model.py

from torch import nn
import torch
import numpy as np
import roma
import copy

from utils import unpatch, inverse_perspective_projection, undo_focal_length_normalization, undo_log_depth
from blocks import Dinov2Backbone, FourierPositionEncoding, TransformerDecoder, SMPL_Layer
from utils import rot6d_to_rotmat, rebatch, pad_to_max
import torch.nn as nn
import numpy as np
import einops
from utils.constants import MEAN_PARAMS

class Model(nn.Module):
    """ A ViT backbone followed by a "HPH" head (stack of cross attention layers with queries corresponding to detected humans.) """

    def __init__(self,
            backbone='dinov2_vitb14',
            pretrained_backbone=False,
            img_size=896,
            camera_embedding='geometric', # geometric encodes viewing directions with fourrier encoding
            camera_embedding_num_bands=16, # increase the size of the camera embedding
            camera_embedding_max_resolution=64, # does not increase the size of the camera embedding
            nearness=True, # regress log(1/z)
            xat_depth=2, # number of cross attention block (SA, CA, MLP) in the HPH head.
            xat_num_heads=8, # Number of attention heads
            dict_smpl_layer=None,
            person_center='head',
            clip_dist=True,
            num_betas=10,
            *args, **kwargs):
        super().__init__()

        # Save options
        self.img_size = img_size
        self.nearness = nearness
        self.clip_dist = clip_dist,
        self.xat_depth = xat_depth
        self.xat_num_heads = xat_num_heads
        self.num_betas = num_betas

        # Setup backbone
        self.backbone = Dinov2Backbone(backbone, pretrained=pretrained_backbone)
        self.embed_dim = self.backbone.embed_dim
        self.patch_size = self.backbone.patch_size
        assert self.img_size % self.patch_size == 0, "Invalid img size"

        # Camera instrinsics
        self.fovn = 60
        self.camera_embedding = camera_embedding
        self.camera_embed_dim = 0
        if self.camera_embedding is not None:
            if not self.camera_embedding == 'geometric':
                raise NotImplementedError("Only geometric camera embedding is implemented")
            self.camera = FourierPositionEncoding(n=3, num_bands=camera_embedding_num_bands,max_resolution=camera_embedding_max_resolution)
            # import pdb
            # pdb.set_trace()
            self.camera_embed_dim = self.camera.channels

        # Heads - Detection
        self.mlp_classif = regression_mlp([self.embed_dim, self.embed_dim, 1]) # bg or human
        
        # Heads - Human properties
        self.mlp_offset = regression_mlp([self.embed_dim, self.embed_dim, 2]) # offset

        # SMPL Layers
        self.nrot = 53
        dict_smpl_layer = {
            'neutral': {
                10: SMPL_Layer(type='smplx', gender='neutral', num_betas=10, kid=False, person_center=person_center),
                11: SMPL_Layer(type='smplx', gender='neutral', num_betas=11, kid=False, person_center=person_center),
                }
            }
        _moduleDict = []
        for k, _smpl_layer in dict_smpl_layer.items():
            for x, y in _smpl_layer.items():
                _moduleDict.append([f"{k}_{x}", copy.deepcopy(y)])
        self.smpl_layer = nn.ModuleDict(_moduleDict)

        self.x_attention_head = HPH(
            num_body_joints=self.nrot-1, #23,
            context_dim=self.embed_dim + self.camera_embed_dim,
            dim=1024,
            depth=self.xat_depth,
            heads=self.xat_num_heads,
            mlp_dim=1024,
            dim_head=32,
            dropout=0.0,
            emb_dropout=0.0,
            at_token_res=self.img_size // self.patch_size,
            num_betas=self.num_betas,
            )
    
    def detection(self, z, nms_kernel_size, det_thresh, N, idx=None, is_training=False):
        """ Detection score on the entire low res image """
        scores = _sigmoid(self.mlp_classif(z)) # per token detection score.
        # Restore Height and Width dimensions.
        scores = unpatch(scores, patch_size=1, c=scores.shape[2], img_size=int(np.sqrt(N)))  

        if not is_training:
            if nms_kernel_size > 1: # Easy nms: supress adjacent high scores with max pooling.
                scores = _nms(scores, kernel=nms_kernel_size)
            _scores = torch.permute(scores, (0, 2, 3, 1))

            # Binary decision (keep confident detections)
            idx = apply_threshold(det_thresh, _scores)
        else:
            assert idx is not None # training time

        # Scores  
        scores_detected = scores[idx[0], idx[3], idx[1],idx[2]] # scores of the detected humans only
        scores = torch.permute(scores, (0, 2, 3, 1))
        return scores, scores_detected, idx

    def embedd_camera(self, K, z):
        """ Embed viewing directions using fourrier encoding."""
        bs = z.shape[0]
        _h, _w = list(z.shape[-2:])
        points = torch.stack([torch.arange(0,_h,1).reshape(-1,1).repeat(1,_w), torch.arange(0,_w,1).reshape(1,-1).repeat(_h,1)],-1).to(z.device).float() # [h,w,2]
        points = points * self.patch_size + self.patch_size // 2 # move to pixel space - we give the pixel center of each token
        points = points.reshape(1,-1,2).repeat(bs,1,1) # (bs, N, 2): 2D points
        distance = torch.ones(bs,points.shape[1],1).to(K.device) # (bs, N, 1): distance in the 3D world
        rays = inverse_perspective_projection(points, K, distance) # (bs, N, 3)
        rays_embeddings = self.camera(pos=rays)

        # Repeat for each element of the batch
        z_K = rays_embeddings.reshape(bs,_h,_w,self.camera_embed_dim) # [bs,h,w,D]
        return z_K 

    def to_euclidean_dist(self, x, dist, _K):
        # Focal length normalization
        focal = _K[:,[0],[0]]
        dist = undo_focal_length_normalization(dist, focal, fovn=self.fovn, img_size=x.shape[-1])
        # log space
        if self.nearness:
            dist = undo_log_depth(dist)

        # Clamping
        if self.clip_dist:
            dist = torch.clamp(dist, 0, 50)

        return dist


    def forward(self,
                x,
                idx=None,
                det_thresh=0.3,
                nms_kernel_size=3,
                K=None,
                is_training=False,
                pre_rotvec=None,
                pre_expression=None,
                pre_shape=None,
                pre_loc=None,
                pre_dist=None,
                pre_K_det=None,
                *args,
                **kwargs):
        """
        Forward pass of the model and compute the loss according to the groundtruth
        Args:
            - x: RGB image - [bs,3,224,224]
            - idx: GT location of persons - tuple of 3 tensor of shape [p]
            - idx_j2d: GT location of 2d-kpts for each detected humans - tensor of shape [bs',14,2] - location in pixel space
        Return:
            - y: [bs,D,16,16]
        """
        persons = []
        out = {}

        # Feature extraction
        z = self.backbone(x)
        B,N,C = z.size() # [bs,256,768]

        # Detection
        scores, scores_det, idx = self.detection(z, nms_kernel_size=nms_kernel_size, det_thresh=det_thresh, N=N,
                                                 idx=idx, is_training=is_training)
        if len(idx[0]) == 0 and not is_training:
            # no humans detected in the frame
            return persons

        # Map of Dense Feature
        z = unpatch(z, patch_size=1, c=z.shape[2], img_size=int(np.sqrt(N))) # [bs,D,16,16]
        z_all = z

        # Extract the 'central' features
        z = torch.reshape(z, (z.shape[0], 1, z.shape[1]//1, z.shape[2], z.shape[3])) # [bs,stack_K,D,16,16]
        z_central = z[idx[0],idx[3],:,idx[1],idx[2]] # dense vectors

        # 2D offset regression
        offset = self.mlp_offset(z_central)

        # Camera instrincs
        K_det = K[idx[0]] # cameras for detected person
        if pre_K_det is not None:
            K_det = matching_pairs(pre_K_det, K_det)
        z_K = self.embedd_camera(K, z) # Embed viewing directions.
        z_central = torch.cat([z_central, z_K[idx[0],idx[1], idx[2]]], 1) # Add to query tokens. 
        z_all = torch.cat([z_all, z_K.permute(0,3,1,2)], 1) # for the cross-attention only
        z = torch.cat([z, z_K.permute(0,3,1,2).unsqueeze(1)],2)

        # Distance for estimating the 3D location in 3D space
        loc = torch.stack([idx[2],idx[1]]).permute(1,0) # Moving from higher resolution the location of the pelvis
        loc = (loc + 0.5 + offset ) * self.patch_size

        # SMPL parameter regression
        kv = z_all[idx[0]] # retrieving dense features associated to each central vector
        pred_smpl_params, pred_cam = self.x_attention_head(z_central, kv, idx_0=idx[0], idx_det=idx)

        # Get outputs from the SMPL layer.
        shape = pred_smpl_params['betas']
        rotmat = torch.cat([pred_smpl_params['global_orient'],pred_smpl_params['body_pose']], 1)
        expression = pred_smpl_params['expression']
        rotvec = roma.rotmat_to_rotvec(rotmat)

        if pre_rotvec is not None:
            rotvec = matching_pairs(pre_rotvec, rotvec)
        if pre_expression is not None:
            expression = matching_pairs(pre_expression, expression)
        if pre_shape is not None:
            shape = matching_pairs(pre_shape, shape)
        if pre_loc is not None:
            loc = matching_pairs(pre_loc, loc)

        # Distance 
        dist = pred_cam[:, 0][:, None]
        out['dist_postprocessed'] = dist # before applying any post-processing such as focal length normalization, inverse or log
        if pre_dist is not None:
            dist = matching_pairs(pre_dist, dist)
        _dist = dist.clone()
        dist = self.to_euclidean_dist(x, dist, K_det)

        # Populate output dictionnary 
        out.update({'scores': scores, 
                    'offset': offset, 
                    'dist': dist, 
                    'expression': expression,
                    'rotmat': rotmat, 
                    'shape': shape, 
                    'rotvec': rotvec, 
                    'loc': loc})

        assert rotvec.shape[0] == shape.shape[0] == loc.shape[0] == dist.shape[0], "Incoherent shapes"
        
        # Neutral
        smpl_out = self.smpl_layer[f"neutral_{self.num_betas}"](rotvec, shape, loc, dist, None, K=K_det, expression=expression)
        out.update(smpl_out)        

        # Return
        if is_training:
            return out
        else:
            # Populate a dictionnary for each person
            for i in range(idx[0].shape[0]):
                person = {
                    # Detection
                    'scores': scores_det[i], # detection scores
                    'loc': out['loc'][i], # 2d pixel location of the primary keypoints
                    # SMPL-X params
                    'transl': out['transl'][i], # from the primary keypoint i.e. the head
                    'transl_pelvis': out['transl_pelvis'][i], # of the pelvis joint
                    'rotvec': out['rotvec'][i],
                    'expression': out['expression'][i],
                    'shape': out['shape'][i],
                    # SMPL-X meshs
                    'v3d': out['v3d'][i],
                    'j3d': out['j3d'][i],
                    'j2d': out['j2d'][i],
                }
                persons.append(person)

            return persons, rotvec, expression, shape, loc, _dist, K_det
        
    def pred_parameters(self,
                x,
                idx=None,
                det_thresh=0.3,
                nms_kernel_size=3,
                K=None,
                is_training=False,
                *args,
                **kwargs):
        persons = []
        out = {}

        # Feature extraction
        z = self.backbone(x)
        B,N,C = z.size() # [bs,256,768]

        # Detection
        scores, scores_det, idx = self.detection(z, nms_kernel_size=nms_kernel_size, det_thresh=det_thresh, N=N,
                                                 idx=idx, is_training=is_training)
        if len(idx[0]) == 0 and not is_training:
            # no humans detected in the frame
            return persons

        # Map of Dense Feature
        z = unpatch(z, patch_size=1, c=z.shape[2], img_size=int(np.sqrt(N))) # [bs,D,16,16]
        z_all = z

        # Extract the 'central' features
        z = torch.reshape(z, (z.shape[0], 1, z.shape[1]//1, z.shape[2], z.shape[3])) # [bs,stack_K,D,16,16]
        z_central = z[idx[0],idx[3],:,idx[1],idx[2]] # dense vectors

        # 2D offset regression
        offset = self.mlp_offset(z_central)

        # Camera instrincs
        K_det = K[idx[0]] # cameras for detected person
        z_K = self.embedd_camera(K, z) # Embed viewing directions.
        z_central = torch.cat([z_central, z_K[idx[0],idx[1], idx[2]]], 1) # Add to query tokens. 
        z_all = torch.cat([z_all, z_K.permute(0,3,1,2)], 1) # for the cross-attention only
        z = torch.cat([z, z_K.permute(0,3,1,2).unsqueeze(1)],2)

        # Distance for estimating the 3D location in 3D space
        loc = torch.stack([idx[2],idx[1]]).permute(1,0) # Moving from higher resolution the location of the pelvis
        loc = (loc + 0.5 + offset ) * self.patch_size

        # SMPL parameter regression
        kv = z_all[idx[0]] # retrieving dense features associated to each central vector
        pred_smpl_params, pred_cam = self.x_attention_head(z_central, kv, idx_0=idx[0], idx_det=idx)

        # Get outputs from the SMPL layer.
        shape = pred_smpl_params['betas']
        rotmat = torch.cat([pred_smpl_params['global_orient'],pred_smpl_params['body_pose']], 1)
        expression = pred_smpl_params['expression']
        rotvec = roma.rotmat_to_rotvec(rotmat)

        # Distance 
        dist = pred_cam[:, 0][:, None]
        out['dist_postprocessed'] = dist # before applying any post-processing such as focal length normalization, inverse or log
        dist = self.to_euclidean_dist(x, dist, K_det)

        # Populate output dictionnary 
        out.update({'scores': scores, 
                    'offset': offset,
                    'K_det': K_det,
                    'dist': dist, 
                    'expression': expression,
                    'rotmat': rotmat, 
                    'shape': shape, 
                    'rotvec': rotvec, 
                    'loc': loc})
        
        return out
        
    def pred_human(self, parameters, K=None, is_training=False):
        """
        Predict the mesh from the parameters.
        Args:
            - parameters: dict of parameters
            - K: camera intrinsics
            - is_training: whether the model is in training mode
        Returns:
            - mesh: predicted mesh
        """
        humans = []
        out = parameters

        # Get SMPL-X parameters
        rotvec = out['rotvec'] 
        shape = out['shape']
        loc = out['loc']
        dist = out['dist']
        expression = out['expression']

        # Get SMPL-X mesh
        smpl_out = self.smpl_layer[f"neutral_{self.num_betas}"](rotvec, shape, loc, dist, None, K=K, expression=expression)
        
        out.update(smpl_out)

        if is_training:
            return out
        else:
            # Populate a dictionnary for each person
            for i in range(rotvec.shape[0]):
                human = {
                    'loc': out['loc'][i], # 2d pixel location of the primary keypoints  
                    'transl': out['transl'][i], # from the primary keypoint i.e. the head
                    'transl_pelvis': out['transl_pelvis'][i], # of the pelvis joint  
                    'v3d': out['v3d'][i],
                    'j3d': out['j3d'][i],
                    'j2d': out['j2d'][i],
                }
                humans.append(human)

            return humans



class HPH(nn.Module):
    """ Cross-attention based SMPL Transformer decoder

    Code modified from:
    https://github.com/shubham-goel/4D-Humans/blob/a0def798c7eac811a63c8220fcc22d983b39785e/hmr2/models/heads/smpl_head.py#L17
    https://github.com/shubham-goel/4D-Humans/blob/a0def798c7eac811a63c8220fcc22d983b39785e/hmr2/models/components/pose_transformer.py#L301
    """

    def __init__(self,
                 num_body_joints=52,
                 context_dim=1280,
                 dim=1024,
                 depth=2,
                 heads=8,
                 mlp_dim=1024,
                 dim_head=64,
                 dropout=0.0,
                 emb_dropout=0.0,
                 at_token_res=32,
                 num_betas=10,
                 ):
        super().__init__()

        self.joint_rep_type, self.joint_rep_dim = '6d', 6
        self.num_body_joints = num_body_joints
        self.nrot = self.num_body_joints + 1

        npose = self.joint_rep_dim * (self.num_body_joints + 1)
        self.npose = npose

        self.depth = depth,
        self.heads = heads,
        self.res = at_token_res
        self.input_is_mean_shape = True
        _context_dim = context_dim # for the central features
        self.num_betas = num_betas
        assert num_betas in [10, 11]

        # Transformer Decoder setup.
        # Based on https://github.com/shubham-goel/4D-Humans/blob/8830bb330558eea2395b7f57088ef0aae7f8fa22/hmr2/configs_hydra/experiment/hmr_vit_transformer.yaml#L35
        transformer_args = dict(
            num_tokens=1,
            token_dim=(npose + self.num_betas + 3 + _context_dim) if self.input_is_mean_shape else 1,
            dim=dim,
            depth=depth,
            heads=heads,
            mlp_dim=mlp_dim,
            dim_head=dim_head,
            dropout=dropout,
            emb_dropout=emb_dropout,
            context_dim=context_dim,
        )
        self.transformer = TransformerDecoder(**transformer_args)

        dim = transformer_args['dim']

        # Final decoders to regress targets 
        self.decpose, self.decshape, self.deccam, self.decexpression = [nn.Linear(dim, od) for od in [npose, num_betas, 3, 10]]

        # Register bufffers for the smpl layer.
        self.set_smpl_init()

        # Init learned embeddings for the cross attention queries
        self.init_learned_queries(context_dim)


    def init_learned_queries(self, context_dim, std=0.2):
        """ Init learned embeddings for queries"""
        self.cross_queries_x = nn.Parameter(torch.zeros(self.res, context_dim))
        torch.nn.init.normal_(self.cross_queries_x, std=std)

        self.cross_queries_y = nn.Parameter(torch.zeros(self.res, context_dim))
        torch.nn.init.normal_(self.cross_queries_y, std=std)

        self.cross_values_x = nn.Parameter(torch.zeros(self.res, context_dim))
        torch.nn.init.normal_(self.cross_values_x, std=std)

        self.cross_values_y = nn.Parameter(nn.Parameter(torch.zeros(self.res, context_dim)))
        torch.nn.init.normal_(self.cross_values_y, std=std)

    def set_smpl_init(self):
        """ Fetch saved SMPL parameters and register buffers."""
        mean_params = np.load(MEAN_PARAMS)
        if self.nrot == 53:
            init_body_pose = torch.eye(3).reshape(1,3,3).repeat(self.nrot,1,1)[:,:,:2].flatten(1).reshape(1, -1)
            init_body_pose[:,:24*6] = torch.from_numpy(mean_params['pose'][:]).float() # global_orient+body_pose from SMPL
        else:
            init_body_pose = torch.from_numpy(mean_params['pose'].astype(np.float32)).unsqueeze(0)

        init_betas = torch.from_numpy(mean_params['shape'].astype('float32')).unsqueeze(0)
        init_cam = torch.from_numpy(mean_params['cam'].astype(np.float32)).unsqueeze(0)
        init_betas_kid = torch.cat([init_betas, torch.zeros_like(init_betas[:,[0]])],1)
        init_expression = 0. * torch.from_numpy(mean_params['shape'].astype('float32')).unsqueeze(0)

        if self.num_betas == 11:
            init_betas = torch.cat([init_betas, torch.zeros_like(init_betas[:,:1])], 1)

        self.register_buffer('init_body_pose', init_body_pose)
        self.register_buffer('init_betas', init_betas)
        self.register_buffer('init_betas_kid', init_betas_kid)
        self.register_buffer('init_cam', init_cam)
        self.register_buffer('init_expression', init_expression)


    def cross_attn_inputs(self, x, x_central, idx_0, idx_det):
        """ Reshape and pad x_central to have the right shape for Cross-attention processing. 
            Inject learned embeddings to query and key inputs at the location of detected people. """

        h, w = x.shape[2], x.shape[3]
        x = einops.rearrange(x, 'b c h w -> b (h w) c')

        assert idx_0 is not None, "Learned cross queries only work with multicross"

        if idx_0.shape[0] > 0:
            # reconstruct the batch/nb_people dimensions: pad for images with fewer people than max.
            counts, idx_det_0 = rebatch(idx_0, idx_det)
            old_shape = x_central.shape

            # Legacy check for old versions 
            assert idx_det is not None, 'idx_det needed for learned_attention'

            # xx is the tensor with all features
            xx = einops.rearrange(x, 'b (h w) c -> b c h w', h=h, w=w)
            # Get learned embeddings for queries, at positions with detected people.
            queries_xy = self.cross_queries_x[idx_det[1]] + self.cross_queries_y[idx_det[2]]
            # Add the embedding to the central features.
            x_central = x_central + queries_xy
            assert x_central.shape == old_shape, "Problem with shape"
        
            # Make it a tensor of dim. [batch, max_ppl_along_batch, ...]
            x_central, mask = pad_to_max(x_central, counts)

            #xx = einops.rearrange(x, 'b (h w) c -> b c h w', h=h, w=w)
            xx = xx[torch.cumsum(counts, dim=0)-1]

            # Inject leared embeddings for key/values at detected locations. 
            values_xy = self.cross_values_x[idx_det[1]] + self.cross_values_y[idx_det[2]]
            xx[idx_det_0, :, idx_det[1], idx_det[2]] += values_xy

            x = einops.rearrange(xx, 'b c h w -> b (h w) c')
            num_ppl =  x_central.shape[1]
        else:
            mask = None
            num_ppl = 1
            counts = None
        return x, x_central, mask, num_ppl, counts


    def forward(self,
                x_central,
                x,
                idx_0=None,
                idx_det=None,
                **kwargs):
        """"
        Forward the HPH module.
        """
        batch_size = x.shape[0]

        # Reshape inputs for cross attention and inject learned embeddings for queries and values.
        x, x_central, mask, num_ppl, counts = self.cross_attn_inputs(x, x_central, idx_0, idx_det)

        # Add init (mean smpl params) to the query for each quantity being regressed.
        bs = x_central.shape[0] if idx_0.shape[0] else batch_size
        expand = lambda x: x.expand(bs, num_ppl , -1)
        pred_body_pose, pred_betas, pred_cam, pred_expression = [expand(x) for x in
                [self.init_body_pose, self.init_betas, self.init_cam, self.init_expression]]
        token = torch.cat([x_central, pred_body_pose, pred_betas, pred_cam], dim=-1)
        if len(token.shape) == 2:
            token = token[:,None,:]
        
        # Process query and inputs with the cross-attention module.
        token_out = self.transformer(token, context=x, mask=mask)

        # Reshape outputs from [batch_size, nmax_ppl, ...] to [total_ppl, ...]
        if mask is not None:
            # Stack along batch axis.
            token_out_list = [token_out[i, :c, ...] for i, c in enumerate(counts)]
            token_out = torch.concat(token_out_list, dim=0)
        else:
            token_out = token_out.squeeze(1) # (B, C)

        # Decoded output token and add to init for each quantity to regress.
        reshape = (lambda x: x) if idx_0.shape[0] == 0 else (lambda x: x[0, 0, ...][None, ...])
        decoders = [self.decpose, self.decshape, self.deccam, self.decexpression]
        inits = [pred_body_pose, pred_betas, pred_cam, pred_expression]
        pred_body_pose, pred_betas, pred_cam, pred_expression = [d(token_out) + reshape(i) for d, i in zip(decoders, inits)]

        # Convert self.joint_rep_type -> rotmat
        joint_conversion_fn = rot6d_to_rotmat

        # conversion
        pred_body_pose = joint_conversion_fn(pred_body_pose).view(batch_size, self.num_body_joints+1, 3, 3)

        # Build the output dict
        pred_smpl_params = {'global_orient': pred_body_pose[:, [0]],
                            'body_pose': pred_body_pose[:, 1:],
                            'betas': pred_betas,
                            #'betas_kid': pred_betas_kid,
                            'expression': pred_expression}
        return pred_smpl_params, pred_cam #, pred_smpl_params_list

def regression_mlp(layers_sizes):
    """
    Return a fully connected network.
    """
    assert len(layers_sizes) >= 2
    in_features = layers_sizes[0]
    layers = []
    for i in range(1, len(layers_sizes)-1):
        out_features = layers_sizes[i]
        layers.append(torch.nn.Linear(in_features, out_features))
        layers.append(torch.nn.ReLU())
        in_features = out_features
    layers.append(torch.nn.Linear(in_features, layers_sizes[-1]))
    return torch.nn.Sequential(*layers)

def apply_threshold(det_thresh, _scores):
    """ Apply thresholding to detection scores; if stack_K is used and det_thresh is a list, apply to each channel separately """
    if isinstance(det_thresh, list):
        det_thresh = det_thresh[0]
    idx = torch.where(_scores >= det_thresh)
    return idx

def _nms(heat, kernel=3):
    """ easy non maximal supression (as in CenterNet) """

    if kernel not in [2, 4]:
        pad = (kernel - 1) // 2
    else:
        if kernel == 2:
            pad = 1
        else:
            pad = 2

    hmax = nn.functional.max_pool2d( heat, (kernel, kernel), stride=1, padding=pad)

    if hmax.shape[2] > heat.shape[2]:
        hmax = hmax[:, :, :heat.shape[2], :heat.shape[3]]

    keep = (hmax == heat).float()

    return heat * keep

def _sigmoid(x):
  y = torch.clamp(x.sigmoid_(), min=1e-4, max=1-1e-4)
  return y


def matching_pairs(pre_objects, cur_objects):
    # Keep as tensors for computation
    pre_objs = pre_objects
    cur_objs = cur_objects
    
    matched_pairs = []
    unmatched_objects = []
    for i, pre_obj in enumerate(pre_objs):
        best_match = -1
        min_distance = float('inf')
        
        for j, cur_obj in enumerate(cur_objs):
            # Calculate similarity using L2 distance
            # Handle different lengths by using minimum length
            min_len = min(len(pre_obj), len(cur_obj))
            if min_len > 0:
                # Compute distance using tensors
                diff = pre_obj[:min_len] - cur_obj[:min_len]
                distance = torch.sqrt(torch.sum(diff ** 2)).item()
                # Normalize by length to make comparison fair
                distance = distance / min_len
                
                if distance < min_distance:
                    min_distance = distance
                    best_match = j
        
        # Use a threshold to determine if it's a valid match
        threshold = 1.0  # Adjust this value as needed
        if best_match != -1 and min_distance < threshold:
            matched_pairs.append((i, best_match))
        else:
            unmatched_objects.append(i)
    
    # Find unmatched current objects
    matched_cur_indices = set(pair[1] for pair in matched_pairs)
    for j in range(len(cur_objs)):
        if j not in matched_cur_indices:
            unmatched_objects.append(j)
            
    # Create a list of matched objects  
    matched_objects = [None for _ in range(len(pre_objs))]
    for pre_idx, cur_idx in matched_pairs:
        if pre_idx != cur_idx:
            if (pre_idx, pre_idx) in matched_pairs:
                matched_objects[pre_idx] = pre_objs[pre_idx]
            else:
                matched_objects[pre_idx] = cur_objs[cur_idx]
        else:
            matched_objects[pre_idx] = cur_objs[cur_idx]
    
    for pre_idx in unmatched_objects:
        matched_objects[pre_idx] = pre_objs[pre_idx]
        
    matched_objects = torch.stack(matched_objects) if matched_objects else None
    return matched_objects

if __name__ == "__main__":
    Model()