run_nerf_helpers.py

import torch
torch.autograd.set_detect_anomaly(True)
import torch.nn as nn
import torch.nn.functional as F
import numpy as np

# # TODO: remove this dependency
# from torchsearchsorted import searchsorted
from torch import searchsorted

from matplotlib import pyplot as plt
from pytorch_msssim import ssim, ms_ssim, SSIM, MS_SSIM

# Misc
img2mse = lambda x, y : torch.mean((x - y) ** 2)
mse2psnr = lambda x : -10. * torch.log(x) / torch.log(torch.Tensor([10.]))
to8b = lambda x : (255*np.clip(x,0,1)).astype(np.uint8)

def img2psnr_redefine(x,y):
    '''
    we redefine the PSNR function,
    [previous]
    average MSE -> PSNR(average MSE)
    
    [new]
    average PSNR(each image pair)
    '''
    image_num = x.size(0)
    mses = ((x-y)**2).reshape(image_num, -1).mean(-1)
    
    psnrs = [mse2psnr(mse) for mse in mses]
    psnr = torch.stack(psnrs).mean()
    return psnr

def img2psnr_mask(x,y,mask):
    '''
    we redefine the PSNR function,
    [previous]
    average MSE -> PSNR(average MSE)
    
    [new]
    average PSNR(each image pair)
    '''
    
    image_num = x.size(0)
    mses = ((x-y)**2).mean(-1)
    qw_mses = ((x-y)**2).mean(-1)
    mses_sum = (mses*mask).reshape(image_num, -1).sum(-1)
    
    mses = mses_sum /mask.reshape(image_num, -1).sum(-1)
    psnrs = [mse2psnr(mse) for mse in mses]
    psnr = torch.stack(psnrs).mean()
    return psnr

def img2ssim(x,y, mask=None):
    if mask is not None:
        x = mask.unsqueeze(-1)*x
        y = mask.unsqueeze(-1)*y
     
    x = x.permute(0,3,1,2)
    y = y.permute(0,3,1,2)
    ssim_ = ssim(x,y, data_range=1)
    ms_ssim_ = ms_ssim(x,y, data_range=1)
    return ssim_, ms_ssim_

# Positional encoding (section 5.1)
class Embedder:
    def __init__(self, **kwargs):
        self.kwargs = kwargs
        self.create_embedding_fn()
        
    def create_embedding_fn(self):
        embed_fns = []
        d = self.kwargs['input_dims']
        out_dim = 0
        if self.kwargs['include_input']:
            embed_fns.append(lambda x : x)
            out_dim += d
            
        max_freq = self.kwargs['max_freq_log2']
        N_freqs = self.kwargs['num_freqs']
        
        if self.kwargs['log_sampling']:
            freq_bands = 2.**torch.linspace(0., max_freq, steps=N_freqs)
        else:
            freq_bands = torch.linspace(2.**0., 2.**max_freq, steps=N_freqs)
            
        for freq in freq_bands:
            for p_fn in self.kwargs['periodic_fns']:
                embed_fns.append(lambda x, p_fn=p_fn, freq=freq : p_fn(x * freq))
                out_dim += d
                    
        self.embed_fns = embed_fns
        self.out_dim = out_dim
        
    def embed(self, inputs):
        return torch.cat([fn(inputs) for fn in self.embed_fns], -1)


def get_embedder(multires, i=0):
    if i == -1:
        return nn.Identity(), 3
    
    embed_kwargs = {
                'include_input' : True,
                'input_dims' : 3,
                'max_freq_log2' : multires-1,
                'num_freqs' : multires,
                'log_sampling' : True,
                'periodic_fns' : [torch.sin, torch.cos],
    }
    
    embedder_obj = Embedder(**embed_kwargs)
    embed = lambda x, eo=embedder_obj : eo.embed(x)
    return embed, embedder_obj.out_dim


# Model
class NeRF(nn.Module):
    def __init__(self, D=8, W=256, input_ch=3, input_ch_views=3, output_ch=4, skips=[4], use_viewdirs=False):
        """ 
        """
        super(NeRF, self).__init__()
        self.D = D
        self.W = W
        self.input_ch = input_ch
        self.input_ch_views = input_ch_views
        self.skips = skips
        self.use_viewdirs = use_viewdirs
        
        self.pts_linears = nn.ModuleList(
            [nn.Linear(input_ch, W)] + [nn.Linear(W, W) if i not in self.skips else nn.Linear(W + input_ch, W) for i in range(D-1)])
        
        ### Implementation according to the official code release (https://github.com/bmild/nerf/blob/master/run_nerf_helpers.py#L104-L105)
        self.views_linears = nn.ModuleList([nn.Linear(input_ch_views + W, W//2)])

        ### Implementation according to the paper
        # self.views_linears = nn.ModuleList(
        #     [nn.Linear(input_ch_views + W, W//2)] + [nn.Linear(W//2, W//2) for i in range(D//2)])
        
        if use_viewdirs:
            self.feature_linear = nn.Linear(W, W)
            self.alpha_linear = nn.Linear(W, 1)
            self.rgb_linear = nn.Linear(W//2, 3)
        else:
            self.output_linear = nn.Linear(W, output_ch)

    def forward(self, x):
        input_pts, input_views = torch.split(x, [self.input_ch, self.input_ch_views], dim=-1)
        h = input_pts
        for i, l in enumerate(self.pts_linears):
            h = self.pts_linears[i](h)
            h = F.relu(h)
            if i in self.skips:
                h = torch.cat([input_pts, h], -1)

        if self.use_viewdirs:
            alpha = self.alpha_linear(h)
            feature = self.feature_linear(h)
            h = torch.cat([feature, input_views], -1)
        
            for i, l in enumerate(self.views_linears):
                h = self.views_linears[i](h)
                h = F.relu(h)

            rgb = self.rgb_linear(h)
            outputs = torch.cat([rgb, alpha], -1)
        else:
            outputs = self.output_linear(h)

        return outputs    

    def load_weights_from_keras(self, weights):
        assert self.use_viewdirs, "Not implemented if use_viewdirs=False"
        
        # Load pts_linears
        for i in range(self.D):
            idx_pts_linears = 2 * i
            self.pts_linears[i].weight.data = torch.from_numpy(np.transpose(weights[idx_pts_linears]))    
            self.pts_linears[i].bias.data = torch.from_numpy(np.transpose(weights[idx_pts_linears+1]))
        
        # Load feature_linear
        idx_feature_linear = 2 * self.D
        self.feature_linear.weight.data = torch.from_numpy(np.transpose(weights[idx_feature_linear]))
        self.feature_linear.bias.data = torch.from_numpy(np.transpose(weights[idx_feature_linear+1]))

        # Load views_linears
        idx_views_linears = 2 * self.D + 2
        self.views_linears[0].weight.data = torch.from_numpy(np.transpose(weights[idx_views_linears]))
        self.views_linears[0].bias.data = torch.from_numpy(np.transpose(weights[idx_views_linears+1]))

        # Load rgb_linear
        idx_rbg_linear = 2 * self.D + 4
        self.rgb_linear.weight.data = torch.from_numpy(np.transpose(weights[idx_rbg_linear]))
        self.rgb_linear.bias.data = torch.from_numpy(np.transpose(weights[idx_rbg_linear+1]))

        # Load alpha_linear
        idx_alpha_linear = 2 * self.D + 6
        self.alpha_linear.weight.data = torch.from_numpy(np.transpose(weights[idx_alpha_linear]))
        self.alpha_linear.bias.data = torch.from_numpy(np.transpose(weights[idx_alpha_linear+1]))

class NeRF_RGB(nn.Module):
    def __init__(self, D=8, W=256, input_ch=3, input_ch_views=3, output_ch=4, skips=[4], use_viewdirs=False, alpha_model=None):
        """ 
        """
        super(NeRF_RGB, self).__init__()
        self.D = D
        self.W = W
        self.input_ch = input_ch
        self.input_ch_views = input_ch_views
        self.skips = skips
        self.use_viewdirs = use_viewdirs
        
        self.pts_linears = nn.ModuleList(
            [nn.Linear(input_ch, W)] + [nn.Linear(W, W) if i not in self.skips else nn.Linear(W + input_ch, W) for i in range(D-1)])
        
        ### Implementation according to the official code release (https://github.com/bmild/nerf/blob/master/run_nerf_helpers.py#L104-L105)
        self.views_linears = nn.ModuleList([nn.Linear(input_ch_views + W, W//2)])

        ### Implementation according to the paper
        # self.views_linears = nn.ModuleList(
        #     [nn.Linear(input_ch_views + W, W//2)] + [nn.Linear(W//2, W//2) for i in range(D//2)])
        
        if use_viewdirs:
            self.feature_linear = nn.Linear(W, W)
            # self.alpha_linear = nn.Linear(W, 1)
            self.rgb_linear = nn.Linear(W//2, 3)
        else:
            self.output_linear = nn.Linear(W, output_ch)

        self.alpha_model = alpha_model

    def forward(self, x):
        input_pts, input_views = torch.split(x, [self.input_ch, self.input_ch_views], dim=-1)
        h = input_pts
        for i, l in enumerate(self.pts_linears):
            h = self.pts_linears[i](h)
            h = F.relu(h)
            if i in self.skips:
                h = torch.cat([input_pts, h], -1)

        if self.use_viewdirs:
            with torch.no_grad():
                alpha = self.alpha_model(x)[...,3][...,None]
            feature = self.feature_linear(h)
            h = torch.cat([feature, input_views], -1)
        
            for i, l in enumerate(self.views_linears):
                h = self.views_linears[i](h)
                h = F.relu(h)

            rgb = self.rgb_linear(h)
            outputs = torch.cat([rgb, alpha], -1)
        else:
            outputs = self.output_linear(h)

        return outputs    

    def load_weights_from_keras(self, weights):
        assert self.use_viewdirs, "Not implemented if use_viewdirs=False"
        
        # Load pts_linears
        for i in range(self.D):
            idx_pts_linears = 2 * i
            self.pts_linears[i].weight.data = torch.from_numpy(np.transpose(weights[idx_pts_linears]))    
            self.pts_linears[i].bias.data = torch.from_numpy(np.transpose(weights[idx_pts_linears+1]))
        
        # Load feature_linear
        idx_feature_linear = 2 * self.D
        self.feature_linear.weight.data = torch.from_numpy(np.transpose(weights[idx_feature_linear]))
        self.feature_linear.bias.data = torch.from_numpy(np.transpose(weights[idx_feature_linear+1]))

        # Load views_linears
        idx_views_linears = 2 * self.D + 2
        self.views_linears[0].weight.data = torch.from_numpy(np.transpose(weights[idx_views_linears]))
        self.views_linears[0].bias.data = torch.from_numpy(np.transpose(weights[idx_views_linears+1]))

        # Load rgb_linear
        idx_rbg_linear = 2 * self.D + 4
        self.rgb_linear.weight.data = torch.from_numpy(np.transpose(weights[idx_rbg_linear]))
        self.rgb_linear.bias.data = torch.from_numpy(np.transpose(weights[idx_rbg_linear+1]))

        # Load alpha_linear
        idx_alpha_linear = 2 * self.D + 6
        self.alpha_linear.weight.data = torch.from_numpy(np.transpose(weights[idx_alpha_linear]))
        self.alpha_linear.bias.data = torch.from_numpy(np.transpose(weights[idx_alpha_linear+1]))


# Ray helpers
def get_rays(H, W, focal, c2w, padding=None):
    # pytorch's meshgrid has indexing='ij'
    if padding is not None:
        i, j = torch.meshgrid(torch.linspace(-padding, W-1+padding, W+2*padding), torch.linspace(-padding, H-1+padding, H+2*padding)) 
    else:
        i, j = torch.meshgrid(torch.linspace(0, W-1, W), torch.linspace(0, H-1, H))
    i = i.t()
    j = j.t()
    dirs = torch.stack([(i-W*.5)/focal, -(j-H*.5)/focal, -torch.ones_like(i)], -1)
    # Rotate ray directions from camera frame to the world frame
    rays_d = torch.sum(dirs[..., np.newaxis, :] * c2w[:3,:3], -1)  # dot product, equals to: [c2w.dot(dir) for dir in dirs]
    # Translate camera frame's origin to the world frame. It is the origin of all rays.
    rays_o = c2w[:3,-1].expand(rays_d.shape)
    return rays_o, rays_d


def get_rays_np(H, W, focal, c2w):
    i, j = np.meshgrid(np.arange(W, dtype=np.float32), np.arange(H, dtype=np.float32), indexing='xy') # i: H x W, j: H x W
    dirs = np.stack([(i-W*.5)/focal, -(j-H*.5)/focal, -np.ones_like(i)], -1) # dirs: H x W x 3
    # Rotate ray directions from camera frame to the world frame
    rays_d = np.sum(dirs[..., np.newaxis, :] * c2w[:3,:3], -1)  # dot product, equals to: [c2w.dot(dir) for dir in dirs]
    # Translate camera frame's origin to the world frame. It is the origin of all rays.
    rays_o = np.broadcast_to(c2w[:3,-1], np.shape(rays_d))  # H x W x 3
    return rays_o, rays_d


def get_rays_by_coord_np(H, W, focal, c2w, coords):
    i, j = (coords[:,0]-W*0.5)/focal, -(coords[:,1]-H*0.5)/focal
    dirs = np.stack([i,j,-np.ones_like(i)],-1)
    rays_d = np.sum(dirs[..., np.newaxis, :] * c2w[:3,:3], -1)
    rays_o = np.broadcast_to(c2w[:3,-1], np.shape(rays_d))
    return rays_o, rays_d

def ndc_rays(H, W, focal, near, rays_o, rays_d):
    # Shift ray origins to near plane
    t = -(near + rays_o[...,2]) / rays_d[...,2]
    rays_o = rays_o + t[...,None] * rays_d
    
    # Projection
    o0 = -1./(W/(2.*focal)) * rays_o[...,0] / rays_o[...,2]
    o1 = -1./(H/(2.*focal)) * rays_o[...,1] / rays_o[...,2]
    o2 = 1. + 2. * near / rays_o[...,2]

    d0 = -1./(W/(2.*focal)) * (rays_d[...,0]/rays_d[...,2] - rays_o[...,0]/rays_o[...,2])
    d1 = -1./(H/(2.*focal)) * (rays_d[...,1]/rays_d[...,2] - rays_o[...,1]/rays_o[...,2])
    d2 = -2. * near / rays_o[...,2]
    
    rays_o = torch.stack([o0,o1,o2], -1)
    rays_d = torch.stack([d0,d1,d2], -1)
    
    return rays_o, rays_d


# Hierarchical sampling (section 5.2)
def sample_pdf(bins, weights, N_samples, det=False, pytest=False):
    # Get pdf
    weights = weights + 1e-5 # prevent nans
    pdf = weights / torch.sum(weights, -1, keepdim=True)
    cdf = torch.cumsum(pdf, -1)
    cdf = torch.cat([torch.zeros_like(cdf[...,:1]), cdf], -1)  # (batch, len(bins))

    # Take uniform samples
    if det:
        u = torch.linspace(0., 1., steps=N_samples)
        u = u.expand(list(cdf.shape[:-1]) + [N_samples])
    else:
        u = torch.rand(list(cdf.shape[:-1]) + [N_samples])

    # Pytest, overwrite u with numpy's fixed random numbersd
    if pytest:
        np.random.seed(0)
        new_shape = list(cdf.shape[:-1]) + [N_samples]
        if det:
            u = np.linspace(0., 1., N_samples)
            u = np.broadcast_to(u, new_shape)
        else:
            u = np.random.rand(*new_shape)
        u = torch.Tensor(u)

    # Invert CDF
    u = u.contiguous()
    inds = searchsorted(cdf, u, right=True)
    below = torch.max(torch.zeros_like(inds-1), inds-1)
    above = torch.min((cdf.shape[-1]-1) * torch.ones_like(inds), inds)
    inds_g = torch.stack([below, above], -1)  # (batch, N_samples, 2)

    # cdf_g = tf.gather(cdf, inds_g, axis=-1, batch_dims=len(inds_g.shape)-2)
    # bins_g = tf.gather(bins, inds_g, axis=-1, batch_dims=len(inds_g.shape)-2)
    matched_shape = [inds_g.shape[0], inds_g.shape[1], cdf.shape[-1]]
    cdf_g = torch.gather(cdf.unsqueeze(1).expand(matched_shape), 2, inds_g)
    bins_g = torch.gather(bins.unsqueeze(1).expand(matched_shape), 2, inds_g)

    denom = (cdf_g[...,1]-cdf_g[...,0])
    denom = torch.where(denom<1e-5, torch.ones_like(denom), denom)
    t = (u-cdf_g[...,0])/denom
    samples = bins_g[...,0] + t * (bins_g[...,1]-bins_g[...,0])

    return samples

def raw2outputs(raw, z_vals, rays_d, raw_noise_std=0, white_bkgd=False, pytest=False, 
               out_alpha=False, out_sigma=False, out_dist=False):
    """Transforms model's predictions to semantically meaningful values.
    Args:
        raw: [num_rays, num_samples along ray, 4]. Prediction from model.
        z_vals: [num_rays, num_samples along ray]. Integration time.
        rays_d: [num_rays, 3]. Direction of each ray.
    Returns:
        rgb_map: [num_rays, 3]. Estimated RGB color of a ray.
        disp_map: [num_rays]. Disparity map. Inverse of depth map.
        acc_map: [num_rays]. Sum of weights along each ray.
        weights: [num_rays, num_samples]. Weights assigned to each sampled color.
        depth_map: [num_rays]. Estimated distance to object.
    """
    raw2alpha = lambda raw, dists, act_fn=F.relu: 1.-torch.exp(-act_fn(raw)*dists)
    
    dists = z_vals[...,1:] - z_vals[...,:-1]
    dists = torch.cat([dists, torch.Tensor([1e10]).expand(dists[...,:1].shape)], -1)  # [N_rays, N_samples]

    dists = dists * torch.norm(rays_d[...,None,:], dim=-1)

    rgb = torch.sigmoid(raw[...,:3])  # [N_rays, N_samples, 3]
    noise = 0.
    if raw_noise_std > 0.:
        noise = torch.randn(raw[...,3].shape) * raw_noise_std

        # Overwrite randomly sampled data if pytest
        if pytest:
            np.random.seed(0)
            noise = np.random.rand(*list(raw[...,3].shape)) * raw_noise_std
            noise = torch.Tensor(noise)

    alpha = raw2alpha(raw[...,3] + noise, dists)  # [N_rays, N_samples]
    sigma = F.relu(raw[...,3]+noise)
    # weights = alpha * tf.math.cumprod(1.-alpha + 1e-10, -1, exclusive=True)
    weights = alpha * torch.cumprod(torch.cat([torch.ones((alpha.shape[0], 1)), 1.-alpha + 1e-10], -1), -1)[:, :-1]
    rgb_map = torch.sum(weights[...,None] * rgb, -2)  # [N_rays, 3]

    depth_map = torch.sum(weights * z_vals, -1)
    disp_map = 1./torch.max(1e-10 * torch.ones_like(depth_map), depth_map / torch.sum(weights, -1))
    acc_map = torch.sum(weights, -1)
    
    if white_bkgd:
        rgb_map = rgb_map + (1.-acc_map[...,None])
    
    others = {}
    if out_alpha or out_sigma or out_dist:
        if out_alpha:
            others['alpha'] = alpha
        if out_sigma:
            others['sigma'] = sigma
        if out_dist:
            others['dists'] = dists
        return rgb_map, disp_map, acc_map, weights, depth_map, others
    return rgb_map, disp_map, acc_map, weights, depth_map


def sample_sigma(rays_o, rays_d, viewdirs, network, z_vals, network_query):
    # N_rays = rays_o.shape[0]
    # N_samples = len(z_vals)
    # z_vals = z_vals.expand([N_rays, N_samples])

    pts = rays_o[...,None,:] + rays_d[...,None,:] * z_vals[...,:,None] # [N_rays, N_samples, 3]
    raw = network_query(pts, viewdirs, network)

    rgb = torch.sigmoid(raw[...,:3])  # [N_rays, N_samples, 3]
    sigma = F.relu(raw[...,3])

    rgb_map, disp_map, acc_map, weights, depth_map = raw2outputs(raw, z_vals, rays_d)

    return rgb, sigma, depth_map


def visualize_sigma(sigma, z_vals, filename):
    plt.plot(z_vals, sigma)
    plt.xlabel('z_vals')
    plt.ylabel('sigma')
    plt.savefig(filename)
    return