- readme

README.md

@@ -1,3 +1,373 @@
-# Image registration
+# image-registration
+
 Find an ND affine transformation that registers an ND test image to a fixed image. Then apply this transformation to
 other images.
+
+`image-registration` is a pure-Rust, dependency-light implementation of intensity-based image registration in the spirit
+of [SimpleElastix]([https://elastix.lumc.nl](https://simpleelastix.github.io/)). It finds an affine (rigid + scale + shear + translation) transform
+that aligns a *moving* image to a *fixed* image by maximizing
+the [Mattes mutual-information](https://doi.org/10.1109/TMI.2003.809072) metric with a B-spline Parzen
+window, using a multi-resolution Gaussian image pyramid and a hybrid ASGD + L-BFGS optimization strategy.
+
+Everything operates on [`ndarray`](https://docs.rs/ndarray) arrays, works in arbitrary dimensions (1D, 2D, 3D, …), and
+is parallelized with [rayon](https://docs.rs/rayon).
+
+## Features
+
+- **Affine registration** in any number of dimensions — rotation, scale, shear, and translation parameters
+  (`Transform::register`).
+- **B-spline interpolation** of order up to 5 (linear, cubic, …) for resampling/warping images under a transform
+  (`interpolate`, `interpolate_par`).
+- **Mattes mutual-information metric** with B-spline joint-histogram Parzen estimation, analytic gradients, and
+  configurable sampling (fixed, fixed-at-points, or random) and binning.
+- **Multi-resolution registration** with a fixed-smoothing image pyramid with Gaussian smoothing.
+- **Two optimizers**: L-BFGS (default, for smooth/consistent gradients) and ASGD (adaptive stochastic gradient descent,
+  robust to noisy gradients).
+- **Flexible parameter control**: fix any subset of transform parameters during registration (`FixedMu`).
+- **Transform algebra**: composition, inverse, matrix forms, coordinate transforms, serialization to/from YAML.
+- **Parallel** interpolation and metric evaluation via rayon.
+- Pure Rust — no BLAS/LAPACK or system libraries required (matrix inversion is implemented internally with LU
+  factorization).
+
+## Quick start
+
+Register a moving image to a fixed image and obtain the affine transform:
+
+```rust
+use image_registration::error::Error;
+use image_registration::transform::Transform;
+use ndarray::Array2;
+
+fn register(fixed: &Array2<f64>, moving: &Array2<f64>) -> Result<Transform, Error> {
+    // All 6 parameters of the 2D affine transform are free (None = optimize).
+    // steps=None uses the default multi-resolution pyramid; initial_guess=None
+    // initializes by aligning the geometric centers of the two images.
+    Transform::<ndarray::Ix2>::register(
+        fixed.view(),
+        moving.view(),
+        vec![None; 6],
+        None,
+        None,
+    )
+}
+```
+
+The returned `Transform` maps coordinates from the *fixed* image to the *moving* image, i.e.
+`moving(transform_point(x)) ≈ fixed(x)`. To warp the moving image into the fixed image's frame:
+
+```rust
+let transform = register(&fixed, &moving)?;
+let registered = transform.interpolate_par::<3, _, _>(moving.view())?; // cubic B-spline, parallel
+```
+
+## Concepts
+
+### Parameterization of an affine transform
+
+An ND affine transform is stored as a flattened `N×N` linear part plus `N` translation parameters, for `N*N + N` values
+in total:
+
+- 1D: `[scale, translation]`
+- 2D: `[m00, m01, m10, m11, tx, ty]` (row-major linear part, then translation)
+- 3D: `[m00, m01, m02, m10, m11, m12, m20, m21, m22, tx, ty, tz]`
+
+The transformation is applied about a center saved in ```Transform```:
+
+```text
+v = A·(p − c) + t + c
+```
+
+where `A` is the linear part, `t` the translation, `c` the center of the transformation, and `p` the input coordinates.
+`Transform::new(parameters, shape)` sets the center to `(shape − 1) / 2` automatically; `Transform::new_with_center`
+lets you override it.
+
+### Registration convention
+
+The registration minimizes the negative Mattes mutual information between the fixed image and the warped moving image.
+For a moving image that was created by applying transform `q` to a fixed image, registration recovers `q⁻¹` (the
+transform that maps fixed coordinates back onto the moving image).
+
+## Examples
+
+### 1. Build transforms and transform coordinates
+
+```rust
+use image_registration::error::Error;
+use image_registration::transform::Transform;
+use ndarray::Ix2;
+
+fn main() -> Result<(), Error> {
+    // Rotation of 45° about the image center of a 200×200 image
+    let rot = Transform::<Ix2>::from_rotation(std::f64::consts::FRAC_PI_4, &[99.5, 99.5]);
+
+    // Compose: translate, then scale, then rotate
+    let t = rot.with_scaling(&[0.9, 1.1]).with_translation(&[10.0, -5.0]);
+
+    // Transform a single point (the center is subtracted and re-added)
+    let p = t.transform_point(&[200, 300]);
+
+    // Transform many points at once (rows of an N×2 array)
+    let points = ndarray::array![[0.0, 0.0], [199.0, 199.0]];
+    let pts = t.transform_points(points.view())?;
+
+    // Matrix form (3×3 homogeneous) and exact inverse
+    let m = t.matrix();
+    let inv = t.inverse()?;
+    assert!(m.dot(&inv.matrix()).iter().all(|x| (x - 1.0).abs() < 1e-9));
+    Ok(())
+}
+```
+
+### 2. Warp an image (resampling)
+
+Interpolate an image under a transform, producing an output image of the same shape. Pixels whose transformed
+coordinates fall outside the input image are set to zero.
+
+```rust
+use image_registration::error::Error;
+use image_registration::transform::Transform;
+
+fn main() -> Result<(), Error> {
+    // `image` is an Array2<f64> (200×150, say)
+    let image = ndarray::Array2::<f64>::zeros((200, 150));
+    let transform = Transform::<ndarray::Ix2>::from_rotation(0.3, &[99.5, 74.5]);
+
+    // Order-1 (linear) interpolation, single-threaded
+    let warped_linear = transform.interpolate::<1, _, _>(image.view())?;
+
+    // Order-3 (cubic) B-spline interpolation, parallel
+    let warped_cubic = transform.interpolate_par::<3, _, _>(image.view())?;
+    Ok(())
+}
+```
+
+### 3. Full affine registration with a known ground truth
+
+Create a moving image by applying a known transform to a fixed image, register, and check that the recovered transform
+matches the inverse of the ground-truth transform (adapted from the crate's `register2_random_affine` test):
+
+```rust
+use image_registration::error::Error;
+use image_registration::julia_image;
+use image_registration::transform::Transform;
+use ndarray::Ix2;
+
+fn main() -> Result<(), Error> {
+    // Fixed image (a Julia fractal, included for testing)
+    let shape = [200, 200];
+    let center = [99.5, 99.5];
+    let fixed = julia_image(&shape, &[1.0, 0.0, 0.0, 1.0, 0.0, 0.0], &center, &[-0.8, 0.156])
+        .mapv(|i| i as f64);
+
+    // Ground-truth affine: 10° rotation, 5% scale change, (12, -8) px translation
+    let theta = 10.0f64.to_radians();
+    let (s, c) = theta.sin_cos();
+    let params = vec![c * 1.05, -s, s, c * 0.95, 12.0, -8.0];
+    let ground_truth =
+        Transform::<Ix2>::new_with_center(params.clone(), center.to_vec(), shape.to_vec());
+
+    // Moving image = ground truth applied to the fixed image
+    let moving = ground_truth.interpolate::<3, _, _>(fixed.view())?;
+
+    // Register (all 6 parameters free, default steps)
+    let t = Transform::<Ix2>::register(fixed.view(), moving.view(), vec![None; 6], None, None)?;
+
+    // The registered transform should equal the inverse of the ground truth
+    let q_inv = ground_truth.inverse()?.parameters;
+    let sse: f64 = t
+        .parameters
+        .iter()
+        .zip(q_inv.iter())
+        .map(|(a, b)| (a - b).powi(2))
+        .sum();
+    assert!(sse < 1.0);
+    Ok(())
+}
+```
+
+### 4. Registration with inspection of every optimization step
+
+```rust
+use image_registration::error::Error;
+use image_registration::transform::Transform;
+
+fn main() -> Result<(), Error> {
+    let (t, steps) = Transform::<ndarray::Ix2>::register_debug(
+        fixed.view(), moving.view(), vec![None; 6], None, None,
+    )?;
+
+    for step in steps {
+        println!(
+            "sigma={:?} n_bins={} optimizer_iters={} converged={} -> {:?}",
+            step.sigma_fixed, step.n_bins, step.iterations, step.converged, step.optimal_point
+        );
+    }
+    Ok(())
+}
+```
+
+### 5. Custom registration steps (multi-resolution pyramid)
+
+`RegistrationStep` gives you full control over the smoothing, sampling, binning, and optimizer at each level. The
+following uses two levels: a coarse level with strong Gaussian smoothing and the robust ASGD optimizer, then a fine
+level with L-BFGS for accuracy.
+
+```rust
+use image_registration::error::Error;
+use image_registration::metric::{SamplingArg, Sigma};
+use image_registration::register::{Optimizer, Registration, RegistrationStep};
+
+fn main() -> Result<(), Error> {
+    let mut coarse = RegistrationStep::new(
+        Sigma::Absolute(vec![4.0, 4.0]), // Gaussian sigma per dimension
+        SamplingArg::Fixed(3000),        // 3000 sampled points (cached)
+        32,                              // histogram bins
+        1e-4,                            // tolerance
+        0.05,                            // edge fraction
+        512,                             // max iterations
+        1.0,                             // learning rate
+    );
+    coarse.optimizer = Optimizer::ASGD; // robust to noisy gradients
+
+    let mut fine = RegistrationStep::new(
+        Sigma::Absolute(vec![0.5, 0.5]),
+        SamplingArg::Fixed(3000),
+        32,
+        1e-8,
+        0.05,
+        2048,
+        1.0,
+    ); // optimizer stays LBFGS (the default)
+
+    let mut reg = Registration::new(vec![None; 6]);
+    reg.set_steps(vec![coarse, fine]);
+    let t = reg.register(fixed.view(), moving.view())?;
+    Ok(())
+}
+```
+
+> **Tip:** `RegistrationStep::default_steps(ndim, n)` returns a sensible default pyramid: a 5-level schedule that starts
+> with ASGD on heavily smoothed images and finishes with L-BFGS on the unsmoothed image.
+
+### 6. Fix (pin) some parameters during registration
+
+Pass a `Vec<Option<f64>>` as `fixed_mu`: `None` optimizes a parameter, `Some(v)` keeps it fixed at `v`. For example,
+register for translation only:
+
+```rust
+use image_registration::error::Error;
+use image_registration::transform::Transform;
+
+fn main() -> Result<(), Error> {
+    // 2D: fix the linear part to identity, optimize tx and ty
+    let t = Transform::<ndarray::Ix2>::register(
+        fixed.view(),
+        moving.view(),
+        vec![Some(1.0), Some(0.0), Some(0.0), Some(1.0), None, None],
+        None,
+        None,
+    )?;
+    Ok(())
+}
+```
+
+For the common "translation only" case there is also the convenience method
+`Transform::register_translation(fixed, moving)`.
+
+### 7. Evaluate the Mattes metric directly
+
+Build a `MattesMetric` and evaluate the (negative) mutual information and its gradient at arbitrary parameters.
+`SamplingArg` controls which points are used:
+
+- `Random(n)` — `n` random continuous positions (drawn from a thread-local RNG, cached per metric).
+- `Fixed(n)` — `n` random positions, frozen at construction.
+- `FixedAt(points)` — an explicit list of sample positions (fully deterministic; recommended for reproducible results).
+
+```rust
+use algos::ObjectiveFunction;
+use image_registration::bspline::BSpline;
+use image_registration::error::Error;
+use image_registration::metric::{MattesMetric, SamplingArg, Sigma};
+
+fn main() -> Result<(), Error> {
+    // `fixed` and `moving` are Array2<f64>
+    let fixed = ndarray::Array2::<f64>::zeros((64, 64));
+    let moving = ndarray::Array2::<f64>::zeros((64, 64));
+
+    let f = Sigma::Absolute(vec![2.0, 2.0]).smooth(fixed.view())?;
+    let m = Sigma::Absolute(vec![2.0, 2.0]).smooth(moving.view())?;
+
+    let metric = MattesMetric::new(
+        BSpline::<0, _>::new(f.view()), // fixed image B-spline (nearest-neighbor)
+        BSpline::<3, _>::new(m.view()), // moving image B-spline (cubic)
+        SamplingArg::FixedAt((0..100).map(|i| vec![i as f64, i as f64]).collect()),
+        32,
+        0.05,
+    )?
+    .with_fixed_mu(vec![None; 6]); // which parameters are variable
+
+    let id = [1.0, 0.0, 0.0, 1.0, 0.0, 0.0];
+    let val = metric.evaluate(&id);
+    let grad = metric.gradient(&id).unwrap();
+    println!("mi({:?}) = {:.6}, grad = {:?}", id, val, grad);
+    Ok(())
+}
+```
+
+### 8. Save and load transforms
+
+Transforms serialize to YAML (via serde):
+
+```rust
+use image_registration::error::Error;
+use image_registration::transform::Transform;
+use std::path::PathBuf;
+
+fn main() -> Result<(), Error> {
+    let t = Transform::<ndarray::Ix2>::from_rotation(0.2, &[99.5, 99.5]);
+    t.to_file(PathBuf::from("transform.yaml"))?;
+    let back = Transform::<ndarray::Ix2>::from_file(PathBuf::from("transform.yaml"))?;
+    assert_eq!(t, back);
+    Ok(())
+}
+```
+
+## Module reference
+
+| Module                                 | Contents                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |
+|----------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| `image_registration::transform`        | `Transform`, the affine transform type: construction (`new`, `new_with_center`, `from_translation`, `from_scaling`, `from_rotation`), algebra (`inverse`, `with_translation`, `with_scaling`, `with_rotation`, `with_rotation_around`, `Mul`), coordinate transforms (`transform_point`, `transform_points`, `matrix`, `dmatrix`), resampling (`interpolate`, `interpolate_par`), registration (`register`, `register_debug`, `register_affine`, `register_translation`), serialization (`to_file`, `from_file`), plus the free function `transform_point` and a blas-free `matrix_inverse`. |
+| `image_registration::register`         | `Registration`, `RegistrationStep`, `RegistrationResult`, `Optimizer` (LBFGS/ASGD).                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
+| `image_registration::metric`           | `MattesMetric` (Mattes mutual information with analytic gradient), `SamplingArg` (Fixed/FixedAt/Random), `Sigma` (None/Absolute/Relative), `FixedMu`.                                                                                                                                                                                                                                                                                                                                                                                                                                        |
+| `image_registration::bspline`          | `BSpline<N, D>` B-spline interpolation of arbitrary order, `BSplineTrait`, `BSplineMem`, Parzen kernel helpers.                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
+| `image_registration::filter`           | Gaussian smoothing and FFT helpers: `gaussian_smooth`, `gaussian_kernel`, `fft`, `ifft`, `fft_freq`, `fft_shift`.                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |
+| `image_registration::optimize`         | Optimizers: `lbfgs_minimize`, `asgd_minimize`, `AsgdConfig`.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
+| `image_registration::par_indexed_iter` | Parallel iterators over array indices.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+| `image_registration::error`            | `Error` type.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |
+| `image_registration::julia_image`      | Test-image generator (Julia fractal on an `Array2<u8>`).                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |
+
+## How it works
+
+1. **Image pyramid.** Each registration level smooths the fixed and moving images with a Gaussian of the configured
+   `Sigma` (and optionally downsamples them). Coarse levels use large sigma so the metric is smooth and far-sighted;
+   fine levels use small sigma for precision.
+2. **Metric.** `MattesMetric` samples points in the fixed image, warps them into the moving image through the current
+   transform, and builds a joint intensity histogram using cubic B-spline Parzen windows. It minimizes (the negative of)
+   the mutual information with an analytic gradient computed via the chain rule (image Jacobian × transform Jacobian).
+3. **Optimization.** ASGD is used at coarse levels (robust to noisy gradients, with automatic parameter estimation),
+   L-BFGS at fine levels (quadratic convergence on smooth objectives).
+4. **Result.** The final transform maps fixed-image coordinates into moving-image coordinates; its inverse maps moving
+   coordinates back into the fixed frame.
+
+## Known limitations
+
+- With `SamplingArg::Random` / `SamplingArg::Fixed`, sample positions are drawn from a thread-local RNG, so different
+  runs can converge to different (local) optima — especially on small or nearly uniform images where the MI signal is
+  weak. For reproducible results, prefer `SamplingArg::FixedAt` with explicit sample points, and use enough samples to
+  cover the structure of interest.
+- The metric is defined only where the warped sample falls inside the moving image; points near the edge are smoothly
+  weighted out of the histogram, so registration can be unreliable if the two images overlap only slightly.
+
+## License
+
+Licensed under either of [Apache-2.0](LICENSE-APACHE) or [MIT](LICENSE-MIT), at your option.

src/metric.rs

@@ -214,8 +214,6 @@ where
     /// memory for (point, value, gradient) combination, refcell gives interior mutability
     metric: RefCell<IntMut>,
     edge: f64,
-    // mem_f: RefCell<BSplineMem>,
-    // mem_m: RefCell<BSplineMem>,
 }
 
 impl<D> MattesMetric<D>
@@ -231,8 +229,6 @@ where
     ) -> Result<Self, Error> {
         let shape = fixed.shape().iter().map(|&i| i as f64).collect::<Vec<_>>();
         let center = shape.iter().map(|i| (i - 1.0) / 2.0).collect();
-        // let mem_f = fixed.get_mem();
-        // let mem_m = moving.get_mem();
         let (min, max) = fixed
             .iter()
             .chain(moving.iter())