Hugues Hoppe    Aug 2022.

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The notebook resampler_notebook.ipynb hosts the source code for the resampler library in PyPI, interleaved with documentation, usage examples, unit tests, and signal-processing experiments.

Overview

The resampler library enables fast differentiable resizing and warping of arbitrary grids. It supports:

• grids of any dimension (e.g., 1D, 2D images, 3D video, 4D batches of videos), containing

• samples of any shape (e.g., scalars, colors, motion vectors, Jacobian matrices) and

• any numeric type (integer, floating, and complex);

• either dual ("half-integer") or primal grid-type for each dimension;

• many boundary rules, specified per dimension, extensible via subclassing;

• an extensible set of filter kernels, selectable per dimension;

• optional gamma transfer functions for correct linear-space filtering;

• prefiltering for accurate antialiasing when downsampling;

• processing within several array libraries (numpy, tensorflow, and torch);

• efficient backpropagation of gradients for both tensorflow and torch;

• easy installation, with no native code, yet

• faster resizing than C++ implementations in tf.image, torch.nn, and torchvision.

A key strategy is to leverage existing sparse matrix representations and operations.

Example usage

!pip install -q mediapy resampler
import mediapy as media
import numpy as np
import resampler

array = np.random.default_rng(1).random((4, 6, 3))  # 4x6 RGB image.
upsampled = resampler.resize(array, (128, 192))  # To 128x192 resolution.
media.show_images({'4x6': array, '128x192': upsampled}, height=128)

image = media.read_image('https://github.com/hhoppe/data/raw/main/image.png')
downsampled = resampler.resize(image, (32, 32))
media.show_images({'128x128': image, '32x32': downsampled}, height=128)

import matplotlib.pyplot as plt

array = [3.0, 5.0, 8.0, 7.0]  # 4 source samples in 1D.
new_dual = resampler.resize(array, (32,))  # (default gridtype='dual') 8x resolution.
new_primal = resampler.resize(array, (25,), gridtype='primal')  # 8x resolution.
_, axs = plt.subplots(1, 2, figsize=(7, 1.5))
axs[0].set_title('gridtype dual')
axs[0].plot((np.arange(len(array)) + 0.5) / len(array), array, 'o')
axs[0].plot((np.arange(len(new_dual)) + 0.5) / len(new_dual), new_dual, '.')
axs[1].set_title('gridtype primal')
axs[1].plot(np.arange(len(array)) / (len(array) - 1), array, 'o')
axs[1].plot(np.arange(len(new_primal)) / (len(new_primal) - 1), new_primal, '.')
plt.show()

batch_size = 4
batch_of_images = media.moving_circle((16, 16), batch_size)
upsampled = resampler.resize(batch_of_images, (batch_size, 64, 64))
spacer = np.ones((64, 16, 3))
media.show_images([*batch_of_images, spacer, *upsampled], border=True, height=64)

media.show_videos({'original': batch_of_images, 'upsampled': upsampled}, fps=1)

original

Most examples above use the default resize() settings:

• gridtype='dual' for both source and destination arrays,
• boundary='auto' which uses 'reflect' for upsampling and 'clamp' for downsampling,
• filter='lanczos3' (a Lanczos kernel with radius 3),
• gamma=None which by default uses the 'power2' transfer function for the uint8 image in the second example,
• scale=1.0, translate=0.0 (no domain transformation),
• default precision and output dtype.

Advanced usage:

Map an image to a wider grid using custom scale and translate vectors, with horizontal 'reflect' and vertical 'natural' boundary rules, providing a constant value for the exterior, using different filters (Lanczos and O-MOMS) in the two dimensions, disabling gamma correction, performing computations in double-precision, and returning an output array in single-precision:

new = resampler.resize(
    image, (128, 512), boundary=('natural', 'reflect'), cval=(0.2, 0.7, 0.3),
    filter=('lanczos3', 'omoms5'), gamma='identity', scale=(0.8, 0.25),
    translate=(0.1, 0.35), precision='float64', dtype='float32')
media.show_images({'image': image, 'new': new})

Warp an image by transforming it using polar coordinates:

shape = image.shape[:2]
yx = ((np.indices(shape).T + 0.5) / shape - 0.5).T  # [-0.5, 0.5]^2
radius, angle = np.linalg.norm(yx, axis=0), np.arctan2(*yx)
angle += (0.8 - radius).clip(0, 1) * 2.0 - 0.6
coords = np.dstack((np.sin(angle) * radius, np.cos(angle) * radius)) + 0.5
resampled = resampler.resample(image, coords, boundary='constant')
media.show_images({'image': image, 'resampled': resampled})

Limitations:

• Filters are assumed to be separable. For rotation equivariance (e.g., bandlimit the signal uniformly in all directions), it would be nice to support the (non-separable) 2D rotationally symmetric sombrero function $f(\textbf{x}) = \text{jinc}(|\textbf{x}|)$, where $\text{jinc}(r) = 2J_1(\pi r)/(\pi r)$. (The Fourier transform of a circle involves the first-order Bessel function of the first kind.)