
# Image to use as query
i = 635
# Similarity: 'SMC', 'Jaccard', 'ExtendedJaccard', 'Cosine', 'Correlation'
similarity_measure = 'jaccard'
# Load the CBCL face database
# Load Matlab data file to python dict structure
X = loadmat('./Data/wildfaces_grayscale.mat')['X']
N, M = shape(X)
# Search the face database for similar faces
# Index of all other images than i
noti = range(0,i) + range(i+1,N)
# Compute similarity between image i and all others
sim = similarity(X[i,:], X[noti,:], similarity_measure)
sim = sim.tolist()[0]
# Tuples of sorted similarities and their indices
sim_to_index = sorted(zip(sim,noti))
# Visualize query image and 5 most/least similar images
figure(figsize=(12,8))
subplot(3,1,1)
imshow(np.reshape(X[i],(40,40)).T, cmap=cm.gray)
xticks([]); yticks([])
title('Query image')
ylabel('image #{0}'.format(i))
for ms in range(5):
# 5 most similar images found
subplot(3,5,6+ms)
im_id = sim_to_index[-ms-1][1]
im_sim = sim_to_index[-ms-1][0]
imshow(np.reshape(X[im_id],(40,40)).T, cmap=cm.gray)
xlabel('sim={0:.3f}'.format(im_sim))
ylabel('image #{0}'.format(im_id))
xticks([]); yticks([])
if ms==2: title('Most similar images')
# 5 least similar images found
subplot(3,5,11+ms)
im_id = sim_to_index[ms][1]
im_sim = sim_to_index[ms][0]
imshow(np.reshape(X[im_id],(40,40)).T, cmap=cm.gray)
xlabel('sim={0:.3f}'.format(im_sim))
ylabel('image #{0}'.format(im_id))
xticks([]); yticks([])
if ms==2: title('Least similar images')
show()
# 1.3.1
# For any two similarity measures, the five least similar are quite different.
# Based on the five most similar images, SMC and Jaccard produce similar
# results. Correlation and Cosine produce some similar results.
# Using image 2 it is clear that SMC and ExtendedJaccard are sensitive to
# lighting conditions, and thus maybe not a very good choice to compare faces.
# Also Correlation seems a little sensitive to this. Lastly Cosine seems to
# recognise faces somewhat better than Jaccard (take e.g. #635).
# 1.3.2
measures = {'Cosine': 'cos', 'ExtJac': 'ext', 'Correl': 'cor'}
scalar = 0.5 # Note: pick from (0,1), values > 1 aren't handled nicely
translation = 0.1 # Note: pick a small value, for similar reasons
# Round list to resist numerical variances (hint #2)
X = np.around(X, decimals = 4)
for name, measure in measures.iteritems():
sim1 = similarity(scalar * X[i,:], X[noti,:], measure)
sim2 = similarity(X[i,:], X[noti,:], measure)
print("Scalar,", name, ":", (sim1 == sim2).all())
for name, measure in measures.iteritems():
sim1 = similarity(translation + X[i,:], X[noti,:], measure)
sim2 = similarity(X[i,:], X[noti,:], measure)
print("Translation,", name, ":", (sim1 == sim2).any())
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