def EMD(saliency_map1, saliency_map2, sub_sample=1/32.0): ''' Earth Mover's Distance measures the distance between two probability distributions by how much transformation one distribution would need to undergo to match another (EMD=0 for identical distributions). Parameters ---------- saliency_map1 : real-valued matrix If the two maps are different in shape, saliency_map1 will be resized to match saliency_map2. saliency_map2 : real-valued matrix Returns ------- EMD : float, positive ''' map2 = np.array(saliency_map2, copy=False) # Reduce image size for efficiency of calculation map2 = resize(map2, np.round(np.array(map2.shape)*sub_sample), order=3, mode='nearest') map1 = resize(saliency_map1, map2.shape, order=3, mode='nearest') # Histogram match the images so they have the same mass map1 = match_hist(map1, *exposure.cumulative_distribution(map2)) # Normalize the two maps to sum up to 1, # so that the score is independent of the starting amount of mass / spread of fixations of the fixation map map1 = normalize(map1, method='sum') map2 = normalize(map2, method='sum') # Compute EMD with OpenCV # - http://docs.opencv.org/modules/imgproc/doc/histograms.html#emd # - http://stackoverflow.com/questions/5101004/python-code-for-earth-movers-distance # - http://stackoverflow.com/questions/12535715/set-type-for-fromarray-in-opencv-for-python r, c = map2.shape x, y = np.meshgrid(range(c), range(r)) signature1 = cv.CreateMat(r*c, 3, cv.CV_32FC1) signature2 = cv.CreateMat(r*c, 3, cv.CV_32FC1) cv.Convert(cv.fromarray(np.c_[map1.ravel(), x.ravel(), y.ravel()]), signature1) cv.Convert(cv.fromarray(np.c_[map2.ravel(), x.ravel(), y.ravel()]), signature2) return cv.CalcEMD2(signature2, signature1, cv.CV_DIST_L2)
def SIM(saliency_map1, saliency_map2): ''' Similarity between two different saliency maps when viewed as distributions (SIM=1 means the distributions are identical). This similarity measure is also called **histogram intersection**. Parameters ---------- saliency_map1 : real-valued matrix If the two maps are different in shape, saliency_map1 will be resized to match saliency_map2. saliency_map2 : real-valued matrix Returns ------- SIM : float, between [0,1] ''' map1 = np.array(saliency_map1, copy=False) map2 = np.array(saliency_map2, copy=False) if map1.shape != map2.shape: map1 = resize(map1, map2.shape, order=3, mode='nearest') # bi-cubic/nearest is what Matlab imresize() does by default # Normalize the two maps to have values between [0,1] and sum up to 1 map1 = normalize(map1, method='range') map2 = normalize(map2, method='range') map1 = normalize(map1, method='sum') map2 = normalize(map2, method='sum') # Compute histogram intersection intersection = np.minimum(map1, map2) return np.sum(intersection)
def AUC_Judd(saliency_map, fixation_map, jitter=True):
'''
AUC stands for Area Under ROC Curve.
This measures how well the saliency map of an image predicts the ground truth human fixations on the image.
ROC curve is created by sweeping through threshold values
determined by range of saliency map values at fixation locations.
True positive (tp) rate correspond to the ratio of saliency map values above threshold
at fixation locations to the total number of fixation locations.
False positive (fp) rate correspond to the ratio of saliency map values above threshold
at all other locations to the total number of possible other locations (non-fixated image pixels).
AUC=0.5 is chance level.
Parameters
----------
saliency_map : real-valued matrix
fixation_map : binary matrix
Human fixation map.
jitter : boolean, optional
If True (default), a small random number would be added to each pixel of the saliency map.
Jitter saliency maps that come from saliency models that have a lot of zero values.
If the saliency map is made with a Gaussian then it does not need to be jittered
as the values vary and there is not a large patch of the same value.
In fact, jittering breaks the ordering in the small values!
Returns
-------
AUC : float, between [0,1]
'''
saliency_map = np.array(saliency_map, copy=False)
fixation_map = np.array(fixation_map, copy=False) > 0.5
# If there are no fixation to predict, return NaN
if not np.any(fixation_map):
print('no fixation to predict')
return np.nan
# Make the saliency_map the size of the fixation_map
if saliency_map.shape != fixation_map.shape:
saliency_map = resize(saliency_map, fixation_map.shape, order=3, mode='nearest')
# Jitter the saliency map slightly to disrupt ties of the same saliency value
if jitter:
saliency_map += random.rand(*saliency_map.shape) * 1e-7
# Normalize saliency map to have values between [0,1]
saliency_map = normalize(saliency_map, method='range')
S = saliency_map.ravel()
F = fixation_map.ravel()
S_fix = S[F] # Saliency map values at fixation locations
n_fix = len(S_fix)
n_pixels = len(S)
# Calculate AUC
thresholds = sorted(S_fix, reverse=True)
tp = np.zeros(len(thresholds)+2)
fp = np.zeros(len(thresholds)+2)
tp[0] = 0; tp[-1] = 1
fp[0] = 0; fp[-1] = 1
for k, thresh in enumerate(thresholds):
above_th = np.sum(S >= thresh) # Total number of saliency map values above threshold
tp[k+1] = (k + 1) / float(n_fix) # Ratio saliency map values at fixation locations above threshold
fp[k+1] = (above_th - k - 1) / float(n_pixels - n_fix) # Ratio other saliency map values above threshold
return np.trapz(tp, fp) # y, x
def CC(saliency_map1, saliency_map2): ''' Pearson's correlation coefficient between two different saliency maps (CC=0 for uncorrelated maps, CC=1 for perfect linear correlation). Parameters ---------- saliency_map1 : real-valued matrix If the two maps are different in shape, saliency_map1 will be resized to match saliency_map2. saliency_map2 : real-valued matrix Returns ------- CC : float, between [-1,1] ''' map1 = np.array(saliency_map1, copy=False) map2 = np.array(saliency_map2, copy=False) if map1.shape != map2.shape: map1 = resize(map1, map2.shape, order=3, mode='nearest') # bi-cubic/nearest is what Matlab imresize() does by default # Normalize the two maps to have zero mean and unit std map1 = normalize(map1, method='standard') map2 = normalize(map2, method='standard') # Compute correlation coefficient return np.corrcoef(map1.ravel(), map2.ravel())[0,1]
def NSS(saliency_map, fixation_map): ''' Normalized scanpath saliency of a saliency map, defined as the mean value of normalized (i.e., standardized) saliency map at fixation locations. You can think of it as a z-score. (Larger value implies better performance.) Parameters ---------- saliency_map : real-valued matrix If the two maps are different in shape, saliency_map will be resized to match fixation_map.. fixation_map : binary matrix Human fixation map (1 for fixated location, 0 for elsewhere). Returns ------- NSS : float, positive ''' s_map = np.array(saliency_map, copy=False) f_map = np.array(fixation_map, copy=False) > 0.5 if s_map.shape != f_map.shape: s_map = resize(s_map, f_map.shape) # Normalize saliency map to have zero mean and unit std s_map = normalize(s_map, method='standard') # Mean saliency value at fixation locations return np.mean(s_map[f_map])
def AUC_Borji(saliency_map, fixation_map, n_rep=100, step_size=0.1, rand_sampler=None):
'''
This measures how well the saliency map of an image predicts the ground truth human fixations on the image.
ROC curve created by sweeping through threshold values at fixed step size
until the maximum saliency map value.
True positive (tp) rate correspond to the ratio of saliency map values above threshold
at fixation locations to the total number of fixation locations.
False positive (fp) rate correspond to the ratio of saliency map values above threshold
at random locations to the total number of random locations
(as many random locations as fixations, sampled uniformly from fixation_map ALL IMAGE PIXELS),
averaging over n_rep number of selections of random locations.
Parameters
----------
saliency_map : real-valued matrix
fixation_map : binary matrix
Human fixation map.
n_rep : int, optional
Number of repeats for random sampling of non-fixated locations.
step_size : int, optional
Step size for sweeping through saliency map.
rand_sampler : callable
S_rand = rand_sampler(S, F, n_rep, n_fix)
Sample the saliency map at random locations to estimate false positive.
Return the sampled saliency values, S_rand.shape=(n_fix,n_rep)
Returns
-------
AUC : float, between [0,1]
'''
saliency_map = np.array(saliency_map, copy=False)
fixation_map = np.array(fixation_map, copy=False) > 0.5
# If there are no fixation to predict, return NaN
if not np.any(fixation_map):
print('no fixation to predict')
return np.nan
# Make the saliency_map the size of the fixation_map
if saliency_map.shape != fixation_map.shape:
saliency_map = resize(saliency_map, fixation_map.shape, order=3, mode='nearest')
# Normalize saliency map to have values between [0,1]
saliency_map = normalize(saliency_map, method='range')
S = saliency_map.ravel()
F = fixation_map.ravel()
S_fix = S[F] # Saliency map values at fixation locations
n_fix = len(S_fix)
n_pixels = len(S)
# For each fixation, sample n_rep values from anywhere on the saliency map
if rand_sampler is None:
r = random.randint(0, n_pixels, [n_fix, n_rep])
S_rand = S[r] # Saliency map values at random locations (including fixated locations!? underestimated)
else:
S_rand = rand_sampler(S, F, n_rep, n_fix)
# Calculate AUC per random split (set of random locations)
auc = np.zeros(n_rep) * np.nan
for rep in range(n_rep):
thresholds = np.r_[0:np.max(np.r_[S_fix, S_rand[:,rep]]):step_size][::-1]
tp = np.zeros(len(thresholds)+2)
fp = np.zeros(len(thresholds)+2)
tp[0] = 0; tp[-1] = 1
fp[0] = 0; fp[-1] = 1
for k, thresh in enumerate(thresholds):
tp[k+1] = np.sum(S_fix >= thresh) / float(n_fix)
fp[k+1] = np.sum(S_rand[:,rep] >= thresh) / float(n_fix)
auc[rep] = np.trapz(tp, fp)
return np.mean(auc) # Average across random splits