[LEGACY] Tutorial 1: optimizing a single triangle

Let's begin by using redner to do a simple task. Given a target image that looks like this:

And an initial guess that looks like this:

We want to iteratively refine the guess to find the three vertex positions of a triangle that is closest to the target. The full code of this can be downloaded at https://github.com/BachiLi/redner/blob/master/tutorials/01_optimize_single_triangle.py

We first render a target image using redner, then perturb the three vertices and optimize to match the target.

Redner is expected to be used in Python. The Python interface of redner is defined in the pyredner package:

import pyredner

We will also need pytorch:

import torch

We need to tell redner first whether we are using GPU or not.

pyredner.set_use_gpu(torch.cuda.is_available())

Now we want to setup a 3D scene, represented in PyTorch tensors, then feed it into redner to render an image. First, we setup a camera, by constructing a pyredner.Camera object. redner assumes all the camera variables live in CPU memory, so you should allocate torch tensors in CPU.

cam = pyredner.Camera(position = torch.tensor([0.0, 0.0, -5.0]),
                      look_at = torch.tensor([0.0, 0.0, 0.0]),
                      up = torch.tensor([0.0, 1.0, 0.0]),
                      fov = torch.tensor([45.0]), # in degree
                      clip_near = 1e-2, # needs to > 0
                      resolution = (256, 256),
                      fisheye = False)

Next, we setup the materials for the scene. All materials in the scene are stored in a single Python list. The index of a material in the list is its material id. Our simple scene only has a single grey material with reflectance 0.5. If you are using GPU, make sure to store the reflectance in GPU memory.

mat_grey = pyredner.Material(\
    diffuse_reflectance = \
        torch.tensor([0.5, 0.5, 0.5], device = pyredner.get_device()))
# The material list of the scene
materials = [mat_grey]

Next, we setup the geometry for the scene. 3D objects in redner are called "Shape". All shapes in the scene are stored in a single Python list, the index of a shape in the list is its shape id. Right now, a shape is always a triangle mesh, which has a list of triangle vertices and a list of triangle indices. The vertices are a Nx3 torch float tensor, and the indices are a Mx3 torch integer tensor. Optionally, for each vertex you can specify its UV coordinate for texture mapping, and a normal for Phong interpolation. Each shape also needs to be assigned a material using material id, which is the index of the material in the material array. If you are using GPU, make sure to store all tensors of the shape in GPU memory.

shape_triangle = pyredner.Shape(\
    vertices = torch.tensor([[-1.7, 1.0, 0.0], [1.0, 1.0, 0.0], [-0.5, -1.0, 0.0]],
        device = pyredner.get_device()),
    indices = torch.tensor([[0, 1, 2]], dtype = torch.int32,
        device = pyredner.get_device()),
    uvs = None,
    normals = None,
    material_id = 0)

Merely having a single triangle is not enough for physically-based rendering. We need to have a light source. Here we setup the shape of a quad area light source, similary to the previous triangle.

shape_light = pyredner.Shape(\
    vertices = torch.tensor([[-1.0, -1.0, -7.0],
                             [ 1.0, -1.0, -7.0],
                             [-1.0,  1.0, -7.0],
                             [ 1.0,  1.0, -7.0]], device = pyredner.get_device()),
    indices = torch.tensor([[0, 1, 2],[1, 3, 2]],
        dtype = torch.int32, device = pyredner.get_device()),
    uvs = None,
    normals = None,
    material_id = 0)

The shape list of our scene contains two shapes:

shapes = [shape_triangle, shape_light]

Now we assign some of the shapes in the scene as light sources. All area light sources in the scene are stored in a single Python list. Each area light is attached to a shape using shape id, additionally we need to assign the intensity of the light, which is a length 3 float tensor in CPU.

light = pyredner.AreaLight(shape_id = 1, 
                           intensity = torch.tensor([20.0,20.0,20.0]))
area_lights = [light]

Finally we construct our scene using all the variables we setup previously.

scene = pyredner.Scene(cam, shapes, materials, area_lights)

All PyTorch functions take a flat array of PyTorch tensors as input, therefore we need to serialize the scene into an array. The following function does this. We also specify how many Monte Carlo samples we want to use per pixel and the number of bounces for indirect illumination here (one bounce means only direct illumination).

scene_args = pyredner.RenderFunction.serialize_scene(\
    scene = scene,
    num_samples = 16,
    max_bounces = 1)

Now we render the scene as our target image. To render the scene, we use our custom PyTorch function in pyredner/render_pytorch.py . First setup the alias of the render function

render = pyredner.RenderFunction.apply

Next we call the render function to render. The first argument is the seed for RNG in the renderer.

img = render(0, *scene_args)

This generates a PyTorch tensor with size [width, height, 3]. The output image is in the GPU memory if you are using GPU. Now we save the generated image to disk.

pyredner.imwrite(img.cpu(), 'results/optimize_single_triangle/target.exr')
pyredner.imwrite(img.cpu(), 'results/optimize_single_triangle/target.png')

This is how our target looks like:

Now we read back the target image we just saved, and copy to GPU if necessary:

target = pyredner.imread('results/optimize_single_triangle/target.exr')
if pyredner.get_use_gpu():
    target = target.cuda()

Next we want to produce the initial guess. We do this by perturb the scene.

shape_triangle.vertices = torch.tensor(\
    [[-2.0,1.5,0.3], [0.9,1.2,-0.3], [-0.4,-1.4,0.2]],
    device = pyredner.get_device(),
    requires_grad = True) # Set requires_grad to True since we want to optimize this

We need to serialize the scene again to get the new arguments. We then render our initial guess

scene_args = pyredner.RenderFunction.serialize_scene(\
    scene = scene,
    num_samples = 16,
    max_bounces = 1)
# Render the initial guess
img = render(1, *scene_args)
# Save the image
pyredner.imwrite(img.cpu(), 'results/optimize_single_triangle/init.png')

This is how the initial guess looks like:

Now we want to refine the initial guess using gradient-based optimization. We use PyTorch's optimizer to do this.

optimizer = torch.optim.Adam([shape_triangle.vertices], lr=5e-2)

We run 200 Adam iterations

for t in range(200):
    print('iteration:', t)
    optimizer.zero_grad()
    # Forward pass: render the image
    scene_args = pyredner.RenderFunction.serialize_scene(\
        scene = scene,
        num_samples = 4, # We use less samples in the Adam loop.
        max_bounces = 1)
    # Important to use a different seed every iteration, otherwise the result
    # would be biased.
    img = render(t+1, *scene_args)
    # Compute the loss function. Here it is L2.
    loss = (img - target).pow(2).sum()

    # Backpropagate the gradients.
    loss.backward()

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

After 200 iterations, our image becomes quite similar to the target:

We can generate a video visualizing the iterations:

And this concludes our first tutorial!