Find homography Jacobian return sometimes nan values

[edgarriba]

Describe the bug

While using the kornia.geometry.find_homography_dlt function, in some scenarios the Jacobian computed by the autograd return nan values.

Reproduction steps

import torch
import kornia as K

"""Code example to verify the DLT Jacobian for the homographies.

|x2|    |h1 h2 h3|   |x1|
|y2| =  |h4 h5 h6| @ |y1|
|1 |    |h7 h8 h9|   |1 |

DLT => x' = H @ x = 0

"""


def f(x):
    x1, x2 = x.unbind(-1)
    # TODO: this returns jacobian with nans
    return K.geometry.find_homography_dlt(x1, x2)
    # NOTE: this works as expected
    # return K.geometry.get_perspective_transform(x1, x2)


# define some points in the corners with a scale factor of 100
x1 = torch.tensor([[[0., 0.], [0., 1.], [1., 0.], [1., 1.]]])
x2 = torch.tensor([[[0., 0.], [0., 100.], [100., 0.], [100., 100.]]])

x = torch.stack((x1, x2), dim=-1)
# NOTE: this guy does not produce nan values
# x = torch.rand_like(x)

H = f(x)  # compute the homography between the set of points
print(H)
print(H.shape)

J = torch.autograd.functional.jacobian(f, x)
print(J)
print(J.shape)

Expected behavior

We should expect the jacobian J to always contain valid values.

Environment

PyTorch version: 1.6.0
Is debug build: False
CUDA used to build PyTorch: 10.2
ROCM used to build PyTorch: N/A

OS: Ubuntu 20.04.2 LTS (x86_64)
GCC version: (Ubuntu 9.3.0-17ubuntu1~20.04) 9.3.0
Clang version: Could not collect
CMake version: version 3.20.5
Libc version: glibc-2.17

Python version: 3.7.11 (default, Jul 27 2021, 14:32:16)  [GCC 7.5.0] (64-bit runtime)
Python platform: Linux-5.11.0-37-generic-x86_64-with-debian-bullseye-sid
Is CUDA available: True
CUDA runtime version: Could not collect
GPU models and configuration: GPU 0: NVIDIA GeForce GTX 1650 with Max-Q Design
Nvidia driver version: 470.63.01
cuDNN version: Could not collect
HIP runtime version: N/A
MIOpen runtime version: N/A

Versions of relevant libraries:
[pip3] mypy==0.910
[pip3] mypy-extensions==0.4.3
[pip3] numpy==1.21.2
[pip3] pytest-mypy==0.8.1
[pip3] torch==1.9.0
[pip3] torchmetrics==0.5.1
[pip3] torchvision==0.7.0
[conda] blas                      1.0                         mkl  
[conda] cudatoolkit               10.2.89              hfd86e86_1  
[conda] ffmpeg                    4.3                  hf484d3e_0    pytorch
[conda] mkl                       2021.3.0           h06a4308_520  
[conda] mkl-service               2.4.0            py37h7f8727e_0  
[conda] mkl_fft                   1.3.0            py37h42c9631_2  
[conda] mkl_random                1.2.2            py37h51133e4_0  
[conda] mypy                      0.910                    pypi_0    pypi
[conda] mypy-extensions           0.4.3                    pypi_0    pypi
[conda] numpy                     1.21.2                   pypi_0    pypi
[conda] numpy-base                1.20.3           py37h74d4b33_0  
[conda] pytest-mypy               0.8.1                    pypi_0    pypi
[conda] pytorch                   1.6.0           py3.7_cuda10.2.89_cudnn7.6.5_0    pytorch
[conda] torch                     1.9.0                    pypi_0    pypi
[conda] torchmetrics              0.5.1                    pypi_0    pypi
[conda] torchvision               0.7.0                py37_cu102    pytorch

Additional context

Seems only to happen when zeros come to the game for some points.