pose2sim/Pose2Sim/personAssociation.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-


'''
###########################################################################
## TRACKING OF PERSON OF INTEREST                                        ##
###########################################################################

Openpose detects all people in the field of view. 
- multi_person = false: Which is the one of interest?
- multi_person = true: How to triangulate the same persons across views?
                       How to associate them across time frames? Done in the 
                       triangulation stage.

If multi_person = false, this module tries all possible triangulations of a chosen
anatomical point, and chooses the person for whom the reprojection error is smallest. 

If multi_person = true, it computes the distance between epipolar lines (camera to 
keypoint lines) for all persons detected in all views, and selects the best correspondences. 
The computation of the affinity matrix from the distance is inspired from the EasyMocap approach.

INPUTS: 
- a calibration file (.toml extension)
- json files from each camera folders with several detected persons
- a Config.toml file
- a skeleton model

OUTPUTS: 
- json files for each camera with only one person of interest
'''


## INIT
import os
import glob
import fnmatch
import numpy as np
import json
import itertools as it
import toml
from tqdm import tqdm
import cv2
from anytree import RenderTree
from anytree.importer import DictImporter
import logging

from Pose2Sim.common import retrieve_calib_params, computeP, weighted_triangulation, \
    reprojection, euclidean_distance, natural_sort
from Pose2Sim.skeletons import *


## AUTHORSHIP INFORMATION
__author__ = "David Pagnon"
__copyright__ = "Copyright 2021, Pose2Sim"
__credits__ = ["David Pagnon"]
__license__ = "BSD 3-Clause License"
__version__ = '0.6'
__maintainer__ = "David Pagnon"
__email__ = "contact@david-pagnon.com"
__status__ = "Development"


## FUNCTIONS
def persons_combinations(json_files_framef):
    '''
    Find all possible combinations of detected persons' ids. 
    Person's id when no person detected is set to -1.
    
    INPUT:
    - json_files_framef: list of strings

    OUTPUT:
    - personsIDs_comb: array, list of lists of int
    '''
    
    n_cams = len(json_files_framef)
    
    # amount of persons detected for each cam
    nb_persons_per_cam = []
    for c in range(n_cams):
        with open(json_files_framef[c], 'r') as js:
            nb_persons_per_cam += [len(json.load(js)['people'])]
    
    # persons_combinations
    id_no_detect = [i for i, x in enumerate(nb_persons_per_cam) if x == 0]  # ids of cameras that have not detected any person
    nb_persons_per_cam = [x if x != 0 else 1 for x in nb_persons_per_cam] # temporarily replace persons count by 1 when no detection
    range_persons_per_cam = [range(nb_persons_per_cam[c]) for c in range(n_cams)] 
    personsIDs_comb = np.array(list(it.product(*range_persons_per_cam)), float) # all possible combinations of persons' ids
    personsIDs_comb[:,id_no_detect] = np.nan # -1 = persons' ids when no person detected
    
    return personsIDs_comb


def triangulate_comb(comb, coords, P_all, calib_params, config):
    '''
    Triangulate 2D points and compute reprojection error for a combination of cameras.
    INPUTS:
    - comb: list of ints: combination of persons' ids for each camera
    - coords: array: x, y, likelihood for each camera
    - P_all: list of arrays: projection matrices for each camera
    - calib_params: dict: calibration parameters
    - config: dictionary from Config.toml file
    OUTPUTS:
    - error_comb: float: reprojection error
    - comb: list of ints: combination of persons' ids for each camera
    - Q_comb: array: 3D coordinates of the triangulated point
    ''' 

    undistort_points = config.get('triangulation').get('undistort_points')
    likelihood_threshold = config.get('personAssociation').get('likelihood_threshold_association')

    # Replace likelihood by 0. if under likelihood_threshold
    coords[:,2][coords[:,2] < likelihood_threshold] = 0.
    comb[coords[:,2] == 0.] = np.nan

    # Filter coords and projection_matrices containing nans
    coords_filt = [coords[i] for i in range(len(comb)) if not np.isnan(comb[i])]
    projection_matrices_filt = [P_all[i] for i in range(len(comb)) if not np.isnan(comb[i])]
    if undistort_points:
        calib_params_R_filt = [calib_params['R'][i] for i in range(len(comb)) if not np.isnan(comb[i])]
        calib_params_T_filt = [calib_params['T'][i] for i in range(len(comb)) if not np.isnan(comb[i])]
        calib_params_K_filt = [calib_params['K'][i] for i in range(len(comb)) if not np.isnan(comb[i])]
        calib_params_dist_filt = [calib_params['dist'][i] for i in range(len(comb)) if not np.isnan(comb[i])]

    # Triangulate 2D points
    x_files_filt, y_files_filt, likelihood_files_filt = np.array(coords_filt).T
    Q_comb = weighted_triangulation(projection_matrices_filt, x_files_filt, y_files_filt, likelihood_files_filt)

    # Reprojection
    if undistort_points:
        coords_2D_kpt_calc_filt = [cv2.projectPoints(np.array(Q_comb[:-1]), calib_params_R_filt[i], calib_params_T_filt[i], calib_params_K_filt[i], calib_params_dist_filt[i])[0] for i in range(len(Q_comb))]
        x_calc = [coords_2D_kpt_calc_filt[i][0,0,0] for i in range(len(Q_comb))]
        y_calc = [coords_2D_kpt_calc_filt[i][0,0,1] for i in range(len(Q_comb))]
    else:
        x_calc, y_calc = reprojection(projection_matrices_filt, Q_comb)

    # Reprojection error
    error_comb_per_cam = []
    for cam in range(len(x_calc)):
        q_file = (x_files_filt[cam], y_files_filt[cam])
        q_calc = (x_calc[cam], y_calc[cam])
        error_comb_per_cam.append( euclidean_distance(q_file, q_calc) )
    error_comb = np.mean(error_comb_per_cam)

    return error_comb, comb, Q_comb


def best_persons_and_cameras_combination(config, json_files_framef, personsIDs_combinations, projection_matrices, tracked_keypoint_id, calib_params):
    '''
    Chooses the right person among the multiple ones found by
    OpenPose & excludes cameras with wrong 2d-pose estimation.
    
    1. triangulate the tracked keypoint for all possible combinations of people,
    2. compute difference between reprojection & original openpose detection,
    3. take combination with smallest error OR all those below the error threshold
    If error is too big, take off one or several of the cameras until err is 
    lower than "max_err_px".
    
    INPUTS:
    - a Config.toml file
    - json_files_framef: list of strings
    - personsIDs_combinations: array, list of lists of int
    - projection_matrices: list of arrays
    - tracked_keypoint_id: int

    OUTPUTS:
    - errors_below_thresh: list of float
    - comb_errors_below_thresh: list of arrays of ints
    '''
    
    error_threshold_tracking = config.get('personAssociation').get('single_person').get('reproj_error_threshold_association')
    likelihood_threshold = config.get('personAssociation').get('likelihood_threshold_association')
    min_cameras_for_triangulation = config.get('triangulation').get('min_cameras_for_triangulation')
    undistort_points = config.get('triangulation').get('undistort_points')

    n_cams = len(json_files_framef)
    error_min = np.inf 
    nb_cams_off = 0 # cameras will be taken-off until the reprojection error is under threshold
    errors_below_thresh = []
    comb_errors_below_thresh = []
    Q_kpt = []
    while error_min > error_threshold_tracking and n_cams - nb_cams_off >= min_cameras_for_triangulation:
        # Try all persons combinations
        for combination in personsIDs_combinations:
            #  Get coords from files
            coords = []
            for index_cam, person_nb in enumerate(combination):
                try:
                    js = read_json(json_files_framef[index_cam])
                    coords.append(js[int(person_nb)][tracked_keypoint_id*3:tracked_keypoint_id*3+3])
                except:
                    coords.append([np.nan, np.nan, np.nan])
            coords = np.array(coords)
            
            # undistort points
            if undistort_points:
                points = np.array(coords)[:,None,:2]
                undistorted_points = [cv2.undistortPoints(points[i], calib_params['K'][i], calib_params['dist'][i], None, calib_params['optim_K'][i]) for i in range(n_cams)]
                coords[:,0] = np.array([[u[i][0][0] for i in range(len(u))] for u in undistorted_points]).squeeze()
                coords[:,1] = np.array([[u[i][0][1] for i in range(len(u))] for u in undistorted_points]).squeeze()

            # For each persons combination, create subsets with "nb_cams_off" cameras excluded
            id_cams_off = list(it.combinations(range(len(combination)), nb_cams_off))
            combinations_with_cams_off = np.array([combination.copy()]*len(id_cams_off))
            for i, id in enumerate(id_cams_off):
                combinations_with_cams_off[i,id] = np.nan

            # Try all subsets
            error_comb_all, comb_all, Q_comb_all = [], [], []
            for comb in combinations_with_cams_off:
                error_comb, comb, Q_comb = triangulate_comb(comb, coords, projection_matrices, calib_params, config)
                error_comb_all.append(error_comb)
                comb_all.append(comb)
                Q_comb_all.append(Q_comb)

            error_min = np.nanmin(error_comb_all)
            comb_error_min = [comb_all[np.argmin(error_comb_all)]]
            Q_kpt = [Q_comb_all[np.argmin(error_comb_all)]]
            if error_min < error_threshold_tracking:
                break 

        nb_cams_off += 1
    
    return error_min, comb_error_min, Q_kpt


def read_json(js_file):
    '''
    Read OpenPose json file
    '''
    with open(js_file, 'r') as json_f:
        js = json.load(json_f)
        json_data = []
        for people in range(len(js['people'])):
            if len(js['people'][people]['pose_keypoints_2d']) < 3: continue
            else:
                json_data.append(js['people'][people]['pose_keypoints_2d'])
    return json_data


def compute_rays(json_coord, calib_params, cam_id):
    '''
    Plucker coordinates of rays from camera to each joint of a person
    Plucker coordinates: camera to keypoint line direction (size 3) 
                         moment: origin ^ line (size 3)
                         additionally, confidence

    INPUTS:
    - json_coord: x, y, likelihood for a person seen from a camera (list of 3*joint_nb)
    - calib_params: calibration parameters from retrieve_calib_params('calib.toml')
    - cam_id: camera id (int)

    OUTPUT:
    - plucker: array. nb joints * (6 plucker coordinates + 1 likelihood)
    '''

    x = json_coord[0::3]
    y = json_coord[1::3]
    likelihood = json_coord[2::3]
    
    inv_K = calib_params['inv_K'][cam_id]
    R_mat = calib_params['R_mat'][cam_id]
    T = calib_params['T'][cam_id]

    cam_center = -R_mat.T @ T
    plucker = []
    for i in range(len(x)):
        q = np.array([x[i], y[i], 1])
        norm_Q = R_mat.T @ (inv_K @ q -T)
        
        line = norm_Q - cam_center
        norm_line = line/np.linalg.norm(line)
        moment = np.cross(cam_center, norm_line)
        plucker.append(np.concatenate([norm_line, moment, [likelihood[i]]]))

    return np.array(plucker)


def broadcast_line_to_line_distance(p0, p1):
    '''
    Compute the distance between two lines in 3D space.

    see: https://faculty.sites.iastate.edu/jia/files/inline-files/plucker-coordinates.pdf
    p0 = (l0,m0), p1 = (l1,m1)
    dist = | (l0,m0) * (l1,m1) | / || l0 x l1 ||
    (l0,m0) * (l1,m1) = l0 @ m1 + m0 @ l1 (reciprocal product)
    
    No need to divide by the norm of the cross product of the directions, since we
    don't need the actual distance but whether the lines are close to intersecting or not
    => dist = | (l0,m0) * (l1,m1) |

    INPUTS:
    - p0: array(nb_persons_detected * 1 * nb_joints * 7 coordinates)
    - p1: array(1 * nb_persons_detected * nb_joints * 7 coordinates)

    OUTPUT:
    - dist: distances between the two lines (not normalized). 
            array(nb_persons_0 * nb_persons_1 * nb_joints)
    '''

    product = np.sum(p0[..., :3] * p1[..., 3:6], axis=-1) + np.sum(p1[..., :3] * p0[..., 3:6], axis=-1)
    dist = np.abs(product)

    return dist


def compute_affinity(all_json_data_f, calib_params, cum_persons_per_view, reconstruction_error_threshold=0.1):
    '''
    Compute the affinity between all the people in the different views.

    The affinity is defined as 1 - distance/max_distance, with distance the
    distance between epipolar lines in each view (reciprocal product of Plucker 
    coordinates).

    Another approach would be to project one epipolar line onto the other camera
    plane and compute the line to point distance, but it is more computationally 
    intensive (simple dot product vs. projection and distance calculation). 
    
    INPUTS:
    - all_json_data_f: list of json data. For frame f, nb_views*nb_persons*(x,y,likelihood)*nb_joints
    - calib_params: calibration parameters from retrieve_calib_params('calib.toml')
    - cum_persons_per_view: cumulative number of persons per view
    - reconstruction_error_threshold: maximum distance between epipolar lines to consider a match

    OUTPUT:
    - affinity: affinity matrix between all the people in the different views. 
                (nb_views*nb_persons_per_view * nb_views*nb_persons_per_view)
    '''

    # Compute plucker coordinates for all keypoints for each person in each view
    # pluckers_f: dims=(camera, person, joint, 7 coordinates)
    pluckers_f = []
    for cam_id, json_cam  in enumerate(all_json_data_f):
        pluckers = []
        for json_coord in json_cam:
            plucker = compute_rays(json_coord, calib_params, cam_id) # LIMIT TO 15 JOINTS? json_coord[:15*3]
            pluckers.append(plucker)
        pluckers = np.array(pluckers)
        pluckers_f.append(pluckers)

    # Compute affinity matrix
    distance = np.zeros((cum_persons_per_view[-1], cum_persons_per_view[-1])) + 2*reconstruction_error_threshold
    for compared_cam0, compared_cam1 in it.combinations(range(len(all_json_data_f)), 2):
        # skip when no detection for a camera
        if cum_persons_per_view[compared_cam0] == cum_persons_per_view[compared_cam0+1] \
            or cum_persons_per_view[compared_cam1] == cum_persons_per_view[compared_cam1 +1]:
            continue

        # compute distance
        p0 = pluckers_f[compared_cam0][:,None] # add coordinate on second dimension
        p1 = pluckers_f[compared_cam1][None,:] # add coordinate on first dimension
        dist = broadcast_line_to_line_distance(p0, p1)
        likelihood = np.sqrt(p0[..., -1] * p1[..., -1])
        mean_weighted_dist = np.sum(dist*likelihood, axis=-1)/(1e-5 + likelihood.sum(axis=-1)) # array(nb_persons_0 * nb_persons_1)
        
        # populate distance matrix
        distance[cum_persons_per_view[compared_cam0]:cum_persons_per_view[compared_cam0+1], \
                 cum_persons_per_view[compared_cam1]:cum_persons_per_view[compared_cam1+1]] \
                 = mean_weighted_dist
        distance[cum_persons_per_view[compared_cam1]:cum_persons_per_view[compared_cam1+1], \
                 cum_persons_per_view[compared_cam0]:cum_persons_per_view[compared_cam0+1]] \
                 = mean_weighted_dist.T

    # compute affinity matrix and clamp it to zero when distance > reconstruction_error_threshold
    distance[distance > reconstruction_error_threshold] = reconstruction_error_threshold
    affinity = 1 - distance / reconstruction_error_threshold

    return affinity


def circular_constraint(cum_persons_per_view):
    '''
    A person can be matched only with themselves in the same view, and with any 
    person from other views

    INPUT:
    - cum_persons_per_view: cumulative number of persons per view

    OUTPUT:
    - circ_constraint: circular constraint matrix
    '''

    circ_constraint = np.identity(cum_persons_per_view[-1])
    for i in range(len(cum_persons_per_view)-1):
        circ_constraint[cum_persons_per_view[i]:cum_persons_per_view[i+1], cum_persons_per_view[i+1]:cum_persons_per_view[-1]] = 1
        circ_constraint[cum_persons_per_view[i+1]:cum_persons_per_view[-1], cum_persons_per_view[i]:cum_persons_per_view[i+1]] = 1
    
    return circ_constraint


def SVT(matrix, threshold):
    '''
    Find a low-rank approximation of the matrix using Singular Value Thresholding.

    INPUTS:
    - matrix: matrix to decompose
    - threshold: threshold for singular values

    OUTPUT:
    - matrix_thresh: low-rank approximation of the matrix
    '''
    
    U, s, Vt = np.linalg.svd(matrix) # decompose matrix
    s_thresh = np.maximum(s - threshold, 0) # set smallest singular values to zero
    matrix_thresh = U @ np.diag(s_thresh) @ Vt # recompose matrix

    return matrix_thresh


def matchSVT(affinity, cum_persons_per_view, circ_constraint, max_iter = 20, w_rank = 50, tol = 1e-4, w_sparse=0.1):
    '''
    Find low-rank approximation of 'affinity' while satisfying the circular constraint.

    INPUTS:
    - affinity: affinity matrix between all the people in the different views
    - cum_persons_per_view: cumulative number of persons per view
    - circ_constraint: circular constraint matrix
    - max_iter: maximum number of iterations
    - w_rank: threshold for singular values
    - tol: tolerance for convergence
    - w_sparse: regularization parameter

    OUTPUT:
    - new_aff: low-rank approximation of the affinity matrix
    '''

    new_aff = affinity.copy()
    N = new_aff.shape[0]
    index_diag = np.arange(N)
    new_aff[index_diag, index_diag] = 0.
    # new_aff = (new_aff + new_aff.T)/2 # symmetric by construction

    Y = np.zeros_like(new_aff) # Initial deviation matrix / residual ()
    W = w_sparse - new_aff # Initial sparse matrix / regularization (prevent overfitting)
    mu = 64 # initial step size

    for iter in range(max_iter):
        new_aff0 = new_aff.copy()
        
        Q = new_aff + Y*1.0/mu
        Q = SVT(Q,w_rank/mu)
        new_aff = Q - (W + Y)/mu

        # Project X onto dimGroups
        for i in range(len(cum_persons_per_view) - 1):
            ind1, ind2 = cum_persons_per_view[i], cum_persons_per_view[i + 1]
            new_aff[ind1:ind2, ind1:ind2] = 0
            
        # Reset diagonal elements to one and ensure X is within valid range [0, 1]
        new_aff[index_diag, index_diag] = 1.
        new_aff[new_aff < 0] = 0
        new_aff[new_aff > 1] = 1
        
        # Enforce circular constraint
        new_aff = new_aff * circ_constraint
        new_aff = (new_aff + new_aff.T) / 2 # kept just in case X loses its symmetry during optimization 
        Y = Y + mu * (new_aff - Q)
        
        # Compute convergence criteria: break if new_aff is close enough to Q and no evolution anymore
        pRes = np.linalg.norm(new_aff - Q) / N # primal residual (diff between new_aff and SVT result)
        dRes = mu * np.linalg.norm(new_aff - new_aff0) / N # dual residual (diff between new_aff and previous new_aff)
        if pRes < tol and dRes < tol:
            break
        if pRes > 10 * dRes: mu = 2 * mu
        elif dRes > 10 * pRes: mu = mu / 2

        iter +=1

    return new_aff


def person_index_per_cam(affinity, cum_persons_per_view, min_cameras_for_triangulation):
    '''
    For each detected person, gives their index for each camera

    INPUTS:
    - affinity: affinity matrix between all the people in the different views
    - min_cameras_for_triangulation: exclude proposals if less than N cameras see them

    OUTPUT:
    - proposals: 2D array: n_persons * n_cams
    '''

    # index of the max affinity for each group (-1 if no detection)
    proposals = []
    for row in range(affinity.shape[0]):
        proposal_row = []
        for cam in range(len(cum_persons_per_view)-1):
            id_persons_per_view = affinity[row, cum_persons_per_view[cam]:cum_persons_per_view[cam+1]]
            proposal_row += [np.argmax(id_persons_per_view) if (len(id_persons_per_view)>0 and max(id_persons_per_view)>0) else -1]
        proposals.append(proposal_row)
    proposals = np.array(proposals, dtype=float)

    # remove duplicates and order
    proposals, nb_detections = np.unique(proposals, axis=0, return_counts=True)
    proposals = proposals[np.argsort(nb_detections)[::-1]]

    # remove row if any value is the same in previous rows at same index (nan!=nan so nan ignored)
    proposals[proposals==-1] = np.nan
    mask = np.ones(proposals.shape[0], dtype=bool)
    for i in range(1, len(proposals)):
        mask[i] = ~np.any(proposals[i] == proposals[:i], axis=0).any()
    proposals = proposals[mask]

    # remove identifications if less than N cameras see them
    nb_cams_per_person = [np.count_nonzero(~np.isnan(p)) for p in proposals]
    proposals = np.array([p for (n,p) in zip(nb_cams_per_person, proposals) if n >= min_cameras_for_triangulation])

    return proposals


def rewrite_json_files(json_tracked_files_f, json_files_f, proposals, n_cams):
    '''
    Write new json files with correct association of people across cameras.

    INPUTS:
    - json_tracked_files_f: list of strings: json files to write
    - json_files_f: list of strings: json files to read
    - proposals: 2D array: n_persons * n_cams
    - n_cams: int: number of cameras

    OUTPUT:
    - json files with correct association of people across cameras
    '''

    for cam in range(n_cams):
        with open(json_tracked_files_f[cam], 'w') as json_tracked_f:
            with open(json_files_f[cam], 'r') as json_f:
                js = json.load(json_f)
                js_new = js.copy()
                js_new['people'] = []
                for new_comb in proposals:
                    if not np.isnan(new_comb[cam]):
                        js_new['people'] += [js['people'][int(new_comb[cam])]]
                    else:
                        js_new['people'] += [{}]
            json_tracked_f.write(json.dumps(js_new))


def recap_tracking(config, error=0, nb_cams_excluded=0):
    '''
    Print a message giving statistics on reprojection errors (in pixel and in m)
    as well as the number of cameras that had to be excluded to reach threshold
    conditions. Also stored in User/logs.txt.

    INPUT:
    - a Config.toml file
    - error: dataframe 
    - nb_cams_excluded: dataframe

    OUTPUT:
    - Message in console
    '''
    
    # Read config
    project_dir = config.get('project').get('project_dir')
    session_dir = os.path.realpath(os.path.join(project_dir, '..', '..'))
    multi_person = config.get('project').get('multi_person')
    likelihood_threshold_association = config.get('personAssociation').get('likelihood_threshold_association')
    tracked_keypoint = config.get('personAssociation').get('single_person').get('tracked_keypoint')
    error_threshold_tracking = config.get('personAssociation').get('single_person').get('reproj_error_threshold_association')
    reconstruction_error_threshold = config.get('personAssociation').get('multi_person').get('reconstruction_error_threshold')
    min_affinity = config.get('personAssociation').get('multi_person').get('min_affinity')
    poseTracked_dir = os.path.join(project_dir, 'pose-associated')
    calib_dir = [os.path.join(session_dir, c) for c in os.listdir(session_dir) if 'calib' in c.lower()][0]
    calib_file = glob.glob(os.path.join(calib_dir, '*.toml'))[0] # lastly created calibration file
    
    if not multi_person:
        logging.info('\nSingle-person analysis selected.')
        # Error
        mean_error_px = np.around(np.mean(error), decimals=1)
        
        calib = toml.load(calib_file)
        calib_cam1 = calib[list(calib.keys())[0]]
        fm = calib_cam1['matrix'][0][0]
        Dm = euclidean_distance(calib_cam1['translation'], [0,0,0])
        mean_error_mm = np.around(mean_error_px * Dm / fm * 1000, decimals=1)
        
        # Excluded cameras
        mean_cam_off_count = np.around(np.mean(nb_cams_excluded), decimals=2)

        # Recap
        logging.info(f'\n--> Mean reprojection error for {tracked_keypoint} point on all frames is {mean_error_px} px, which roughly corresponds to {mean_error_mm} mm. ')
        logging.info(f'--> In average, {mean_cam_off_count} cameras had to be excluded to reach the demanded {error_threshold_tracking} px error threshold after excluding points with likelihood below {likelihood_threshold_association}.')
    
    else:
        logging.info('\nMulti-person analysis selected.')
        logging.info(f'\n--> A person was reconstructed if the lines from cameras to their keypoints intersected within {reconstruction_error_threshold} m and if the calculated affinity stayed below {min_affinity} after excluding points with likelihood below {likelihood_threshold_association}.')
        logging.info(f'--> Beware that people were sorted across cameras, but not across frames. This will be done in the triangulation stage.')

    logging.info(f'\nTracked json files are stored in {os.path.realpath(poseTracked_dir)}.')
    

def track_2d_all(config):
    '''
    For each frame,
    - Find all possible combinations of detected persons
    - Triangulate 'tracked_keypoint' for all combinations
    - Reproject the point on all cameras
    - Take combination with smallest reprojection error
    - Write json file with only one detected person
    Print recap message
    
    INPUTS: 
    - a calibration file (.toml extension)
    - json files from each camera folders with several detected persons
    - a Config.toml file
    - a skeleton model
    
    OUTPUTS: 
    - json files for each camera with only one person of interest    
    '''
    
    # Read config
    project_dir = config.get('project').get('project_dir')
    session_dir = os.path.realpath(os.path.join(project_dir, '..', '..'))
    multi_person = config.get('project').get('multi_person')
    pose_model = config.get('pose').get('pose_model')
    tracked_keypoint = config.get('personAssociation').get('single_person').get('tracked_keypoint')
    likelihood_threshold = config.get('personAssociation').get('likelihood_threshold_association')
    min_cameras_for_triangulation = config.get('triangulation').get('min_cameras_for_triangulation')
    reconstruction_error_threshold = config.get('personAssociation').get('multi_person').get('reconstruction_error_threshold')
    min_affinity = config.get('personAssociation').get('multi_person').get('min_affinity')
    frame_range = config.get('project').get('frame_range')
    undistort_points = config.get('triangulation').get('undistort_points')
    
    calib_dir = [os.path.join(session_dir, c) for c in os.listdir(session_dir) if 'calib' in c.lower() ][0]
    try:
        calib_file = glob.glob(os.path.join(calib_dir, '*.toml'))[0] # lastly created calibration file
    except:
        raise Exception(f'No .toml calibration file found in the {calib_dir}.')
    pose_dir = os.path.join(project_dir, 'pose')
    poseTracked_dir = os.path.join(project_dir, 'pose-associated')

    if multi_person:
        logging.info('\nMulti-person analysis selected. Note that you can set this option to false if you only need the main person in the scene.')
    else:
        logging.info('\nSingle-person analysis selected.')

    # projection matrix from toml calibration file
    P_all = computeP(calib_file, undistort=undistort_points)
    calib_params = retrieve_calib_params(calib_file)
        
    # selection of tracked keypoint id
    try: # from skeletons.py
        model = eval(pose_model)
    except:
        try: # from Config.toml
            model = DictImporter().import_(config.get('pose').get(pose_model))
            if model.id == 'None':
                model.id = None
        except:
            raise NameError('Model not found in skeletons.py nor in Config.toml')
    tracked_keypoint_id = [node.id for _, _, node in RenderTree(model) if node.name==tracked_keypoint][0]
    
    # 2d-pose files selection
    pose_listdirs_names = next(os.walk(pose_dir))[1]
    pose_listdirs_names = natural_sort(pose_listdirs_names)
    json_dirs_names = [k for k in pose_listdirs_names if 'json' in k]
    json_files_names = [fnmatch.filter(os.listdir(os.path.join(pose_dir, js_dir)), '*.json') for js_dir in json_dirs_names]
    json_files_names = [natural_sort(j) for j in json_files_names]
    json_files = [[os.path.join(pose_dir, j_dir, j_file) for j_file in json_files_names[j]] for j, j_dir in enumerate(json_dirs_names)]
    
    # 2d-pose-associated files creation
    if not os.path.exists(poseTracked_dir): os.mkdir(poseTracked_dir)   
    try: [os.mkdir(os.path.join(poseTracked_dir,k)) for k in json_dirs_names]
    except: pass
    json_tracked_files = [[os.path.join(poseTracked_dir, j_dir, j_file) for j_file in json_files_names[j]] for j, j_dir in enumerate(json_dirs_names)]
    
    f_range = [[min([len(j) for j in json_files])] if frame_range==[] else frame_range][0]
    n_cams = len(json_dirs_names)
    error_min_tot, cameras_off_tot = [], []
    
    # Check that camera number is consistent between calibration file and pose folders
    if n_cams != len(P_all):
        raise Exception(f'Error: The number of cameras is not consistent:\
                    Found {len(P_all)} cameras in the calibration file,\
                    and {n_cams} cameras based on the number of pose folders.')
    
    Q_kpt = [np.array([0., 0., 0., 1.])]
    for f in tqdm(range(*f_range)):
        # print(f'\nFrame {f}:')
        json_files_f = [json_files[c][f] for c in range(n_cams)]
        json_tracked_files_f = [json_tracked_files[c][f] for c in range(n_cams)]
        Q_kpt_old = Q_kpt

        if not multi_person:
            # all possible combinations of persons
            personsIDs_comb = persons_combinations(json_files_f) 
            
            # choose persons of interest and exclude cameras with bad pose estimation
            error_proposals, proposals, Q_kpt = best_persons_and_cameras_combination(config, json_files_f, personsIDs_comb, P_all, tracked_keypoint_id, calib_params)

            error_min_tot.append(np.mean(error_proposals))
            cameras_off_count = np.count_nonzero([np.isnan(comb) for comb in proposals]) / len(proposals)
            cameras_off_tot.append(cameras_off_count)            

        else:
            # read data
            all_json_data_f = []
            for js_file in json_files_f:
                all_json_data_f.append(read_json(js_file))
            #TODO: remove people with average likelihood < 0.3, no full torso, less than 12 joints... (cf filter2d in dataset/base.py L498)
            
            # obtain proposals after computing affinity between all the people in the different views
            persons_per_view = [0] + [len(j) for j in all_json_data_f]
            cum_persons_per_view = np.cumsum(persons_per_view)
            affinity = compute_affinity(all_json_data_f, calib_params, cum_persons_per_view, reconstruction_error_threshold=reconstruction_error_threshold)
            circ_constraint = circular_constraint(cum_persons_per_view)
            affinity = affinity * circ_constraint
            #TODO: affinity without hand, face, feet (cf ray.py L31)
            affinity = matchSVT(affinity, cum_persons_per_view, circ_constraint, max_iter = 20, w_rank = 50, tol = 1e-4, w_sparse=0.1)
            affinity[affinity<min_affinity] = 0
            proposals = person_index_per_cam(affinity, cum_persons_per_view, min_cameras_for_triangulation)
        
        # rewrite json files with a single or multiple persons of interest
        rewrite_json_files(json_tracked_files_f, json_files_f, proposals, n_cams)


    # recap message
    recap_tracking(config, error_min_tot, cameras_off_tot)