bilateral_solver.py

from scipy.sparse import diags
from scipy.sparse.linalg import cg
from scipy.sparse import csr_matrix
import numpy as np
from skimage.io import imread
from scipy import ndimage
import torch
import PIL.Image as Image
import os
from argparse import ArgumentParser, Namespace
from typing import Dict, Union
from collections import defaultdict
import yaml
import ujson as json
import numpy as np
import torch
import torch.nn.functional as F
from PIL import Image


RGB_TO_YUV = np.array([
    [0.299, 0.587, 0.114],
    [-0.168736, -0.331264, 0.5],
    [0.5, -0.418688, -0.081312]])
YUV_TO_RGB = np.array([
    [1.0, 0.0, 1.402],
    [1.0, -0.34414, -0.71414],
    [1.0, 1.772, 0.0]])
YUV_OFFSET = np.array([0, 128.0, 128.0]).reshape(1, 1, -1)
MAX_VAL = 255.0


def rgb2yuv(im):
    return np.tensordot(im, RGB_TO_YUV, ([2], [1])) + YUV_OFFSET


def yuv2rgb(im):
    return np.tensordot(im.astype(float) - YUV_OFFSET, YUV_TO_RGB, ([2], [1]))


def get_valid_idx(valid, candidates):
    """Find which values are present in a list and where they are located"""
    locs = np.searchsorted(valid, candidates)
    # Handle edge case where the candidate is larger than all valid values
    locs = np.clip(locs, 0, len(valid) - 1)
    # Identify which values are actually present
    valid_idx = np.flatnonzero(valid[locs] == candidates)
    locs = locs[valid_idx]
    return valid_idx, locs


class BilateralGrid(object):
    def __init__(self, im, sigma_spatial=32, sigma_luma=8, sigma_chroma=8):
        im_yuv = rgb2yuv(im)
        # Compute 5-dimensional XYLUV bilateral-space coordinates
        Iy, Ix = np.mgrid[:im.shape[0], :im.shape[1]]
        x_coords = (Ix / sigma_spatial).astype(int)
        y_coords = (Iy / sigma_spatial).astype(int)
        luma_coords = (im_yuv[..., 0] / sigma_luma).astype(int)
        chroma_coords = (im_yuv[..., 1:] / sigma_chroma).astype(int)
        coords = np.dstack((x_coords, y_coords, luma_coords, chroma_coords))
        coords_flat = coords.reshape(-1, coords.shape[-1])
        self.npixels, self.dim = coords_flat.shape
        # Hacky "hash vector" for coordinates,
        # Requires all scaled coordinates be < MAX_VAL
        self.hash_vec = (MAX_VAL ** np.arange(self.dim))
        # Construct S and B matrix
        self._compute_factorization(coords_flat)

    def _compute_factorization(self, coords_flat):
        # Hash each coordinate in grid to a unique value
        hashed_coords = self._hash_coords(coords_flat)
        unique_hashes, unique_idx, idx = \
            np.unique(hashed_coords, return_index=True, return_inverse=True)
        # Identify unique set of vertices
        unique_coords = coords_flat[unique_idx]
        self.nvertices = len(unique_coords)
        # Construct sparse splat matrix that maps from pixels to vertices
        self.S = csr_matrix((np.ones(self.npixels), (idx, np.arange(self.npixels))))
        # Construct sparse blur matrices.
        # Note that these represent [1 0 1] blurs, excluding the central element
        self.blurs = []
        for d in range(self.dim):
            blur = 0.0
            for offset in (-1, 1):
                offset_vec = np.zeros((1, self.dim))
                offset_vec[:, d] = offset
                neighbor_hash = self._hash_coords(unique_coords + offset_vec)
                valid_coord, idx = get_valid_idx(unique_hashes, neighbor_hash)
                blur = blur + csr_matrix((np.ones((len(valid_coord),)),
                                          (valid_coord, idx)),
                                         shape=(self.nvertices, self.nvertices))
            self.blurs.append(blur)

    def _hash_coords(self, coord):
        """Hacky function to turn a coordinate into a unique value"""
        return np.dot(coord.reshape(-1, self.dim), self.hash_vec)

    def splat(self, x):
        return self.S.dot(x)

    def slice(self, y):
        return self.S.T.dot(y)

    def blur(self, x):
        """Blur a bilateral-space vector with a 1 2 1 kernel in each dimension"""
        assert x.shape[0] == self.nvertices
        out = 2 * self.dim * x
        for blur in self.blurs:
            out = out + blur.dot(x)
        return out

    def filter(self, x):
        """Apply bilateral filter to an input x"""
        return self.slice(self.blur(self.splat(x))) / \
               self.slice(self.blur(self.splat(np.ones_like(x))))


def bistochastize(grid, maxiter=10):
    """Compute diagonal matrices to bistochastize a bilateral grid"""
    m = grid.splat(np.ones(grid.npixels))
    n = np.ones(grid.nvertices)
    for i in range(maxiter):
        n = np.sqrt(n * m / grid.blur(n))
    # Correct m to satisfy the assumption of bistochastization regardless
    # of how many iterations have been run.
    m = n * grid.blur(n)
    Dm = diags(m, 0)
    Dn = diags(n, 0)
    return Dn, Dm


class BilateralSolver(object):
    def __init__(self, grid, params):
        self.grid = grid
        self.params = params
        self.Dn, self.Dm = bistochastize(grid)

    def solve(self, x, w):
        # Check that w is a vector or a nx1 matrix
        if w.ndim == 2:
            assert (w.shape[1] == 1)
        elif w.dim == 1:
            w = w.reshape(w.shape[0], 1)
        A_smooth = (self.Dm - self.Dn.dot(self.grid.blur(self.Dn)))
        w_splat = self.grid.splat(w)
        A_data = diags(w_splat[:, 0], 0)
        A = self.params["lam"] * A_smooth + A_data
        xw = x * w
        b = self.grid.splat(xw)
        # Use simple Jacobi preconditioner
        A_diag = np.maximum(A.diagonal(), self.params["A_diag_min"])
        M = diags(1 / A_diag, 0)
        # Flat initialization
        y0 = self.grid.splat(xw) / w_splat
        yhat = np.empty_like(y0)
        for d in range(x.shape[-1]):
            yhat[..., d], info = cg(A, b[..., d], x0=y0[..., d], M=M, maxiter=self.params["cg_maxiter"],
                                    tol=self.params["cg_tol"])
        xhat = self.grid.slice(yhat)
        return xhat


def bilateral_solver_output(
        img: Image.Image,
        target: np.ndarray,
        sigma_spatial=16,
        sigma_luma=16,
        sigma_chroma=8
):
    reference = np.array(img)
    h, w = target.shape
    confidence = np.ones((h, w)) * 0.999

    grid_params = {
        'sigma_luma': sigma_luma,  # Brightness bandwidth
        'sigma_chroma': sigma_chroma,  # Color bandwidth
        'sigma_spatial': sigma_spatial  # Spatial bandwidth
    }

    bs_params = {
        'lam': 256,  # The strength of the smoothness parameter
        'A_diag_min': 1e-5,  # Clamp the diagonal of the A diagonal in the Jacobi preconditioner.
        'cg_tol': 1e-5,  # The tolerance on the convergence in PCG
        'cg_maxiter': 25  # The number of PCG iterations
    }

    grid = BilateralGrid(reference, **grid_params)

    t = target.reshape(-1, 1).astype(np.double)
    c = confidence.reshape(-1, 1).astype(np.double)

    ## output solver, which is a soft value
    output_solver = BilateralSolver(grid, bs_params).solve(t, c).reshape((h, w))

    binary_solver = ndimage.binary_fill_holes(output_solver > 0.5)
    labeled, nr_objects = ndimage.label(binary_solver)

    nb_pixel = [np.sum(labeled == i) for i in range(nr_objects + 1)]
    pixel_order = np.argsort(nb_pixel)
    try:
        binary_solver = labeled == pixel_order[-2]
    except:
        binary_solver = np.ones((h, w), dtype=bool)

    return output_solver, binary_solver