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import numpy as np
from .cpd_nonlin import cpd_nonlin
def cpd_auto(K, ncp, vmax, desc_rate=1, **kwargs):
"""Main interface
Detect change points automatically selecting their number
K - kernel between each pair of frames in video
ncp - maximum ncp
vmax - special parameter
Optional arguments:
lmin - minimum segment length
lmax - maximum segment length
desc_rate - rate of descriptor sampling (vmax always corresponds to 1x)
Note:
- cps are always calculated in subsampled coordinates irrespective to
desc_rate
- lmin and m should be in agreement
---
Returns: (cps, costs)
cps - best selected change-points
costs - costs for 0,1,2,...,m change-points
Memory requirement: ~ (3*N*N + N*ncp)*4 bytes ~= 16 * N^2 bytes
That is 1,6 Gb for the N=10000.
"""
m = ncp
(_, scores) = cpd_nonlin(K, m, backtrack=False, **kwargs)
# print("scores ",scores)
N = K.shape[0]
N2 = N*desc_rate # length of the video before subsampling
penalties = np.zeros(m+1)
# Prevent division by zero (in case of 0 changes)
ncp = np.arange(1, m+1)
penalties[1:] = (vmax*ncp/(2.0*N2))*(np.log(float(N2)/ncp)+1)
costs = scores/float(N) + penalties
m_best = np.argmin(costs)
# print("cost ",costs)
# print("m_best ",m_best)
(cps, scores2) = cpd_nonlin(K, m_best, **kwargs)
return (cps, costs)
# ------------------------------------------------------------------------------
# Extra functions (currently not used)
def estimate_vmax(K_stable):
"""K_stable - kernel between all frames of a stable segment"""
n = K_stable.shape[0]
vmax = np.trace(centering(K_stable)/n)
return vmax
def centering(K):
"""Apply kernel centering"""
mean_rows = np.mean(K, 1)[:, np.newaxis]
return K - mean_rows - mean_rows.T + np.mean(mean_rows)
def eval_score(K, cps):
""" Evaluate unnormalized empirical score
(sum of kernelized scatters) for the given change-points """
N = K.shape[0]
cps = [0] + list(cps) + [N]
V1 = 0
V2 = 0
for i in range(len(cps)-1):
K_sub = K[cps[i]:cps[i+1], :][:, cps[i]:cps[i+1]]
V1 += np.sum(np.diag(K_sub))
V2 += np.sum(K_sub) / float(cps[i+1] - cps[i])
return (V1 - V2)
def eval_cost(K, cps, score, vmax):
""" Evaluate cost function for automatic number of change points selection
K - kernel between all frames
cps - selected change-points
score - unnormalized empirical score (sum of kernelized scatters)
vmax - vmax parameter"""
N = K.shape[0]
penalty = (vmax*len(cps)/(2.0*N))*(np.log(float(N)/len(cps))+1)
return score/float(N) + penalty
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