[LEGACY] Tutorial 5: coarse to fine estimation

This time we will learn the following through a Cornell box example

• Loading from a Mitsuba scene file
• Global illumination and glossy/specular materials
• Coarse to fine estimation with a Gaussian pyramid loss
• Incorporate box constraints in your optimizer

The full source code is here: https://github.com/BachiLi/redner/blob/master/tutorials/05_coarse_to_fine_estimation.py

In addition to Wavefront obj file, redner also supports loading from a Mitsuba scene file. Currently we only support a limited amount of features. In particular we only support two kinds of materials: diffuse and roughplastic. Note that the "alpha" values in roughplastic is the square root of the roughness. See cbox.xml for how a Mitsuba scene file should look like. We can load a scene using pyredner.load_mitsuba() utility, and render it as usual. This will be our target this time.

scene = pyredner.load_mitsuba('cbox/cbox.xml')
scene_args = pyredner.RenderFunction.serialize_scene(\
    scene = scene,
    num_samples = 512,
    max_bounces = 5) # Set max_bounces = 5 for global illumination
render = pyredner.RenderFunction.apply
img = render(0, *scene_args)

The target looks like the following:

(For graphics people: redner by default disables caustics light path because their derivatives are too noisy. We use an approach similar to the Arnold renderer by always taking the maximum roughness along the light path.)

Now let's generate an initial guess by perturbing the reference. Let's set all the diffuse color to gray by manipulating material.diffuse_reflectance. We also store all the material variables to optimize in a list.

material_vars = []
for mi, m in enumerate(scene.materials):
    var = torch.tensor([0.5, 0.5, 0.5],
                       device = pyredner.get_device(),
                       requires_grad = True)
    material_vars.append(var)
    m.diffuse_reflectance = pyredner.Texture(var)

And let's also slightly perturb the camera up vector and field of view a bit, and store the variables into a list called cam vars.

up = torch.tensor([0.2, 0.8, -0.2], requires_grad = True)
fov = torch.tensor([41.0], requires_grad = True)
cam_vars = [up, fov]
scene.camera = pyredner.Camera(\
    position = scene.camera.position,
    look_at = scene.camera.look_at,
    up = up,
    fov = fov,
    clip_near = scene.camera.clip_near,
    resolution = scene.camera.resolution)

The initial guess looks like the following:

Now we optimize for the parameters. We run a coarse-to-fine estimation here to prevent being trapped in local minimum. The final resolution is 256x256, but we will start from an 64x64 image. We can also tweak the number of iterations, samples per pixel, number of bounces, learning rate for each resolution.

optimizer = torch.optim.Adam(material_vars + cam_vars, lr=5e-3)
res = [64, 256]
iters = [400, 200]
spp = [16, 4]
bounces = [5, 5]
lrs = [5e-3, 1e-3]

The optimization loop will be two-level. The first level decides the resolution, number of iterations for the second level, etc, and generates a target image for the second level by properly downsample the target.

iter_count = 0
for ri, r in enumerate(res):
    scene.camera.resolution = (r, r)
    # Downsample the target to match our current resolution
    resampled_target = target.cpu().numpy()
    if r != 256:
        resampled_target = scipy.ndimage.interpolation.zoom(\
            resampled_target, (r/256.0, r/256.0, 1.0),
            order=1)
    resampled_target = torch.from_numpy(resampled_target)
    if pyredner.get_use_gpu():
        resampled_target = resampled_target.cuda()

    for param_group in optimizer.param_groups:
        param_group['lr'] = lrs[ri]

The second level loop looks similar to previous tutorials, with two exceptions: First, we use a Gaussian pyramid loss by using PyTorch's Conv2d function and average pooling. Second, since we do not allow negative reflectance, we clamp the reflectance value between 1e-5 and 1 after a gradient descent step.

    for t in range(iters[ri]):
        print('resolution:', r, ', iteration:', iter_count)
        optimizer.zero_grad()
        # Forward pass: serialize the scene and render the image
        # Need to redefine the camera
        scene.camera = pyredner.Camera(\
            position = scene.camera.position,
            look_at = scene.camera.look_at,
            up = up,
            fov = fov,
            clip_near = scene.camera.clip_near,
            resolution = scene.camera.resolution)
        scene_args = pyredner.RenderFunction.serialize_scene(\
            scene = scene,
            num_samples = spp[ri],
            max_bounces = bounces[ri])
        # Important to use a different seed every iteration, otherwise the result
        # would be biased.
        img = render(iter_count+1, *scene_args)
        # Save the intermediate render.
        img_np = img.data.cpu().numpy()
        img_np = scipy.ndimage.interpolation.zoom(\
            img_np, (256.0/r, 256.0/r, 1.0),
            order=1)
        pyredner.imwrite(torch.from_numpy(img_np),
            'results/coarse_to_fine_estimation/iter_{}.png'.format(iter_count))
        iter_count += 1

        # Compute the loss function. Here we use a Gaussian pyramid loss function
        # We also clamp the difference between -1 and 1 to prevent
        # light source from being dominating the loss function
        diff = (img - resampled_target).clamp(-1.0, 1.0)

        # Now we convolve diff with Gaussian filter and downsample.
        # We use PyTorch's conv2d function and AvgPool2d to achieve this.
        # We need to first define a Gaussian kernel:
        dirac = np.zeros((7,7), dtype = np.float32)
        dirac[3,3] = 1.0
        f = np.zeros([3, 3, 7, 7], dtype = np.float32)
        gf = scipy.ndimage.filters.gaussian_filter(dirac, 1.0)
        f[0, 0, :, :] = gf
        f[1, 1, :, :] = gf
        f[2, 2, :, :] = gf
        f = torch.from_numpy(f)
        m = torch.nn.AvgPool2d(2)
        if pyredner.get_use_gpu():
            f = f.cuda()

        diff_0 = diff.view(1, r, r, 3).permute(0, 3, 2, 1)
        # Convolve then downsample
        diff_1 = m(torch.nn.functional.conv2d(diff_0, f, padding=3))
        diff_2 = m(torch.nn.functional.conv2d(diff_1, f, padding=3))
        diff_3 = m(torch.nn.functional.conv2d(diff_2, f, padding=3))
        diff_4 = m(torch.nn.functional.conv2d(diff_3, f, padding=3))
        loss = diff_0.pow(2).sum() / (r * r) + \
               diff_1.pow(2).sum() / ((r/2.)*(r/2.)) + \
               diff_2.pow(2).sum() / ((r/4.)*(r/4.)) + \
               diff_3.pow(2).sum() / ((r/8.)*(r/8.)) + \
               diff_4.pow(2).sum() / ((r/16.)*(r/16.))
        print('loss:', loss.item())

        # Backpropagate the gradients.
        loss.backward()

        # Take a gradient descent step.
        optimizer.step()

        # Important: the material parameters has hard constraints: the
        # reflectance and roughness cannot be negative. We enforce them here
        # by projecting the values to the boundaries.
        for var in material_vars:
            var.data = var.data.clamp(1e-5, 1.0)

The final optimized image looks like the following:

Here is the optimization video. Notice that at the beginning the images are blurry, this is because we render and optimize the images at 64x64.