tf_registration: Registration Result Object

In tf: S3 Classes and Methods for Tidy Functional Data

Registration Result Object

Description

tf_registration objects store the result of tf_register(), including the aligned (registered) curves, estimated inverse warping functions h_i^{-1} (observed \to aligned time), and the template used. Use accessors tf_aligned(), tf_inv_warps(), and tf_template() to extract components.

Usage

tf_aligned(x)

tf_inv_warps(x)

tf_template(x)

## S3 method for class 'tf_registration'
print(x, ...)

## S3 method for class 'tf_registration'
summary(object, ...)

## S3 method for class 'summary.tf_registration'
print(x, ...)

## S3 method for class 'tf_registration'
plot(x, ...)

## S3 method for class 'tf_registration'
x[i]

## S3 method for class 'tf_registration'
length(x)

Arguments

x	a tf_registration object
...	additional arguments (currently unused)
object	a tf_registration object
i	index for subsetting (integer, logical, or character)

Value

For tf_registration objects: a list with entries registered (tf-vector of aligned/registered functions from x), inv_warps (inverse warping functions aligning x to the template function), the template function, the original data x (if store_x = TRUE was used in tf_register()), and the call to tf_register() that created the object. Accessors return the respective component.

Summary diagnostics

summary() computes per-curve diagnostics for assessing registration quality and prints their averages and/or deciles. The printed output contains four sections:

Amplitude variance reduction (only if store_x = TRUE): the proportion of pointwise variance removed by registration, computed as 1 - \bar{V}_{\mathrm{registered}} / \bar{V}_{\mathrm{original}} where \bar{V} is the mean (across the domain) of the pointwise variance (across curves). Values near 1 indicate that registration removed most of the original variability; values near 0 indicate little change; negative values indicate that registration increased variability (a sign that something went wrong).

Warp deviation from identity (deciles across curves): each curve's inverse warping function h_i^{-1} is compared to the identity via the normalized integral 2/L^2 \int |h_i^{-1}(t) - t|\, dt , where L is the domain length. The normalizing constant L^2/2 is the theoretical upper limit deviation for a monotone, domain-preserving warp that maps all timepoints to the first or last timepoint, so values range from 0 (identity warp, no time deformation) to 1 (maximal crazy warping). Values above \approx 0.3 may suggest aggressive warping that could warrant inspection.

Warp slopes (deciles of per-curve min and max dh^{-1}/dt): a slope of 1 of the warp corresponds to no local time deformation (identity). Slopes > 1 indicate local time dilation (the warped curve is "stretched" relative to the template), slopes < 1 indicate local time compression, so slopes near 0 or very large slopes indicate extreme local deformation. For affine shift warps, all slopes are exactly 1.

Domain coverage loss (only printed if any loss occurs): the fraction of the original domain range that is lost per curve after alignment, computed as 1 - range(aligned_arg) / range(original_arg). This is only relevant for affine (non-domain-preserving) warps where alignment can shift parts of curves outside the original domain. Domain-preserving methods (srvf, cc, landmark) always have zero domain loss.

Accessors

• tf_aligned(x): extract the registered/aligned curves (tfd vector).

• tf_inv_warps(x): extract the estimated inverse warping functions h_i^{-1}(t) that map observed time to aligned time (tfd vector). Use tf_invert() on the result to obtain forward warps if needed.

• tf_template(x): extract the template function (tf vector of length 1).

Author(s)

Fabian Scheipl, Claude Opus 4.6

See Also

Other registration functions: tf_align(), tf_estimate_warps(), tf_landmarks_extrema(), tf_register(), tf_warp()

Examples

reg <- tf_register(pinch[1:5], method = "affine", type = "shift_scale")
reg
summary(reg)
plot(reg)

tf documentation built on April 7, 2026, 5:07 p.m.