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
import cv2
from plyfile import PlyData, PlyElement
import sys


# 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)


# 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]))


# Ray helpers
def get_rays(H, W, K, c2w):
    i, j = torch.meshgrid(torch.linspace(0, W-1, W), torch.linspace(0, H-1, H))  # pytorch's meshgrid has indexing='ij'
    i = i.t()
    j = j.t()
    dirs = torch.stack([(i-K[0][2])/K[0][0], -(j-K[1][2])/K[1][1], -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, K, c2w):
    i, j = np.meshgrid(np.arange(W, dtype=np.float32), np.arange(H, dtype=np.float32), indexing='xy')
    dirs = np.stack([(i-K[0][2])/K[0][0], -(j-K[1][2])/K[1][1], -np.ones_like(i)], -1)
    # 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))
    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 numbers
    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 = torch.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 visualize_depth(depth, mask=None, depth_min=None, depth_max=None, direct=False):
    """Visualize the depth map with colormap.
       Rescales the values so that depth_min and depth_max map to 0 and 1,
       respectively.
    """
    if not direct:
        depth = 1.0 / (depth + 1e-6)
    invalid_mask = np.logical_or(np.isnan(depth), np.logical_not(np.isfinite(depth)))
    if mask is not None:
        invalid_mask += np.logical_not(mask)
    if depth_min is None:
        depth_min = np.percentile(depth[np.logical_not(invalid_mask)], 5)
    if depth_max is None:
        depth_max = np.percentile(depth[np.logical_not(invalid_mask)], 95)
    depth[depth < depth_min] = depth_min
    depth[depth > depth_max] = depth_max
    depth[invalid_mask] = depth_max

    depth_scaled = (depth - depth_min) / (depth_max - depth_min)
    depth_scaled_uint8 = np.uint8(depth_scaled * 255)
    depth_color = cv2.applyColorMap(depth_scaled_uint8, cv2.COLORMAP_MAGMA)
    depth_color[invalid_mask, :] = 0

    return depth_color

def save_ply(plyfilename, vert_pos, vert_colors):
    # vert pos has shape N x 3
    # vert_colors has shape N x 3
    # save
    vertexs = vert_pos.cpu().numpy()
    vertex_colors = ((vert_colors.cpu().numpy() + 1.0) / 2.0 * 255.0).astype(np.uint8)[...,[2,1,0]]
    vertexs = np.array([tuple(v) for v in vertexs], dtype=[('x', 'f4'), ('y', 'f4'), ('z', 'f4')])
    vertex_colors = np.array([tuple(v) for v in vertex_colors], dtype=[('red', 'u1'), ('green', 'u1'), ('blue', 'u1')])

    vertex_all = np.empty(len(vertexs), vertexs.dtype.descr + vertex_colors.dtype.descr)
    for prop in vertexs.dtype.names:
        vertex_all[prop] = vertexs[prop]
    for prop in vertex_colors.dtype.names:
        vertex_all[prop] = vertex_colors[prop]

    el = PlyElement.describe(vertex_all, 'vertex')
    PlyData([el]).write(plyfilename)
    print("saving the final model to", plyfilename)

def write_pfm(file: str, image, scale=1):
    with open(file, 'wb') as f:
        color = None

        if image.dtype.name != 'float32':
            raise Exception('Image dtype must be float32.')

        image = np.flipud(image)

        if len(image.shape) == 3 and image.shape[2] == 3: # color image
            color = True
        elif len(image.shape) == 2 or len(image.shape) == 3 and image.shape[2] == 1: # greyscale
            color = False
        else:
            raise Exception('Image must have H x W x 3, H x W x 1 or H x W dimensions.')

        f.write(b'PF\n' if color else b'Pf\n')
        f.write(b'%d %d\n' % (image.shape[1], image.shape[0]))

        endian = image.dtype.byteorder

        if endian == '<' or endian == '=' and sys.byteorder == 'little':
            scale = -scale

        f.write(b'%f\n' % scale)

        image.tofile(f)

# adapted from barf:
# https://github.com/chenhsuanlin/bundle-adjusting-NeRF/blob/f04e37cc3417bab25d71ccd9146bf696534ff3b1/camera.py#L83
class Lie():
    """
    Lie algebra for SO(3) and SE(3) operations in PyTorch
    """

    def so3_to_SO3(self,w): # [...,3]
        wx = self.skew_symmetric(w)
        theta = w.norm(dim=-1)[...,None,None]
        I = torch.eye(3,device=w.device,dtype=torch.float32)
        A = self.taylor_A(theta)
        B = self.taylor_B(theta)
        R = I+A*wx+B*wx@wx
        return R

    def SO3_to_so3(self,R,eps=1e-7): # [...,3,3]
        trace = R[...,0,0]+R[...,1,1]+R[...,2,2]
        theta = ((trace-1)/2).clamp(-1+eps,1-eps).acos_()[...,None,None]%np.pi # ln(R) will explode if theta==pi
        lnR = 1/(2*self.taylor_A(theta)+1e-8)*(R-R.transpose(-2,-1)) # FIXME: wei-chiu finds it weird
        w0,w1,w2 = lnR[...,2,1],lnR[...,0,2],lnR[...,1,0]
        w = torch.stack([w0,w1,w2],dim=-1)
        return w

    def se3_to_SE3(self,wu): # [...,6]
        w,u = wu.split([3,3],dim=-1)
        wx = self.skew_symmetric(w)
        theta = w.norm(dim=-1)[...,None,None]
        I = torch.eye(3,device=w.device,dtype=torch.float32)
        A = self.taylor_A(theta)
        B = self.taylor_B(theta)
        C = self.taylor_C(theta)
        R = I+A*wx+B*wx@wx
        V = I+B*wx+C*wx@wx
        Rt = torch.cat([R,(V@u[...,None])],dim=-1)
        return Rt

    def SE3_to_se3(self,Rt,eps=1e-8): # [...,3,4]
        R,t = Rt.split([3,1],dim=-1)
        w = self.SO3_to_so3(R)
        wx = self.skew_symmetric(w)
        theta = w.norm(dim=-1)[...,None,None]
        I = torch.eye(3,device=w.device,dtype=torch.float32)
        A = self.taylor_A(theta)
        B = self.taylor_B(theta)
        invV = I-0.5*wx+(1-A/(2*B))/(theta**2+eps)*wx@wx
        u = (invV@t)[...,0]
        wu = torch.cat([w,u],dim=-1)
        return wu

    def skew_symmetric(self,w):
        w0,w1,w2 = w.unbind(dim=-1)
        O = torch.zeros_like(w0)
        wx = torch.stack([torch.stack([O,-w2,w1],dim=-1),
                          torch.stack([w2,O,-w0],dim=-1),
                          torch.stack([-w1,w0,O],dim=-1)],dim=-2)
        return wx

    def taylor_A(self,x,nth=10):
        # Taylor expansion of sin(x)/x
        ans = torch.zeros_like(x)
        denom = 1.
        for i in range(nth+1):
            if i>0: denom *= (2*i)*(2*i+1)
            ans = ans+(-1)**i*x**(2*i)/denom
        return ans
    def taylor_B(self,x,nth=10):
        # Taylor expansion of (1-cos(x))/x**2
        ans = torch.zeros_like(x)
        denom = 1.
        for i in range(nth+1):
            denom *= (2*i+1)*(2*i+2)
            ans = ans+(-1)**i*x**(2*i)/denom
        return ans
    def taylor_C(self,x,nth=10):
        # Taylor expansion of (x-sin(x))/x**3
        ans = torch.zeros_like(x)
        denom = 1.
        for i in range(nth+1):
            denom *= (2*i+2)*(2*i+3)
            ans = ans+(-1)**i*x**(2*i)/denom
        return ans