SplineOps

Continuous spline models for precise interpolation, antialiased resizing, and derivatives.

From samples to continuous models

01 · Reconstruct

Build a continuous cubic spline from discrete samples.

Spline Interpolation

02 · Resample

Resize with antialiasing, then apply an affine rotation.

Resize

03 · Differentiate

Measure local changes with spline-derived gradients.

Differentials

One synthetic 2-D field, shown as height maps from actual SplineOps outputs. White dots mark input samples; gradient magnitude uses its own display scale.

SplineOps turns samples on regular grids into continuous spline models. Evaluate between samples, resize with projection-based antialiasing, apply geometric transforms, and compute derivatives in N dimensions. Explicit coordinate and boundary conventions make results reproducible; reusable plans accelerate repeated resizing with the same geometry.

Start here

import numpy as np
from splineops import resize

volume = np.random.default_rng(0).random((64, 192, 192), dtype=np.float32)
coarse = resize(
    volume,
    output_size=(32, 96, 96),
    method="cubic-antialiasing",
)

The antialiasing methods project the input spline onto a coarser spline space instead of treating downsampling as interpolation alone. Continue with the Five-minute quickstart, then use the Volume downsampling tutorial for a batched 3-D workflow.

Choose SplineOps when

• continuous-valued 2-D or 3-D NumPy data must be downsampled;

• coordinate, boundary, and output-shape semantics must be explicit;

• aliasing matters; or

• many arrays share one resize geometry.

Choose another tool when differentiable GPU execution or automatic physical-space image metadata is required. For ordinary display-image scaling, OpenCV or Pillow may be simpler. Categorical labels normally require nearest-neighbour rather than spline-projection semantics.

Release status

SplineOps 2.3 public maturity

Module	Status	Public position
Resize and ResizePlan	Stable	Native N-D interpolation and projection antialiasing with a Python reference path.
TensorSpline	Stable CPU	Continuous tensor-product models evaluated at arbitrary coordinates.
Affine, differentials, smoothing, regression, and multiscale	Stable CPU	Documented operators with independent numerical references and cross-platform tests. See API stability and support for exact support.

SplineOps does not claim to be the fastest generic 2-D resizer. Its strongest position is continuous spline models, N-D projection antialiasing, explicit coordinate conventions, and reusable fixed-geometry execution. See Performance evidence for measured wins, losses, and limitations.

The current flagship is the 3-D microvessel quality-at-speed validation: on 18 held-out expert-labelled 3-D microscopy patches, SplineOps passed a predeclared narrow quality-and-speed superiority rule against named SciPy, scikit-image, and PyTorch pipelines. It is a preprocessing result, not segmentation or universal resampling superiority.

Explore the package

Modules

Choose interpolation, geometry, derivatives, smoothing, or multiscale tools.

Modules

Examples

Browse the executable gallery by module or complete workflow.

Examples

Benchmarks

Compare accuracy, speed, and memory on reproducible scientific workloads.

Benchmarks

Research lineage

SplineOps modernizes spline methods developed across the Biomedical Imaging Group at EPFL and its collaborators. Method citations, implementation history, and source provenance are recorded in Method and source provenance.

These two artworks from the original SplineOps homepage celebrate those roots.

Wavelet Bird 1999

SIAM Cover Page 1999

Explore the Biomedical Imaging Group’s art gallery for the original collection.