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pose2sim/Pose2Sim/synchronize_cams.py
davidpagnon 2bb5bbbc4b a
2024-03-20 14:16:38 +01:00

615 lines
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
'''
#########################################
## SYNCHRONIZE CAMERAS ##
#########################################
TODO:
- no ref cam (least amount of frames), no kpt selection
- recap
- whole sequence or around approx time (if long)
- somehow fix demo (offset 0 frames when 0 frames offset, right now [0,-2,-2]) -> min_conf = 0.4 (check problem with 0.0)
Steps undergone in this script
0. Converting json files to pandas dataframe
1. Computing speeds (vertical)
2. Plotting paired correlations of speeds from one camera viewpoint to another (work on one single keypoint, or on all keypoints, or on a weighted selection of keypoints)
3.
Ideally, this should be done automatically for all views, checking pairs 2 by 2 with the highest correlation coefficient,
and ask for confirmation before deleting the frames in question (actually renamed .json.del - reset_sync option in Config.toml).
'''
## INIT
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy import signal
from scipy import interpolate
import json
import os
import fnmatch
import pickle as pk
import re
## AUTHORSHIP INFORMATION
__author__ = "HunMin Kim, David Pagnon"
__copyright__ = "Copyright 2021, Pose2Sim"
__credits__ = ["David Pagnon"]
__license__ = "BSD 3-Clause License"
__version__ = '0.7'
__maintainer__ = "David Pagnon"
__email__ = "contact@david-pagnon.com"
__status__ = "Development"
# FUNCTIONS
def convert_json2pandas(json_dir, min_conf=0.6):
'''
Convert JSON files in a directory to a pandas DataFrame.
INPUTS:
- json_dir: str. The directory path containing the JSON files.
- min_conf: float. Drop values if confidence is below min_conf.
OUTPUT:
- df_json_coords: dataframe. Extracted coordinates in a pandas dataframe.
'''
nb_coord = 25 # int(len(json_data)/3)
json_files_names = fnmatch.filter(os.listdir(os.path.join(json_dir)), '*.json') # modified ( 'json' to '*.json' )
json_files_names = sort_stringlist_by_last_number(json_files_names)
json_files_path = [os.path.join(json_dir, j_f) for j_f in json_files_names]
json_coords = []
for j_p in json_files_path:
with open(j_p) as j_f:
try:
json_data = json.load(j_f)['people'][0]['pose_keypoints_2d']
# remove points with low confidence
json_data = np.array([[json_data[3*i],json_data[3*i+1],json_data[3*i+2]] if json_data[3*i+2]>min_conf else [0.,0.,0.] for i in range(nb_coord)]).ravel().tolist()
except:
# print(f'No person found in {os.path.basename(json_dir)}, frame {i}')
json_data = [0] * 25*3
json_coords.append(json_data)
df_json_coords = pd.DataFrame(json_coords)
return df_json_coords
def drop_col(df, col_nb):
'''
Drops every nth column from a DataFrame.
INPUTS:
- df: dataframe. The DataFrame from which columns will be dropped.
- col_nb: int. The column number to drop.
OUTPUT:
- dataframe: DataFrame with dropped columns.
'''
idx_col = list(range(col_nb-1, df.shape[1], col_nb))
df_dropped = df.drop(idx_col, axis=1)
df_dropped.columns = range(df_dropped.columns.size)
return df_dropped
def vert_speed(df, axis='y'):
'''
Calculate the vertical speed of a DataFrame along a specified axis.
Parameters:
- df: dataframe. DataFrame of 2D coordinates.
- axis (str): The axis along which to calculate the speed. Default is 'y'.
OUTPUT:
- DataFrame: The DataFrame containing the vertical speed values.
'''
axis_dict = {'x':0, 'y':1, 'z':2}
df_diff = df.diff()
df_diff = df_diff.fillna(df_diff.iloc[1]*2)
df_vert_speed = pd.DataFrame([df_diff.loc[:, 2*k + axis_dict[axis]] for k in range(int(df_diff.shape[1] / 2))]).T # modified ( df_diff.shape[1]*2 to df_diff.shape[1] / 2 )
df_vert_speed.columns = np.arange(len(df_vert_speed.columns))
return df_vert_speed
def interpolate_zeros_nans(col, kind):
'''
Interpolate missing points (of value nan)
INPUTS
- col: pandas column of coordinates
- kind: 'linear', 'slinear', 'quadratic', 'cubic'. Default 'cubic'
OUTPUT
- col_interp: interpolated pandas column
'''
mask = ~(np.isnan(col) | col.eq(0)) # true where nans or zeros
idx_good = np.where(mask)[0]
try:
f_interp = interpolate.interp1d(idx_good, col[idx_good], kind=kind, bounds_error=False)
col_interp = np.where(mask, col, f_interp(col.index))
return col_interp
except:
# print('No good values to interpolate')
return col
def time_lagged_cross_corr(camx, camy, lag_range, show=True):
'''
'''
pearson_r = [camx.corr(camy.shift(lag)) for lag in range(-lag_range, lag_range)]
offset = int(np.floor(len(pearson_r)/2)-np.argmax(pearson_r))
if not np.isnan(pearson_r).all():
max_corr = np.nanmax(pearson_r)
if show:
f, ax = plt.subplots(2,1)
# speed
camx.plot(ax=ax[0], label = f'ref cam')
camy.plot(ax=ax[0], label = f'compared cam')
ax[0].set(xlabel='Frame', ylabel='Speed (px/frame)')
ax[0].legend()
# time lagged cross-correlation
ax[1].plot(list(range(-lag_range, lag_range)), pearson_r)
ax[1].axvline(np.ceil(len(pearson_r)/2) - lag_range,color='k',linestyle='--')
ax[1].axvline(np.argmax(pearson_r) - lag_range,color='r',linestyle='--',label='Peak synchrony')
plt.annotate(f'Max correlation={np.round(max_corr,2)}', xy=(0.05, 0.9), xycoords='axes fraction')
ax[1].set(title=f'Offset = {offset} frames', xlabel='Offset (frames)',ylabel='Pearson r')
plt.legend()
f.tight_layout()
plt.show()
else:
max_corr = 0
offset = 0
if show:
# print('No good values to interpolate')
pass
return offset, max_corr
def find_highest_wrist_position(df_coords, wrist_index):
'''
Find the frame with the highest wrist position in a list of coordinate DataFrames.
Highest wrist position frame use for finding the fastest frame.
INPUT:
- df_coords (list): List of coordinate DataFrames.
- wrist_index (int): The index of the wrist in the keypoint list.
OUTPUT:
- list: The index of the frame with the highest wrist position.
'''
start_frames = []
min_y_coords = []
for df in df_coords:
# Wrist y-coordinate column index (2n where n is the keypoint index)
# Assuming wrist_index is a list and we want to use the first element
y_col_index = wrist_index[0] * 2 + 1
# Replace 0 with NaN to avoid considering them and find the index of the lowest y-coordinate value
min_y_coord = df.iloc[:, y_col_index].replace(0, np.nan).min()
min_y_index = df.iloc[:, y_col_index].replace(0, np.nan).idxmin()
if min_y_coord <= 100: # if the wrist is too high, it is likely to be an outlier
print("The wrist is too high. Please check the data for outliers.")
start_frames.append(min_y_index)
min_y_coords.append(min_y_coord)
return start_frames, min_y_coords
def find_motion_end(df_coords, wrist_index, start_frame, lowest_y, fps):
'''
Find the frame where hands down movement ends.
Hands down movement is defined as the time when the wrist moves down from the highest position.
INPUT:
- df_coord (DataFrame): The coordinate DataFrame of the reference camera.
- wrist_index (int): The index of the wrist in the keypoint list.
- start_frame (int): The frame where the hands down movement starts.
- fps (int): The frame rate of the cameras in Hz.
OUTPUT:
- int: The index of the frame where hands down movement ends.
'''
y_col_index = wrist_index * 2 + 1
wrist_y_values = df_coords.iloc[:, y_col_index].values # wrist y-coordinates
highest_y_value = lowest_y
highest_y_index = start_frame
# Find the highest y-coordinate value and its index
for i in range(highest_y_index + 1, len(wrist_y_values)):
if wrist_y_values[i] - highest_y_value >= 50:
start_increase_index = i
break
else:
raise ValueError("The wrist does not move down.")
start = start_increase_index - start_frame
time = (start + fps) / fps
return time
def find_fastest_frame(df_speed_list):
'''
Find the frame with the highest speed in a list of speed DataFrames.
Fastest frame should locate in after highest wrist position frame.
INPUT:
- df_speed_list (list): List of speed DataFrames.
- df_speed (DataFrame): The speed DataFrame of the reference camera.
- fps (int): The frame rate of the cameras in Hz.
- lag_time (float): The time lag in seconds.
OUTPUT:
- int: The index of the frame with the highest speed.
'''
for speed_series in df_speed_list:
max_speed = speed_series.abs().max()
max_speed_index = speed_series.abs().idxmax()
if max_speed < 10:
print(" !!Warning!! : The maximum speed is likely to be not representative of the actual movement. Consider increasing the time parameter in Config.toml.")
return max_speed_index, max_speed
def plot_time_lagged_cross_corr(camx, camy, ax, fps, lag_time):
'''
Calculate and plot the max correlation between two cameras with a time lag.
How it works:
1. Reference camera is camx and the other is camy. (Reference camera should record last. If not, the offset will be positive.)
2. The initial shift alppied to camy to match camx is calculated.
3. Additionally shift camy by max_lag frames to find the max correlation.
INPUT:
- camx: pd.Series. Speed series of the reference camera.
- camy: pd.Series). Speed series of the other camera.
- ax: plt.axis. Plot correlation on second axis.
- fps: int. Framerate of the cameras in Hz.
- lag_time: float. Time lag in seconds.
OUTPUT:
- offset: int. Offset value to apply to synchronize the cameras.
- max_corr: float. Maximum correlation value.
'''
max_lag = int(fps * lag_time)
pearson_r = []
lags = range(-max_lag, 1)
for lag in lags:
if lag < 0:
shifted_camy = camy.shift(lag).dropna() # shift the camy segment by lag
corr = camx.corr(shifted_camy) # calculate the correlation between the camx segment and the shifted camy segment
elif lag == 0:
corr = camx.corr(camy)
else:
continue
pearson_r.append(corr)
# Handle NaN values in pearson_r and find the max correlation ignoring NaNs
pearson_r = np.array(pearson_r)
max_corr = np.nanmax(pearson_r) # Use nanmax to ignore NaNs
offset = np.nanargmax(pearson_r) - max_lag # Use nanargmax to find the index of the max correlation ignoring NaNs
# real_offset = offset + initial_shift
# visualize
ax.plot(lags, pearson_r)
ax.axvline(offset, color='r', linestyle='--', label='Peak synchrony')
plt.annotate(f'Max correlation={np.round(max_corr,2)}', xy=(0.05, 0.9), xycoords='axes fraction')
# ax.set(title=f'Offset = {offset}{initial_shift} = {real_offset} frames', xlabel='Offset (frames)', ylabel='Pearson r')
ax.set(title=f'Offset = {offset} frames', xlabel='Offset (frames)', ylabel='Pearson r')
plt.legend()
return offset, max_corr
def apply_offset(offset, json_dirs, reset_sync, cam1_nb, cam2_nb):
'''
Apply the offset to synchronize the cameras.
Offset is always applied to the second camera.
Offset would be always negative if the first camera is the last to start recording.
Delete the camy json files from initial frame to offset frame.
INPUT:
- offset (int): The offset value to apply to synchronize the cameras.
- json_dirs (list): List of directories containing the JSON files for each camera.
- reset_sync (bool): Whether to reset the synchronization by deleting the .del files.
- cam1_nb (int): The number of the reference camera.
- cam2_nb (int): The number of the other camera.
'''
if offset == 0:
print(f"Cams {cam1_nb} and {cam2_nb} are already synchronized. No offset applied.")
json_dir_to_offset = json_dirs[cam2_nb]
elif offset > 0 and not reset_sync:
print(f"Consider adjusting the lag time.")
raise ValueError(f"Are you sure the reference camera is the last to start recording?")
else:
offset = abs(offset)
json_dir_to_offset = json_dirs[cam2_nb]
json_files = sorted(fnmatch.filter(os.listdir(json_dir_to_offset), '*.json'), key=lambda x: int(re.findall('\d+', x)[0]))
if reset_sync:
del_files = fnmatch.filter(os.listdir(json_dir_to_offset), '*.del')
for del_file in del_files:
os.rename(os.path.join(json_dir_to_offset, del_file), os.path.join(json_dir_to_offset, del_file[:-4]))
else:
for i in range(offset):
os.rename(os.path.join(json_dir_to_offset, json_files[i]), os.path.join(json_dir_to_offset, json_files[i] + '.del'))
def sort_stringlist_by_last_number(string_list):
'''
Sort a list of strings based on the last number in the string.
Works if other numbers in the string, if strings after number. Ignores alphabetical order.
Example: ['json1', 'js4on2.b', 'eypoints_0000003.json', 'ajson0', 'json10']
gives: ['ajson0', 'json1', 'js4on2.b', 'eypoints_0000003.json', 'json10']
'''
def sort_by_last_number(s):
return int(re.findall(r'\d+', s)[-1])
return sorted(string_list, key=sort_by_last_number)
def synchronize_cams_all(config_dict):
'''
'''
# get parameters from Config.toml
project_dir = config_dict.get('project').get('project_dir')
pose_dir = os.path.realpath(os.path.join(project_dir, 'pose'))
fps = config_dict.get('project').get('frame_rate')
reset_sync = config_dict.get('synchronization').get('reset_sync')
approx_time_maxspeed = config_dict.get('synchronization').get('approx_time_maxspeed')
min_conf = 0.4
filter_order = 4
filter_cutoff = 6
# vmax = 4 # px/s # in average for each keypoint -> vmax sum = 100 px/s
# corr_threshold = 0.8
# top_N_corr = 10
# List json files
pose_listdirs_names = next(os.walk(pose_dir))[1]
pose_listdirs_names = sort_stringlist_by_last_number(pose_listdirs_names)
json_dirs_names = [k for k in pose_listdirs_names if 'json' in k]
json_dirs = [os.path.join(pose_dir, j_d) for j_d in json_dirs_names] # list of json directories in pose_dir
cam_nb = len(json_dirs)
# Extract, interpolate, and filter keypoint coordinates
df_coords = []
b, a = signal.butter(filter_order/2, filter_cutoff/(fps/2), 'low', analog = False)
for i, json_dir in enumerate(json_dirs):
df_coords.append(convert_json2pandas(json_dir, min_conf=min_conf))
df_coords[i] = drop_col(df_coords[i],3) # drop likelihood
df_coords[i] = df_coords[i].apply(interpolate_zeros_nans, axis=0, args = ['linear'])
df_coords[i] = df_coords[i].bfill().ffill()
df_coords[i] = pd.DataFrame(signal.filtfilt(b, a, df_coords[i], axis=0))
# for i in range(25):
# df_coords[0].iloc[:,i*2+1].plot(label='0')
# df_coords[1].iloc[:,i*2+1].plot(label='1')
# df_coords[2].iloc[:,i*2+1].plot(label='2')
# df_coords[3].iloc[:,i*2+1].plot(label='3')
# plt.title(i)
# plt.legend()
# plt.show()
# Save keypoint coordinates to pickle
# with open(os.path.join(pose_dir, 'coords'), 'wb') as fp:
# pk.dump(df_coords, fp)
# with open(os.path.join(pose_dir, 'coords'), 'rb') as fp:
# df_coords = pk.load(fp)
# Set reference camera (with least amount of frames)
nb_frames_per_cam = [len(d) for d in df_coords]
ref_cam_id = nb_frames_per_cam.index(min(nb_frames_per_cam))
ref_frame_nb = len(df_coords[ref_cam_id])
cam_list = list(range(cam_nb))
cam_list.pop(ref_cam_id)
# Detect best moment for synchronization search (highest correlation for sum of speeds for each camera)
approx_offset, approx_frame_maxspeed, search_sync_around_frame = [], [], []
# If auto approx_time_maxspeed, search approximate synchronization offset on the whole video sequence
if approx_time_maxspeed == 'auto':
# compute vertical speed
df_speed = []
sum_speeds = []
lag_range = int(ref_frame_nb/2)
for i in range(cam_nb):
df_speed.append(vert_speed(df_coords[i]))
# nb_coord = df_speed[i].shape[1]
sum_speeds.append(abs(df_speed[i]).sum(axis=1))
# sum_speeds[i][ sum_speeds[i]>vmax*nb_coord ] = 0
sum_speeds[i] = pd.DataFrame(signal.filtfilt(b, a, sum_speeds[i], axis=0)).squeeze()
approx_frame_maxspeed_ref = np.argmax(sum_speeds[ref_cam_id])
# frame with highest correlation of sum of absolute speeds for each cam compared to reference cam
for cam_id in cam_list:
frame_nb = len(sum_speeds[cam_id])
approx_offset_cam, _ = time_lagged_cross_corr(sum_speeds[ref_cam_id], sum_speeds[cam_id], lag_range, show=True)
approx_offset.append(approx_offset_cam)
approx_frame_maxspeed.append(approx_frame_maxspeed_ref+approx_offset_cam)
search_sync_around_frame.append([max(0,approx_frame_maxspeed_ref+approx_offset_cam-fps), min(frame_nb, approx_frame_maxspeed_ref+approx_offset_cam+fps)])
# Else search best synchronization offset around the time specified +/- 2 sec
else:
approx_frame_maxspeed_ref = int(fps * approx_time_maxspeed[ref_cam_id])
for cam_id in cam_list:
frame_nb = len(df_coords[cam_id])
approx_frame_maxspeed_cam = int(fps * approx_time_maxspeed[cam_id])
approx_frame_maxspeed.append(approx_frame_maxspeed_cam)
search_sync_around_frame.append([max(0,approx_frame_maxspeed_cam-2*fps), min(frame_nb, approx_frame_maxspeed_cam+2*fps)])
approx_offset.append(approx_frame_maxspeed_ref-approx_frame_maxspeed_cam)
approx_frame_maxspeed.insert(ref_cam_id, approx_frame_maxspeed_ref)
search_sync_around_frame.insert(ref_cam_id, [max(0,approx_frame_maxspeed_ref-2*fps), min(ref_frame_nb, approx_frame_maxspeed_ref+2*fps)])
approx_offset.insert(ref_cam_id, 0)
# Refine synchronization offset: -> not needed
# Time-lagged cross-correlation for each keypoint, select top N highest correlations, take median offset
offset = []
for cam_id in cam_list:
coords_nb = int(len(df_coords[cam_id].columns)/2)
lag_range = min(int(ref_frame_nb/2), fps)
offset_cam, corr_cam = [], []
for coord_id in range(coords_nb):
camx = df_speed[ref_cam_id][coord_id][search_sync_around_frame[ref_cam_id][0]:search_sync_around_frame[ref_cam_id][1]]
camy = df_speed[cam_id][coord_id][search_sync_around_frame[cam_id][0]:search_sync_around_frame[cam_id][1]]
offset_cam_coord, corr_cam_coord = time_lagged_cross_corr(camx, camy, lag_range, show=False)
offset_cam.append(offset_cam_coord)
corr_cam.append(corr_cam_coord)
# print(f'{coord_id} keypoint: offset = {offset_cam} frames and correlation = {corr_cam}.')
corr_cam = np.array(corr_cam)
offset_cam = np.array(offset_cam)
# take highest correlations and retrieve median offset
top_five_offset_coord = np.argpartition(-corr_cam, top_N_corr)[:top_N_corr]
top_five_offset_coord = top_five_offset_coord[np.argsort(corr_cam[top_five_offset_coord])][::-1]
top_five_corr_coord = corr_cam[top_five_offset_coord]
top_five_offset_coord = [c for i,c in enumerate(top_five_offset_coord) if top_five_corr_coord[i]>corr_threshold]
best_offset_cam = round(np.median(offset_cam[top_five_offset_coord]))
print('\n', best_offset_cam, offset_cam[top_five_offset_coord], corr_cam[top_five_offset_coord])
offset.append(best_offset_cam)
print(offset)
# test time-lagged c-c for sum_speeds
search_sync_min_frame_nb = min([(s[1]-s[0]) for s in search_sync_around_frame])
lag_range = min(int(search_sync_min_frame_nb/2), 2*fps)
ref_cam_selected = sum_speeds[ref_cam_id][search_sync_around_frame[ref_cam_id][0]:search_sync_around_frame[ref_cam_id][1]]
for cam_id in cam_list:
cam_selected = sum_speeds[cam_id][search_sync_around_frame[cam_id][0]:search_sync_around_frame[cam_id][1]].reset_index(drop=True)
lag_index = int((search_sync_around_frame[cam_id][1] - search_sync_around_frame[cam_id][0]) / 2)
offset, max_corr = time_lagged_cross_corr(ref_cam_selected, cam_selected, lag_index, show=True)
print(f'Camera {ref_cam_id} and camera {cam_id} have a max correlation of {max_corr} with an offset of {offset} frames.')
# time-lagged cross-correlation for each point, weighted by corr
#############################################
# 2. PLOTTING PAIRED CORRELATIONS OF SPEEDS #
#############################################
# Do this on all cam pairs
# Choose pair with highest correlation
# on a particular point (typically the wrist on a vertical movement)
# or on a selection of weighted points
# find the lowest position of the wrist
lowest_frames, lowest_y_coords = find_highest_wrist_position(df_coords, id_kpt)
max_speeds = []
cam_list = list(range(cam_nb))
cam_list.pop(ref_cam_id)
for cam_id in cam_list:
# find the highest wrist position for each camera
camx_start_frame = lowest_frames[ref_cam_id]
camy_start_frame = lowest_frames[cam_id]
camx_lowest_y = lowest_y_coords[ref_cam_id]
camy_lowest_y = lowest_y_coords[cam_id]
camx_time = find_motion_end(df_coords[ref_cam_id], id_kpt[0], camx_start_frame, camx_lowest_y, fps)
camy_time = find_motion_end(df_coords[cam_id], id_kpt[0], camy_start_frame, camy_lowest_y, fps)
camx_end_frame = camx_start_frame + int(camx_time * fps)
camy_end_frame = camy_start_frame + int(camy_time * fps)
camx_segment = df_speed[ref_cam_id].iloc[camx_start_frame:camx_end_frame+1, id_kpt[0]]
camy_segment = df_speed[cam_id].iloc[camy_start_frame:camy_end_frame+1, id_kpt[0]]
# Find the fastest speed and the frame
camx_max_speed_index, camx_max_speed = find_fastest_frame([camx_segment])
camy_max_speed_index, camy_max_speed = find_fastest_frame([camy_segment])
max_speeds.append(camx_max_speed)
max_speeds.append(camy_max_speed)
vmax = max(max_speeds)
# Find automatically the best lag time
lag_time = round((camy_max_speed_index - camx_max_speed_index) / fps + 1)
# FInd the fatest frame
camx_start_frame = camx_max_speed_index - (fps) * (lag_time)
if camx_start_frame < 0:
camx_start_frame = 0
else:
camx_start_frame = int(camx_start_frame)
camy_start_frame = camy_max_speed_index - (fps) * (lag_time)
camx_end_frame = camx_max_speed_index + (fps) * (lag_time)
camy_end_frame = camy_max_speed_index + (fps) * (lag_time)
if len(id_kpt) == 1 and id_kpt[0] != 'all':
camx = df_speed[ref_cam_id].iloc[camx_start_frame:camx_end_frame+1, id_kpt[0]]
camy = df_speed[cam_id].iloc[camy_start_frame:camy_end_frame+1, id_kpt[0]]
elif id_kpt == ['all']:
camx = df_speed[ref_cam_id].iloc[camx_start_frame:camx_end_frame+1].sum(axis=1)
camy = df_speed[cam_id].iloc[camy_start_frame:camy_end_frame+1].sum(axis=1)
elif len(id_kpt) == 1 and len(id_kpt) == len(weights_kpt):
dict_id_weights = {i:w for i, w in zip(id_kpt, weights_kpt)}
camx = df_speed[ref_cam_id] @ pd.Series(dict_id_weights).reindex(df_speed[ref_cam_id].columns, fill_value=0)
camy = df_speed[cam_id] @ pd.Series(dict_id_weights).reindex(df_speed[cam_id].columns, fill_value=0)
camx = camx.iloc[camx_start_frame:camx_end_frame+1]
camy = camy.iloc[camy_start_frame:camy_end_frame+1]
else:
raise ValueError('wrong values for id_kpt or weights_kpt')
# filter the speeds
camx = camx.where(lambda x: (x <= vmax) & (x >= -vmax), other=np.nan)
camy = camy.where(lambda x: (x <= vmax) & (x >= -vmax), other=np.nan)
f, ax = plt.subplots(2,1)
# speed
camx.plot(ax=ax[0], label = f'cam {ref_cam_id+1}')
camy.plot(ax=ax[0], label = f'cam {cam_id+1}')
ax[0].set(xlabel='Frame',ylabel='Speed (pxframe)')
ax[0].legend()
# time lagged cross-correlation
offset, max_corr = plot_time_lagged_cross_corr(camx, camy, ax[1], fps, lag_time, camx_max_speed_index, camy_max_speed_index)
f.tight_layout()
plt.show()
print(f'Using number{id_kpt} keypoint, synchronized camera {ref_cam_id+1} and camera {cam_id+1}, with an offset of {offset} and a max correlation of {max_corr}.')
# apply offset
apply_offset(offset, json_dirs, reset_sync, ref_cam_id, cam_id)
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