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permutohedral_lattice.py
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permutohedral_lattice.py
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import numpy as np
from time import time
import logging
__author__ = 'Ido Freeman'
__email__ = "[email protected]"
log = logging.getLogger(__name__)
__all__ = ['PermutohedralLattice']
class HashTablePermutohedral(object):
def __init__(self, kd_, vd_):
"""
Constructor
Attributes
----------
kd_ : int
the dimensionality of the position vectors on the hyperplane.
vd_ : int
the dimensionality of the value vectors
"""
self.kd = kd_
self.vd = vd_
self.capacity = 2 ** 15
self.filled = 0
self.entries = [{'key_idx': -1, 'value_idx': -1} for _ in range(self.capacity)]
self.keys = np.zeros((kd_ * self.capacity / 2), dtype='int16')
self.values = np.zeros((vd_ * self.capacity / 2), dtype='float32')
def size(self):
return self.filled
def get_keys(self):
return self.keys
def get_values(self):
return self.values
def lookup_offset(self, key, h, create=True):
# Double hash table size if necessary
if self.filled >= (self.capacity / 2) - 1:
self._grow()
# Find the entry with the given key
while True:
e = self.entries[h]
if e['key_idx'] == -1:
if not create:
# return not found
return -1
# need to create an entry. Store the given key
for i in range(self.kd):
self.keys[self.filled * self.kd + i] = key[i]
e['key_idx'] = self.filled * self.kd
e['value_idx'] = self.filled * self.vd
self.entries[h] = e
self.filled += 1
return e['value_idx']
# check if the cell has a matching key
match = self.keys[e['key_idx']] == key[0]
i = 1
while i < self.kd and match:
match = self.keys[e['key_idx'] + i] == key[i]
i += 1
if match:
return e['value_idx']
# increment the bucket with wraparound
h += 1
if h == self.capacity:
h = 0
def lookup(self, k, create=True):
"""
Look up an object in the hash-table
Attributes
----------
k : numpy array
A list of keys to match
create : boolean, default True
Whether a new entry should be created it nothing is matched
Return
------
The index of the first object in k, when k is completely matched
"""
h = self._hash(k) % self.capacity
offset = self.lookup_offset(k, h, create)
if offset < 0:
return None
else:
return offset
def _hash(self, key):
k = 0
for i in range(self.kd):
k += key[i]
k *= 2531011
return k
def _grow(self):
log.info('Resizing hash table')
old_capacity = self.capacity
self.capacity *= 2
# Migrate the value vectors.
new_values = np.zeros((self.vd * self.capacity / 2), dtype='float32')
new_values[:self.vd * old_capacity / 2] = self.values
self.values = new_values
# Migrate the key vectors.
new_keys = np.zeros((self.kd * self.capacity / 2), dtype='int16')
new_keys[:self.kd * old_capacity / 2] = self.keys
self.keys = new_keys
# Migrate the table of indices.
new_entries = [{'key_idx': -1, 'value_idx': -1} for _ in range(self.capacity)]
for i in range(old_capacity):
if self.entries[i]['key_idx'] == -1:
continue
h = self.hash(
self.keys[self.entries[i]['key_idx']:self.entries[i]['key_idx'] + self.kd]
) % self.capacity
while new_entries[h]['key_idx'] != -1:
h += 1
if h == self.capacity:
h = 0
new_entries[h] = self.entries[i]
self.entries = new_entries
class PermutohedralLattice(object):
"""
Image filtering using a permutohedral lattice.
Notice the method filter() does all the work
"""
def __init__(self, d, vd, inp_len):
"""
Initialise a new lattice object
Attributes
----------
d : int
dimensionality of key vectors
vd : int
dimensionality of value vectors
inp_len : int
number of points in the input
"""
self.d = d
self.d1 = d + 1
self.vd = vd
self.inp_len = inp_len
self.hash_table = HashTablePermutohedral(d, vd)
self.elevated = np.zeros(self.d1, dtype='float32')
self.scale_factor = np.zeros((d), dtype='float32')
self.greedy = np.zeros(self.d1, dtype='int16')
self.rank = np.zeros(self.d1, dtype='int16')
self.barycentric = np.zeros((d + 2), dtype='float32')
self.replay = [{'offset': 0, 'weight': 0.} for _ in range(inp_len * self.d1)]
self.nReplay = 0
self.canonical = np.zeros((self.d1 ** 2), dtype='int16')
self.key = np.zeros(self.d1, dtype='int16')
self.splat_scale = 1. / self.d1
# compute the coordinates of the canonical simplex, in which
# the difference between a contained point and the zero
# remainder vertex is always in ascending order. (See pg.4 of paper.)
for i in range(self.d1):
for j in range(self.d1 - i):
self.canonical[i * self.d1 + j] = i
for j in range(self.d1 - i, self.d1):
self.canonical[i * self.d1 + j] = i - self.d1
expected_std = self.d1 * np.sqrt(2 / 3.)
# Compute parts of the rotation matrix E. (See pg.4-5 of paper.)
for i in range(d):
# the diagonal entries for normalization
self.scale_factor[i] = expected_std / np.sqrt((i + 1) * (i + 2))
"""
We presume that the user would like to do a Gaussian blur of standard deviation
1 in each dimension (or a total variance of d, summed over dimensions.)
Because the total variance of the blur performed by this algorithm is not d,
we must scale the space to offset this.
The total variance of the algorithm is (See pg.6 and 10 of paper):
[variance of splatting] + [variance of blurring] + [variance of splatting]
= d(d+1)(d+1)/12 + d(d+1)(d+1)/2 + d(d+1)(d+1)/12
= 2d(d+1)(d+1)/3.
So we need to scale the space by (d+1)sqrt(2/3).
"""
# self.scale_factor[i] *= self.d1 * np.sqrt(2. / 3)
@staticmethod
def filter(inp, ref, debug=True):
"""
Filter the image inp using the lattice defined by ref
Attributes
----------
inp : numpy array
The image to filter, should have the shape (rows, cols, channels)
ref : numpy array
The lattice to use for filtering
debug : boolean, default True
Whether the function should print its current state and the different run times
"""
run_times = [time()]
# create lattice
lattice = PermutohedralLattice(ref.shape[-1], inp.shape[-1] + 1, inp.shape[0] * inp.shape[1])
run_times.append(time())
if debug:
log.info('Splatting...')
col = np.zeros((inp.shape[-1] + 1), dtype='float32')
col[-1] = 1. # homogeneous coordinate
# roll out ref to support running indexing
ref_channels = ref.shape[-1]
ref = ref.flatten()
ref_ptr = 0
for r in range(inp.shape[0]): # height
for c in range(inp.shape[1]): # width
col[:-1] = inp[r, c, :]
lattice.splat(ref, ref_ptr, col)
ref_ptr += ref_channels
# Blur the lattice
if debug:
run_times.append(time())
log.info('Blurring...')
lattice.blur()
# Slice from the lattice
if debug:
run_times.append(time())
log.info('Slicing...')
out = np.zeros_like(inp)
lattice.begin_slice()
for r in range(inp.shape[0]): # height
for c in range(inp.shape[1]): # width
lattice.slice(col)
scale = 1. / col[-1]
out[r, c, :] = col[:-1] * scale
if debug:
run_times.append(time())
names = ['Init', 'Splat', 'Blur', 'Slice']
log.info('Timing table (including prints)')
for i in range(len(names)):
log.info('{}: {}s'.format(names[i], run_times[i + 1] - run_times[i]))
return out
def splat(self, position, pos_idx, value):
"""
Performs splatting with given position and value vectors
Attributes
----------
position : numpy array
The lattice
pos_idx : int
The index of the relevant position on the grid
"""
# first rotate position into the (d+1)-dimensional hyperplane
self.elevated[self.d] = -self.d * position[pos_idx + self.d - 1] * self.scale_factor[self.d - 1]
for i in range(self.d - 1, 0, -1):
self.elevated[i] = self.elevated[i + 1] - \
i * position[pos_idx + i - 1] * self.scale_factor[i - 1] + \
(i + 2) * position[pos_idx + i] * self.scale_factor[i]
self.elevated[0] = self.elevated[1] + 2 * position[pos_idx] * self.scale_factor[0]
v = self.elevated * self.splat_scale
v_ceil = np.ceil(v) * self.d1
v_floor = np.floor(v) * self.d1
self.greedy = np.where(v_ceil - self.elevated < self.elevated - v_floor, v_ceil, v_floor).astype('int16')
sum = np.sum(self.greedy) / self.d1
# reset rank
self.rank *= 0
# rank differential to find the permutation between this simplex and the canonical one.
# (See pg. 3-4 in paper.)
el_minus_gr = self.elevated - self.greedy
for i in range(self.d):
for j in range(i + 1, self.d1):
if el_minus_gr[i] < el_minus_gr[j]:
self.rank[i] += 1
else:
self.rank[j] += 1
if sum > 0:
# sum too large - the point is off the hyperplane.
# need to bring down the ones with the smallest differential
cond_mask = self.rank >= self.d1 - sum
self.greedy[cond_mask] -= self.d1
self.rank[cond_mask] -= self.d1
elif sum < 0:
# sum too small - the point is off the hyperplane
# need to bring up the ones with largest differential
cond_mask = self.rank < -sum
self.greedy[cond_mask] += self.d1
self.rank[cond_mask] += self.d1
self.rank += sum
# reset barycentric
self.barycentric *= 0
t = (self.elevated - self.greedy) * self.splat_scale
# Compute barycentric coordinates (See pg.10 of paper.)
for i in range(self.d1):
self.barycentric[self.d - self.rank[i]] += t[i]
self.barycentric[self.d1 - self.rank[i]] -= t[i]
self.barycentric[0] += 1. + self.barycentric[self.d1]
# Splat the value into each vertex of the simplex, with barycentric weights.
for remainder in range(self.d1):
# Compute the location of the lattice point explicitly
# (all but the last coordinate - it's redundant because they sum to zero)
self.key[:-1] = self.greedy[:-1] + self.canonical[remainder * self.d1 + self.rank[:-1]]
# Retrieve pointer to the value at this vertex.
hash_idx = self.hash_table.lookup(self.key, True)
# Accumulate values with barycentric weight.
# tmp = self.hash_table.values[hash_idx:hash_idx + self.vd] + self.barycentric[remainder] * value[
# :self.vd]
self.hash_table.values[hash_idx:hash_idx + self.vd] += self.barycentric[remainder] * value[:self.vd]
# Record this interaction to use later when slicing
self.replay[self.nReplay]['offset'] = hash_idx
self.replay[self.nReplay]['weight'] = self.barycentric[remainder]
self.nReplay += 1
def slice(self, col):
"""
Performs slicing out of position vectors. Note that the barycentric weights and the simplex
containing each position vector were calculated and stored in the splatting step.
We may reuse this to accelerate the algorithm. (See pg. 6 in paper.)
Attributes
----------
col : numpy array
A single position on the lattice
"""
base = self.hash_table.get_values()
col[:self.vd] = 0
for i in range(self.d1):
r = self.replay[self.nReplay]
self.nReplay += 1
for j in range(self.vd):
col[j] += r['weight'] * base[r['offset'] + j]
def blur(self, reverse=False):
"""
Performs a Gaussian blur along each projected axis in the hyperplane
Args
----
reverse: bool, default False
used for backprop (not supported in this version of the code)
"""
neighbour1 = np.zeros((self.d1), dtype='int16')
neighbour2 = np.zeros((self.d1), dtype='int16')
# new_vals = np.zeros((self.vd * self.hash_table.size()), dtype='float32')
new_vals_idx = 0
old_vals_idx = 0
hash_table_base_idx = 0
key = self.hash_table.get_keys()
new_vals = np.zeros((self.vd * self.hash_table.size()), dtype='float64')
old_vals = np.copy(self.hash_table.values)
# For each of d+1 axes, reverse takes care of the gradient computation during the backward pass
r = range(self.d, -1, -1) if reverse else range(self.d1)
for j in r:
# log.info(j)
# For each vertex in the lattice
for i in range(self.hash_table.size()): # blur point i in dimension j
neighbour1[:self.d] = key[i * self.d:(i + 1) * self.d] + 1
neighbour2[:self.d] = key[i * self.d:(i + 1) * self.d] - 1
neighbour1[j] = key[j + i * self.d] - self.d
neighbour2[j] = key[j + i * self.d] + self.d # keys to the neighbors along the given axis.
old_val_offset = old_vals_idx + i * self.vd
new_val_offset = new_vals_idx + i * self.vd
vm1_idx = self.hash_table.lookup(neighbour1, False) # look up first neighbor
if vm1_idx is not None:
vm1_idx -= hash_table_base_idx + old_vals_idx
else:
vm1_idx = None
vp1_idx = self.hash_table.lookup(neighbour2, False) # look up second neighbor
if vp1_idx is not None:
vp1_idx -= hash_table_base_idx + old_vals_idx
else:
vp1_idx = None
# Mix values of the three vertices
if vm1_idx is None:
vm1_val = 0
else:
vm1_val = old_vals[vm1_idx:vm1_idx + self.vd]
if vp1_idx is None:
vp1_val = 0
else:
vp1_val = old_vals[vp1_idx:vp1_idx + self.vd]
# applies the convolution with a 1d kernel [1, 2, 1]
# self.hash_table.values[new_val_offset:new_val_offset + self.vd] = \
new_vals[new_val_offset:new_val_offset + self.vd] = \
.25 * (vm1_val + vp1_val) + \
.5 * old_vals[old_val_offset:old_val_offset + self.vd]
tmp = new_vals_idx
new_vals_idx = old_vals_idx
old_vals_idx = tmp
tmp = new_vals
new_vals = old_vals
old_vals = tmp
# the freshest data is now in oldValue, and newValue is ready to be written over
self.hash_table.values = old_vals
def begin_slice(self):
"""
Prepare for slicing
"""
self.nReplay = 0