def testBenchmarkMinimizeErrorPlot(self):
fileprint = False
sigma_R = 0.005
sigma_T = 0.007
N_training = 30
N_plot = 4
line1, line2 = createRandomLines(2)
R_real = RotorLine2Line(line1, line2)
traininglinesets = createNoisyLineSet(R_real, sigma_R, sigma_T,
N_training)
R_min, nit = minimizeError(traininglinesets, RotorLineMapping)
validationlines = createRandomLines(N_plot)
plot = Plot3D()
for line in validationlines:
line_real = R_real * line * ~R_real
line_est = R_min * line * ~R_min
plot.addLine(line_real)
plot.addLine(line_est)
if fileprint:
timestring = time.strftime("%Y%m%d-%H%M%S")
figname = "../benchmarkreports/plot_%s.png" % timestring
plot.save(figname)
def testBenchmarkLinesMinimizeError(self):
seed = 21
sigma_T = 0.005
sigma_R = 0.002
N = 10
line1, line2 = createRandomLines(2)
R_real = RotorLine2Line(line1, line2)
traininglinesets = createNoisyLineSet(R_real, sigma_R, sigma_T, N)
validationlinesets = createNoisyLineSet(R_real, sigma_R, sigma_T, N)
print(
"Training and validation sets created with sig_r = %f and sig_t = %f, N = %d"
% (sigma_R, sigma_T, N))
map_list = [BivectorLineMapping]
for map_obj in map_list:
np.random.seed(seed)
print(map_obj.name)
benchmarkMinimizeError(R_real,
traininglinesets,
validationlinesets,
fileout=None,
mapping=map_obj)
def setUpMultiView(self, N_lines, K_imgs, sigma_R_image = 0.001, sigma_T_image = 0.001):
#Define random rotations for our cameras
R_list = [ga_exp(createRandomBivector()) for _ in range(K_imgs)]
#Create N lines
lines = createRandomLines(N_lines, scale = 2)
for i in range(len(lines)):
lines[i] = Sandwich(lines[i], Translator(e3*4))
#Create our noise free images for comparison
lines_img_base_d_real = [projectLineToPlane(line, one) for line in lines] #Real base lines
lines_imgs_d_real = [[projectLineToPlane(line, R_list[i]) for line in lines] for i in range(K_imgs)]
#Create noisy images
lines_img_base_d = [perturbeObjectInplane(projectLineToPlane(line, one) , sigma_R_image, sigma_T_image) for line in lines]
lines_imgs_d = [[perturbeObjectInplane(projectLineToPlane(line, R_list[i]), sigma_R_image, sigma_T_image) for line in lines] for i in range(K_imgs)]
i = 0
#for j in range(len(lines_imgs_d[i])):
# print((R_list[i]*(-no ^ lines_imgs_d_real[i][j])* ~R_list[i]).normal())
# print(((R_list[i]*(-no)* ~R_list[i])^lines[j]).normal())
# print("")
return R_list, lines, lines_img_base_d, lines_img_base_d_real , lines_imgs_d, lines_imgs_d_real
def testNoisyRotationExtendedExtraction(self):
verbose = True
np.random.seed(2)
O1 = up(0)
B = 0.1 * e12 + 0.2*e13 + 0.1 *e23 + 1*(3*e1 -1*e2 + 2*e3)*ninf + 0.1 * E0
R = np.exp(B)
N = 100
lines = createRandomLines(N, scale = 2)
for i in range(len(lines)):
lines[i] = Sandwich(lines[i], Translator(e3*3))
sigma_R_model = 0.001
sigma_T_model = 0.001
lines_perturbed = [perturbeObject(line, sigma_T_model, sigma_R_model) for line in lines] #Model noise
lines_img_d_real = [projectLineToPlane(line, R) for line in lines] #Real lines
sigma_R_image = 0.001
sigma_T_image = 0.001
lines_img_d = [perturbeObjectInplane(projectLineToPlane(line, R), sigma_R_image, sigma_T_image) for line in lines]
#using our noisy model and the noisy image of them to estimate R
R_min, Nint = minimizeError((lines_perturbed, lines_img_d), ExtendedBivectorLineImageMapping , x0 = None)
if verbose:
print("R: ", R)
print("R_min", R_min)
assert(MVEqual(R_min, R, rtol = 1e-2, atol = 1e-2, verbose = False)) #Hard coded values.
#Weird condition. But we hope to find a "better" solution than the true one for the data we see, but worse than the true projection
assert(sumImageFunction(R, lines, lines_img_d) > sumImageFunction(R_min, lines, lines_img_d) > sumImageFunction(R, lines, lines_img_d_real))
def testThreeViewAllPairsEstimation(self):
np.random.seed(3)
N = 5
#Defining the external parameters
B_A = (0.1 * e12 + 0.2*e13 + 0.1 *e23 + (3*e1 -1*e2 + 2*e3)*ninf)
R_A = ga_exp(B_A)
B_B = (-0.2 * e12 + -0.1*e13- 0.05 *e23 + (1*e1 +2*e2 - 3*e3)*ninf)
R_B = ga_exp(B_B)
dx = np.random.normal(size=12, scale=0.01) #Starting estimate is slightly off
x0 = MultiViewLineImageMapping.inverserotorconversion([R_A, R_B]) + dx
R_A_start, R_B_start = MultiViewLineImageMapping.rotorconversion(x0)
lines = createRandomLines(N, scale = 2)
for i in range(len(lines)):
lines[i] = Sandwich(lines[i], Translator(e3*10))
lines_img_d_base_real = [projectLineToPlane(line, one) for line in lines] #Real lines A
lines_img_d_A_real = [projectLineToPlane(line, R_A) for line in lines] #Real lines A
lines_img_d_B_real = [projectLineToPlane(line, R_B) for line in lines] #Real lines A
sigma_R_image = 0.00001
sigma_T_image = 0.00001
lines_img_base_d = [perturbeObjectInplane(projectLineToPlane(line, one), sigma_R_image, sigma_T_image) for line in lines]
lines_img_A_d = [perturbeObjectInplane(projectLineToPlane(line, R_A), sigma_R_image, sigma_T_image) for line in lines]
lines_img_B_d = [perturbeObjectInplane(projectLineToPlane(line, R_B), sigma_R_image, sigma_T_image) for line in lines]
#print("No noise cost =", MultiViewLineImageMapping.costfunction(R_A, R_B, lines_img_d_base_real, lines_img_d_A_real, lines_img_d_B_real))
#Computation
lines_imgs_d = [lines_img_A_d, lines_img_B_d]
args = (lines_img_base_d, )
R_list, Nint = minimizeError(args ,MultiViewLineImageMapping, x0 = x0)
R_A_min, R_B_min = R_list
#Output
print("Nint = ", Nint)
print("")
print("R_A_real : ", R_A)
print("R_A_min : ", R_A_min)
print("R_A_start: ", R_A_start)
print("")
print("R_B_real: ", R_B)
print("R_B_min : ", R_B_min)
print("R_B_start: ", R_B_start)
print("")
print("Start cost =", MultiViewLineImageMapping.costfunction(R_A_start, R_B_start, lines_img_base_d, lines_img_A_d, lines_img_B_d))
print("Final cost =", MultiViewLineImageMapping.costfunction(R_A_min, R_B_min, lines_img_base_d, lines_img_A_d, lines_img_B_d))
print("Target cost =", MultiViewLineImageMapping.costfunction(R_A, R_B, lines_img_base_d, lines_img_A_d, lines_img_B_d))
print("No noise cost =", MultiViewLineImageMapping.costfunction(R_A, R_B, lines_img_d_base_real, lines_img_d_A_real, lines_img_d_B_real))
def testImageCostFunction(self):
O1 = up(0)
B = 0.1 * e12 + 0.2*e13 + 0.1 *e23 + (3*e1 -1*e2 + 2*e3)*ninf
R = ga_exp(B)
N = 10
lines = createRandomLines(N, scale = 30)
cPlane1 = (ninf + e3)*I5 #Camera plane 1
cPlane2 = R * cPlane1 * ~R
lines_img_d = [projectLineToPlane(line, R) for line in lines]
assert(sumImageFunction(R, lines, lines_img_d) < 1e-20) #Very small
R_wrong = ga_exp(B * 0.5)
assert(sumImageFunction(R_wrong, lines, lines_img_d) > 1e-5) #not very small
def testLineAveraging(self):
seed = 1
sigma_T = 0.005
sigma_R = 0.002
N = 100
mapping = BivectorLineMapping
line_start, line_target = createRandomLines(2)
R_real_min, N_int = minimizeError([(line_start, line_target)],
mapping=BivectorLineMapping)
R_real = RotorLine2Line(line_start, line_target)
print("R_real ", R_real)
print("R_real_min", R_real_min)
print("B_real_min", ga_log(R_real_min))
print("B_real ", ga_log(R_real))
print("L_real_min", R_real_min * line_start * ~R_real_min)
traingingdata = [
line_start,
[perturbeObject(line_target, sigma_R, sigma_T) for _ in range(N)]
]
validationdata = [
line_start,
[perturbeObject(line_target, sigma_R, sigma_T) for _ in range(N)]
]
print(
"Training and validation sets created with sig_r = %f and sig_t = %f, N = %d"
% (sigma_R, sigma_T, N))
map_list = [BivectorLineEstimationMapping]
for map_obj in map_list:
np.random.seed(seed)
print(map_obj.name)
realtrainingcost, minimumvalidationcost, R_min = benchmarkMinimizeError(
R_real,
traingingdata,
validationdata,
N=N,
fileout=None,
mapping=map_obj)
print("L_real = ", line_target)
print("L_min = ", R_min * line_start * ~R_min)
print("L_example= ", validationdata[0])
def testRotationExtraction(self):
np.random.seed(2)
O1 = up(0)
B = 0.1 * e12 + 0.2*e13 + 0.1 *e23 + (3*e1 -1*e2 + 2*e3)*ninf
R = ga_exp(B)
N = 10
lines = createRandomLines(N, scale = 30)
cPlane1 = (ninf + e3)*I5 #Camera plane 1
cPlane2 = R * cPlane1 * ~R
lines_img_d = [projectLineToPlane(line, R) for line in lines]
R_min, Nint = minimizeError((lines, lines_img_d), BivectorLineImageMapping, x0 = None)
assert(MVEqual(R_min, R, rtol = 1e-2, atol = 1e-2, verbose = False)) #Hard coded values.
assert(sumImageFunction(R, lines, lines_img_d) < sumImageFunction(R_min, lines, lines_img_d))
def testExtremeRotationExtraction(self):
verbose = True
np.random.seed(2)
O1 = up(0)
rot_scale = 10
tran_scale = 10
spread_scale = 10
B = 0.1 * e12 + 0.2*e13 + 0.1 *e23 + rot_scale*(3*e1 -1*e2 + 2*e3)*ninf
R = ga_exp(B)
N = 10
lines = createRandomLines(N, scale = spread_scale)
for i in range(len(lines)):
lines[i] = Sandwich(lines[i], Translator(e3*tran_scale))
sigma_R_model = 0.001
sigma_T_model = 0.001
lines_perturbed = [perturbeObject(line, sigma_T_model, sigma_R_model) for line in lines] #Model noise
lines_img_d_real = [projectLineToPlane(line, R) for line in lines] #Real lines
sigma_R_image = 0.001
sigma_T_image = 0.001
lines_img_d = [perturbeObjectInplane(projectLineToPlane(line, R), sigma_R_image, sigma_T_image) for line in lines]
mapping = BivectorLineImageMapping
x0 = mapping.inverserotorconversion(R)
x0[:3] += np.array([0.1, 0.9, -0.17])
R_start = mapping.rotorconversion(x0)
#using our noisy model and the noisy image of them to estimate R
R_min, Nint = minimizeError((lines_perturbed, lines_img_d), mapping, x0 = x0)
if verbose:
print("R: ", R)
print("R_min ", R_min/np.sign(R_min[0]))
print("R_start", R_start/np.sign(R_start[0]))
print("")
print("B: ", B)
print("B_min - B ", ga_log(R_min/np.sign(R_min[0])) - B)
print("B_start - B ", ga_log(R_start/np.sign(R_start[0])) - B)
def testLinePointError(self):
print("\nWARNING: SLOW")
#Testing how using the distance from certain points on a line as a good external metric of how well we are performing.
np.random.seed(10)
sigma_R = 0.05
sigma_T = 0.07
N = 20
line1, line2 = createRandomLines(2)
R_real = RotorLine2Line(line1, line2)
traininglinesets = createNoisyLineSet(R_real, sigma_R, sigma_T, N)
#Test various minimazation algorithms
R_rotor, nit = minimizeError(traininglinesets, RotorLineMapping)
R_bivector, nit = minimizeError(traininglinesets, BivectorLineMapping)
R_lineproduct, nit = minimizeError(traininglinesets,
LinePropertyBivectorMapping)
R_dummy = RotorLine2Line(
traininglinesets[0][0], traininglinesets[0]
[1]) #comparing it to just taking the first one we find
R_list = [R_rotor, R_bivector, R_lineproduct, R_dummy]
costs = []
N_val = 10
N_points = 4
for R in R_list:
costs.append(linePointCostMetric(R, R_real, N_val=N_val))
print("rotor_pointcost ", costs[0])
print("bivector_pointcost ", costs[1])
print("lineproduct_pointcost ", costs[2])
print("dummy_pointcost ", costs[3])
def benchmarkImageCostFunction():
np.random.seed(123)
B = createRandomBivector()
R_real = ga_exp(B)
N = 10
lines = createRandomLines(N, scale = 2)
for i in range(len(lines)):
lines[i] = Sandwich(lines[i], Translator(e3*3))
sigma_R_model = 0.01
sigma_T_model = 0.01
lines_perturbed = [perturbeObject(line, sigma_T_model, sigma_R_model) for line in lines] #Model noise
lines_img_d_real = [projectLineToPlane(line, R_real) for line in lines] #Real lines
sigma_R_image = 0.01
sigma_T_image = 0.01
lines_img_d = [perturbeObjectInplane(projectLineToPlane(line, R_real), sigma_R_image, sigma_T_image) for line in lines]
traininglinesets = (lines_perturbed, lines_img_d)
benchmarkMinimizeError(R_real, traininglinesets, traininglinesets, fileout = None, mapping = BivectorLineImageMapping)
def plotCostFunctionEffect():
print("\nRunning plotCostFunctionEffect")
print("")
np.random.seed(1)
N_train = 20
line_scale = 10
translation_scale = 10
#Test extreme values
sigma_R = 0.01
sigma_T = 1
line1, line2 = createRandomLines(2)
a = createRandomVector(scale=translation_scale)
print("Translated lineA by ", a)
b = createRandomVector(scale=translation_scale)
print("Translated lineB by ", b)
T_a = Translator(a)
T_b = Translator(b)
#Move them far away from the origin
lineA = T_a * line1 * ~T_a
lineB = T_b * line2 * ~T_b
R_real = RotorLine2Line(lineA, lineB)
linesets = createNoisyLineSet(R_real,
sigma_R,
sigma_T,
N_train,
scale=line_scale)
mapping = BivectorWeightedLineMapping
mapping.costfunction = sumWeightedLineSquaredErrorCost(1. /
translation_scale)
x0 = mapping.inverserotorconversion(R_real)
x_test = x0[0]
y_test = x0[3]
N_rot = 50
N_tran = 50
rot_range = 0.4
translation_range = 10
rotation = np.linspace(-rot_range, rot_range, N_rot)
translation = np.linspace(-translation_range, translation_range, N_tran)
ans = np.zeros((N_rot, N_tran))
for i, rot in enumerate(rotation):
for j, tran in enumerate(translation):
x0[0] = x_test + tran
x0[3] = y_test + rot
ans[i, j] = np.log(
mapping.costfunction(mapping.rotorconversion(x0), linesets))
xv, yv = np.meshgrid(translation, rotation)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_xlabel("Translation error")
ax.set_ylabel("Rotation error")
ax.set_zlabel("log(objective function)")
ax.plot_wireframe(xv, yv, ans)
plt.show()
def testWeigthingFunction(self):
print("\nRunning testWeigthingFunction")
print("")
#np.random.seed(5)
#Test on some extreme values
sigma_R = 0.01
sigma_T = 0.1
N_train = 100
N_val = 20
line_scale = 10
translation_scale = 100
line1, line2 = createRandomLines(2)
a = createRandomVector(scale=translation_scale)
print("Translated lineA by ", a)
b = createRandomVector(scale=translation_scale)
print("Translated lineB by ", b)
T_a = Translator(a)
T_b = Translator(b)
#Move them far away from the origin
lineA = T_a * line1 * ~T_a
lineB = T_b * line2 * ~T_b
R_real = RotorLine2Line(lineA, lineB)
#x0 = BivectorWeightedLineMapping.inverserotorconversion(R_real)
#x0 += np.array([15, 21, -11, 0.1, -0.1, 0.21])
#R_start = BivectorWeightedLineMapping.
#R_start = BivectorWeightedLineMapping.rotorconversion(x0)
traininglinesets = createNoisyLineSet(R_real,
sigma_R,
sigma_T,
N_train,
scale=line_scale)
validationlinesets = createNoisyLineSet(R_real,
sigma_R,
sigma_T,
N_val,
scale=line_scale)
mapping = BivectorWeightedLineMapping
weightList = [1e-4, 1e-2, 1, 1e2, 1e4]
#mappingList = [BivectorLineMapping, LinePropertyBivectorMapping, BivectorLogCostLineMapping]
plot = Plot3D()
testline = validationlinesets[0][0]
plot.addLine(R_real * testline * ~R_real, color='r')
for weight in weightList:
t0 = time.time()
print("Running %s" % mapping.name)
print("Weight = %e" % weight)
#Test various minimazation algorithms
mapping = BivectorWeightedLineMapping
mapping.costfunction = sumWeightedLineSquaredErrorCost(weight)
R_min, nit = minimizeError(traininglinesets, mapping, x0=None)
#mapping.costfunction = logSumWeightedLineSquaredErrorCost(weight)
#Finding the cost if we used the actual rotor used to generate the matrix
realtrainingcost = mapping.costfunction(R_real, traininglinesets)
print("Real training cost is %s" % str(realtrainingcost))
realvalidationcost = mapping.costfunction(R_real,
validationlinesets)
print("Real validation cost is %s" % str(realvalidationcost))
minimumtrainingcost = mapping.costfunction(R_min, traininglinesets)
print("minimized training cost %f" % minimumtrainingcost)
minimumvalidationcost = mapping.costfunction(
R_min, validationlinesets)
print("minimized validation cost = %f" % minimumvalidationcost)
realpointcost = linePointCostMetric(R_real, R_min, 10)
print(
"Averaged cost for points a: %f, a + m: %f, a + 10m: %f, a + 100m: %f, a + 1000m: %f"
% tuple(realpointcost))
print("")
print("R_real= %s" % str(R_real / np.sign(float(R_real(0)))))
print("R_min = %s" % str(R_min / np.sign(float(R_min(0)))))
#print("R_start = %s" % str(R_start/np.sign(float(R_start(0)))))
B_real = ga_log(R_real / np.sign(float(R_real(0))))
B_min = ga_log(R_min / np.sign(float(R_min(0))))
#B_start = ga_log(R_start/np.sign(float(R_start(0))))
print("")
print("B_real= %s" % str(B_real))
print("B_min = %s" % str(B_min))
#print("B_start = %s" % str(B_start))
print("")
print("C(R(B_real - B_min)) = %f" %
rotorAbsCostFunction(ga_exp(B_min - B_real)))
plot.addLine(R_min * testline * ~R_min, color=mapping.color)
t_end = time.time()
print("")
print(
"Running time for extracting best rotor for %d line pairs is %f s"
% (N_train, t_end - t0))
print("\n\n")
plot.show(False)
def testExtremeLineRotation(self):
print("\nRunning testExtremeLineRotation")
print("")
np.random.seed(1)
#Test extreme values
sigma_R = 0.1
sigma_T = 1
N_train = 100
N_val = 20
line_scale = 1000
translation_scale = 1000
line1, line2 = createRandomLines(2)
a = createRandomVector(scale=translation_scale)
print("Translated lineA by ", a)
b = createRandomVector(scale=translation_scale)
print("Translated lineB by ", b)
T_a = Translator(a)
T_b = Translator(b)
#Move them far away from the origin
lineA = T_a * line1 * ~T_a
lineB = T_b * line2 * ~T_b
R_real = RotorLine2Line(lineA, lineB)
traininglinesets = createNoisyLineSet(R_real,
sigma_R,
sigma_T,
N_train,
scale=line_scale)
validationlinesets = createNoisyLineSet(R_real,
sigma_R,
sigma_T,
N_val,
scale=line_scale)
mappingList = [BivectorLineMapping]
x0 = BivectorLineMapping.inverserotorconversion(R_real)
x0 += np.array([0.1, 0.2, -0.1, 1, -0.1, 0.21])
plot = Plot3D()
testline = validationlinesets[0][0]
plot.addLine(R_real * testline * ~R_real, color='r')
for mapping in mappingList:
t0 = time.time()
print("Running %s" % mapping.name)
#Test various minimazation algorithms
R_min, nit = minimizeError(traininglinesets, mapping, x0=x0)
costfunction = mapping.costfunction
#Finding the cost if we used the actual rotor used to generate the matrix
realtrainingcost = costfunction(R_real, traininglinesets)
print("Real training cost is %s" % str(realtrainingcost))
realvalidationcost = costfunction(R_real, validationlinesets)
print("Real validation cost is %s" % str(realvalidationcost))
minimumtrainingcost = costfunction(R_min, traininglinesets)
print("minimized training cost %f" % minimumtrainingcost)
minimumvalidationcost = costfunction(R_min, validationlinesets)
print("minimized validation cost = %f" % minimumvalidationcost)
realpointcost = linePointCostMetric(R_real, R_min, 10)
print(
"Averaged cost for points a: %f, a + m: %f, a + 10m: %f, a + 100m: %f, a + 1000m: %f"
% tuple(realpointcost))
print("")
print("R_real= %s" % str(R_real / np.sign(float(R_real(0)))))
print("R_min = %s" % str(R_min / np.sign(float(R_min(0)))))
B_real = ga_log(R_real / np.sign(float(R_real(0))))
B_min = ga_log(R_min / np.sign(float(R_min(0))))
print("B_real= %s" % str(B_real))
print("B_min = %s" % str(B_min))
print("")
print("C(R(B_real - B_min)) = %f" %
rotorAbsCostFunction(ga_exp(B_min - B_real)))
plot.addLine(R_min * testline * ~R_min, color=mapping.color)
t_end = time.time()
print("")
print(
"Running time for extracting best rotor for %d line pairs is %f s"
% (N_train, t_end - t0))
print("\n\n")
plot.show(False)
def plotCostFunctionEffect():
print("\nRunning plotCostFunctionEffect")
print("")
np.random.seed(1)
#Test extreme values
np.random.seed(2)
O1 = up(0)
rot_scale = 1
tran_scale = 10
spread_scale = 10
B = 0.1 * e12 + 0.2*e13 - 0.1 *e23 + rot_scale*(3*e1 -1*e2 + 2*e3)*ninf
R = ga_exp(B)
N = 10
lines = createRandomLines(N, scale = spread_scale)
for i in range(len(lines)):
lines[i] = Sandwich(lines[i], Translator(e3*tran_scale))
sigma_R_model = 0.01
sigma_T_model = 0.1
lines_perturbed = [perturbeObject(line, sigma_T_model, sigma_R_model) for line in lines] #Model noise
lines_img_d_real = [projectLineToPlane(line, R) for line in lines] #Real lines
sigma_R_image = 0.002
sigma_T_image = 0.01
lines_img_d = [perturbeObjectInplane(projectLineToPlane(line, R), sigma_R_image, sigma_T_image) for line in lines]
mapping = BivectorLineImageMapping
x0 = mapping.inverserotorconversion(R)
x_test = x0[0]
y_test = x0[3]
N_rot = 50
N_tran = 50
rot_range = 0.4
translation_range = 10
rotation = np.linspace(-rot_range, rot_range, N_rot)
translation = np.linspace(-translation_range, translation_range, N_tran)
ans = np.zeros((N_rot, N_tran))
for i, rot in enumerate(rotation):
for j, tran in enumerate(translation):
x0[0] = x_test + tran
x0[3] = y_test + rot
ans[i, j] = np.log(mapping.costfunction(mapping.rotorconversion(x0), lines_perturbed, lines_img_d, O1))
xv, yv = np.meshgrid(translation, rotation)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_xlabel("Translation error")
ax.set_ylabel("Rotation error")
ax.set_zlabel("log(objective function)")
ax.plot_wireframe(xv, yv, ans)
plt.show()
def testPlotProjections(self):
np.random.seed(2)
#A, B = createRandomPoints(2, 100) #Real points
#L = createLine(A, B) #Real line
O1 = up(0)
F1 = up(e3) #Image origin
Q1 = up(e3 + e2) #Defines image rotation
#O1 = up(3*e1 + 4*e2)
#cPlane1 = createRandomPlane(2)
B = 0.1 * e12 + 0.2*e13 + 0.1 *e23 + 1*(3*e1 -1*e2 + 2*e3)*ninf
#x0 = np.array([0.54, 0.85, 0.29, 1*3.1, -1.4 * 1, 1*1.89]) #Close to the real answer
N = 10
R = ga_exp(B)
O2 = R * O1 * ~R #O2
F2 = R * F1 * ~R
Q2 = R * Q1 * ~R
cPlane1 = (ninf + e3)*I5 #Camera plane 1
cPlane2 = R * cPlane1 * ~R
lines = createRandomLines(N, scale = 2)
for i in range(len(lines)):
lines[i] = Sandwich(lines[i], Translator(e3*3))
sigma_R_model = 0.01
sigma_T_model = 0.05
lines_perturbed = [perturbeObject(line, sigma_T_model, sigma_R_model) for line in lines] #Model noise
lines_img_d_real = [projectLineToPlane(line, R) for line in lines] #Real lines
sigma_R_image = 0.0001
sigma_T_image = 0.0001
lines_img_d = [perturbeObjectInplane(projectLineToPlane(line, R), sigma_R_image, sigma_T_image) for line in lines]
print("")
print("Inital cost", sumImageFunction(R, lines_perturbed, lines_img_d))
print("R_real: ", R)
R_min, Nint = minimizeError((lines_perturbed, lines_img_d), BivectorLineImageMapping, x0 = None)
print("R_min: ", R_min)
print("Nint = ", Nint)
print("Final cost= ", sumImageFunction(R_min, lines, lines_img_d))
lines_img_d_min = [projectLineToPlane(line, R_min) for line in lines]
lines_img_d_model = [projectLineToPlane(line, R_min) for line in lines_perturbed]
#Printing
color_print = ['m', 'y', 'k']
N_print = len(color_print)
plot_img = Plot2D()
for i in range(N_print):
Limg = lines_img_d[i]
Limg_min = lines_img_d_min[i]
Limg_real = lines_img_d_real[i]
Limg_model = lines_img_d_model[i]
plot_img.plotLine2D(Limg_min, color = 'g') #Green: estimate of the real line (hidden)
plot_img.plotLine2D(Limg_model, color = 'c') #Cyan: estimate of model line
plot_img.plotLine2D(Limg, color = 'b') #Blue: image (with image noise)
plot_img.plotLine2D(Limg_real, color = color_print[i]) #Other: real line (hidden)
plot = Plot3D()
plot.configure(5)
plot.addPoint(O1, color='r')
plot.addPoint(O2, color='b')
#plot.addPoint(F1, color='r')
plot.addPoint(F2, color='b')
#plot.addPoint(Q1, color='r')
plot.addPoint(Q2, color='b')
for i in range(N_print):
L = lines[i]
L_img = R*lines_img_d_real[i]*~R
L_perturbed = lines_perturbed[i]
plot.addLine(L_perturbed, color = 'c')
plot.addLine(L_img, color = color_print[i])
plot.addLine(L, color = color_print[i])
#plot.addPlane(cPlane1, center = F1, color='r')
plot.addPlane(cPlane2, center = F2, color='b')
plot_img.show(block = False)
plot.show(block = False)