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powell method.py
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import cv2
import numpy as np
from loss import NCCS, NCCL
from module import prost_generator
import torch
import os
loss_func = NCCL
os.environ['CUDA_VISIBLE_DEVICES'] = '0'
device_ids = [0]
device = torch.device('cuda:{}'.format(device_ids[0]))
def gaussian(ori_image, down_times=2):
# 1：add the original image
temp_gau = ori_image.copy()
gaussian_pyramid = [temp_gau]
for i in range(down_times):
temp_gau = cv2.pyrDown(temp_gau)
gaussian_pyramid.append(temp_gau)
return gaussian_pyramid
def calculate_loss(pose, ct, fixed, corner_pt, param, norm_factor, H, W):
moving = prost_generator(pose, param, device, norm_factor, ct, fixed, corner_pt, H, W)
return loss_func(moving, fixed)
# Golden Section method for linear search
def line_search_test(a, b, f0, xtol, image_fixed, ct, corner_pt, param, norm_factor, H, W):
a1 = a + 0.382 * (b - a)
a2 = a + 0.618 * (b - a)
f1, f2 = calculate_loss(a1, image_fixed, ct, corner_pt, param, norm_factor, H, W).cpu(), calculate_loss(a2,
image_fixed,
ct,
corner_pt,
param,
norm_factor,
H, W).cpu()
while np.dot((b - a).squeeze(), (b - a).squeeze()) > xtol * xtol:
if f1 < f2:
if f1 < f0:
return np.around(a1, 1)
else:
b, a2, f2 = a2, a1, f1
a1 = b - 0.618 * (b - a)
f1 = calculate_loss(a1, image_fixed, ct, corner_pt, param, norm_factor, H, W).cpu()
else:
if f2 < f0:
return np.around(a2, 1)
else:
a, a1, f1 = a1, a2, f2
a2 = a + 0.618 * (b - a)
f2 = calculate_loss(a2, image_fixed, ct, corner_pt, param, norm_factor, H, W).cpu()
a = (a + b) / 2
a = np.around(a, 1)
return a
def get_line_bounds(start_parm, direction, down_bound, up_bound):
# start_parm=np.array([-1,-0.5]),direction=np.array([2,4]),down_bound=np.array([-1,-1]),up_bound=np.array([1,1])
bound = [[], []]
flag = 0
for i in range(len(direction)):
if abs(direction[i]) < 1e-5:
continue
# print(down_bound,start_parm)
k1 = (down_bound[i] - start_parm[0][i]) / direction[i]
# print("k1=",k1)
if check_valid(start_parm, direction, down_bound, up_bound, k1):
bound[flag] = (start_parm + k1 * direction).tolist()
# print(flag," ",bound[flag])
flag = flag + 1
if flag == 2:
res = np.array(bound)
return res[0], res[1]
k2 = (up_bound[i] - start_parm[0][i]) / direction[i]
# print("k2=",k2)
if check_valid(start_parm, direction, down_bound, up_bound, k2):
bound[flag] = (start_parm + k2 * direction).tolist()
# print(flag," ",bound[flag])
flag = flag + 1
if flag == 2:
res = np.array(bound)
return res[0], res[1]
print("error in get line bounds,Start point is in bound")
res = np.array(bound)
print("bounds:", res[0], res[1])
print("start_parm", start_parm)
print("down_bound", down_bound)
print("up_bound", up_bound)
print("direction", direction)
return res[0], res[1]
def check_valid(start_parm, direction, down_bound, up_bound, k):
err = 1e-5
point = start_parm + k * direction
for i in range(len(point)):
if point[0][i] > up_bound[i] + err or point[0][i] < down_bound[i] - err:
return False
return True
def powell_search_double(down_bound, up_bound, start_parm, tol, xtol, image_fixed,
max_iterations, corner_pt, param, ct, norm_factor, H, W):
directions = np.identity(6)
pos = start_parm
f_val_ori = calculate_loss(pos, ct, image_fixed, corner_pt, param, norm_factor, H, W).cpu()
f_val = f_val_ori
iteration_count = 0
order = [3, 1, 2, 4, 5, 0]
# store all the intermediate results
global list_err
while True:
iteration_count = iteration_count + 1
f_val_pre = f_val
pos_pre = pos
list_one_iteration = []
lambda_turn = []
list_err = []
for j in range(6):
i = order[j]
direction = directions[i].squeeze()
a, b = get_line_bounds(pos, direction, down_bound, up_bound)
if len(a) == 0 or len(b) == 0:
print("get line bound error")
return f_val, pos
pos_pre_line = pos
pos = line_search_test(a, b, f_val, xtol, image_fixed, ct, corner_pt, param,
norm_factor, H, W)
if (pos < pos_pre_line).all():
up_bound = pos_pre_line
if (pos > pos_pre_line).all():
down_bound = pos_pre_line
f_val_pre_line = f_val
f_val = calculate_loss(pos, ct, image_fixed, corner_pt, param, norm_factor, H, W).cpu()
if (f_val > f_val_pre_line):
f_val = f_val_pre_line
pos = pos_pre_line
lambda_turn.append(np.dot((np.array(pos_pre_line) - np.array(pos)).squeeze(),
(np.array(pos_pre_line) - np.array(pos)).squeeze()))
list_one_iteration.append(f_val)
new_direction = (pos - pos_pre).squeeze()
if np.dot(new_direction, new_direction) < 1e-5:
print("early stop")
return f_val, pos
a, b = get_line_bounds(pos, new_direction, down_bound, up_bound)
if len(a) == 0 or len(b) == 0:
print("get line bound error")
return f_val, pos
pos_pre = pos
pos = line_search_test(a, b, f_val, xtol, image_fixed, ct, corner_pt, param,
norm_factor, H, W)
if (pos < pos_pre).all():
up_bound = pos_pre_line
if (pos > pos_pre).all():
down_bound = pos_pre_line
f_val = calculate_loss(pos, ct, image_fixed, corner_pt, param, norm_factor, H, W).cpu()
list_one_iteration.append(f_val)
list_err.append(list_one_iteration)
max_lambda = 0.0
res_directions = np.array(directions, copy=True)
for i in range(6):
if lambda_turn[i] > max_lambda:
t = np.array(directions, copy=True)
t[i, :] = new_direction
if abs(np.linalg.det(t)) > 1e-5:
res_directions = t
max_lambda = lambda_turn[i]
if abs(max_lambda) < 1e-5:
print("Error updating direction vector")
return f_val, pos
directions = res_directions
if (abs(f_val_pre - f_val) < tol) or (iteration_count >= max_iterations):
print("------------------------------------\nEnd of search")
if (iteration_count == max_iterations):
print("Maximum number of iterations reached")
break
return f_val, pos
def multi_resolution_search(ct, x_ray, initial_pose, corner_pt, param, norm_factor, H, W):
gaussian_pyramid = gaussian(x_ray, down_times=2)
lower_bound_1 = np.array([90, 0, 0, 900, 0, 0], dtype=np.float32) + np.array([-40, -40, -40, -100, -40, -25],
dtype=np.float32)
upper_bound_1 = np.array([90, 0, 0, 900, 0, 0], dtype=np.float32) + np.array([40, 40, 40, 200, 40, 25],
dtype=np.float32)
_, pos = powell_search_double(lower_bound_1, upper_bound_1, initial_pose, 1, 0.1, gaussian_pyramid[2],
max_iterations=10,
corner_pt=corner_pt, param=param, norm_factor=norm_factor, H=H / 4, W=W / 4)
lower_bound_2 = np.array([90, 0, 0, 900, 0, 0], dtype=np.float32) + np.array([-20, -20, -20, -50, -20, -10],
dtype=np.float32)
upper_bound_2 = np.array([90, 0, 0, 900, 0, 0], dtype=np.float32) + np.array([20, 20, 20, 50, 20, 10],
dtype=np.float32)
_, pos = powell_search_double(lower_bound_2, upper_bound_2, pos, 0.1, 0.01, gaussian_pyramid[1], max_iterations=5,
corner_pt=corner_pt, param=param, norm_factor=norm_factor, H=H / 2, W=W / 2)
lower_bound_3 = np.array([90, 0, 0, 900, 0, 0], dtype=np.float32) + np.array([-2, -2, -2, -5, -5, -5],
dtype=np.float32)
upper_bound_3 = np.array([90, 0, 0, 900, 0, 0], dtype=np.float32) + np.array([2, 2, 2, 5, 5, 5],
dtype=np.float32)
_, pos = powell_search_double(lower_bound_3, upper_bound_3, pos, 1e-3, 1e-4, gaussian_pyramid[0], max_iterations=5,
corner_pt=corner_pt, param=param, norm_factor=norm_factor, H=H, W=W)
return pos