# Source code for pysptools.distance.dist

#
#------------------------------------------------------------------------------
# Copyright (c) 2013-2014, Christian Therien
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
#------------------------------------------------------------------------------
#
# dist.py - This file is part of the PySptools package.
#

"""
SAM, SID, NormXCorr, chebyshev functions
"""

from __future__ import division

import numpy as np
import math

[docs]def SAM(s1, s2):
"""
Computes the spectral angle mapper between two vectors (in radians).

Parameters:
s1: numpy array
The first vector.

s2: numpy array
The second vector.

Returns: float
The angle between vectors s1 and s2 in radians.
"""
try:
s1_norm = math.sqrt(np.dot(s1, s1))
s2_norm = math.sqrt(np.dot(s2, s2))
sum_s1_s2 = np.dot(s1, s2)
angle = math.acos(sum_s1_s2 / (s1_norm * s2_norm))
except ValueError:
# python math don't like when acos is called with
# a value very near to 1
return 0.0
return angle

[docs]def SID(s1, s2):
"""
Computes the spectral information divergence between two vectors.

Parameters:
s1: numpy array
The first vector.

s2: numpy array
The second vector.

Returns: float
Spectral information divergence between s1 and s2.

Reference
C.-I. Chang, "An Information-Theoretic Approach to SpectralVariability,
Similarity, and Discrimination for Hyperspectral Image"
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 46, NO. 5, AUGUST 2000.

"""
p = (s1 / np.sum(s1)) + np.spacing(1)
q = (s2 / np.sum(s2)) + np.spacing(1)
return np.sum(p * np.log(p / q) + q * np.log(q / p))

[docs]def chebyshev(s1, s2):
"""
Computes the chebychev distance between two vector.

Parameters:
s1: numpy array
The first vector.

s2: numpy array
The second vector.

Returns: float
Chebychev distance between s1 and s2.
"""
return np.amax(np.abs(s1 - s2))

[docs]def NormXCorr(s1, s2):
"""
Computes the normalized cross correlation distance between two vector.

Parameters:
s1: numpy array
The first vector.

s2: numpy array
The second vector.

Returns: float
NormXCorr distance between s1 and s2, dist is between [-1, 1].
A value of one indicate a perfect match.
"""
# s1 and s2 have the same length
import scipy.stats as ss
s = s1.shape[0]
corr = np.sum((s1 - np.mean(s1)) * (s2 - np.mean(s2))) / (ss.tstd(s1) * ss.tstd(s2))
return corr * (1./(s-1))

def classify(fn, M, E):
"""
Classify SAM or SID on a HSI cube
Can't be use with NormXCorr
"""
import pysptools.util as util
width, height, bands = M.shape
M = util.convert2d(M)
cmap = np.zeros(M.shape[0])
for i in range(M.shape[0]):
T = M[i]
floor = np.PINF
k = 0
for j in range(E.shape[0]):
R = E[j]
result = fn(T, R)
if result < floor:
floor = result
k = j
cmap[i] = k
return util.convert3d(cmap, width, height)