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REVIEW 4 major objections 5 minor 73 references

Learning Conditional Deformable Templates with Convolutional Networks

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that a single convolutional network can jointly estimate a deformable template for a whole population—or one conditioned on attributes such as age and sex—and provide fast diffeomorphic alignment to any new image.

desk verdict A clean, novel method for learning conditional templates jointly with a registration network; the MNIST evidence is solid, but the neuroimaging evaluation does not yet show that conditioning helps. read the letter →

arxiv 1908.02738 v2 pith:AKIAJJUB submitted 2019-08-07 cs.CV cs.LGeess.IV

Adrian V. Dalca , Marianne Rakic , John Guttag , Mert R. Sabuncu This is my paper · ORCID
classification cs.CVcs.LGeess.IV
keywords deformabletemplatesconditionalatlasesdiffeomorphicimageregistrationprobabilisticmodelsneuroimagingconvolutionalnetworkstemplateestimationbrainMRI
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper introduces a learning-based alternative to traditional deformable-template construction, which iteratively registers an entire population to a central image and can take days to weeks. It proposes a probabilistic generative model in which every image is a spatially deformed version of a template, and a neural network that, in one pass, outputs a template conditioned on given attributes and the velocity field that aligns the template to the input image. If the method works as claimed, on-demand templates can be synthesized in under a second, and the same network returns both the template and the deformation to any new image. The paper demonstrates this on handwritten-digit and sketch datasets and on a large brain MRI collection, showing unconditional and age-conditioned templates with anatomical trends such as ventricle growth and hippocampal shrinkage.

What carries the argument

The central objects are a conditional template network $g_{t,\theta_t}(a_i) = t$, implemented as a decoder, and a registration network $g_{v,\theta_v}(t, x_i) = v$, implemented as a U-Net, joined by the stationary-velocity-field parametrization of diffeomorphisms: integrating $v$ via scaling and squaring gives the deformation $\phi_v$, and warping the template by $\phi_v$ reconstructs the image. The generative model ties these together through the likelihood $p(x_i \mid v_i; a_i) = \mathcal{N}(x_i;\, f_{\theta_t}(a_i) \circ \phi_{v_i},\, \sigma^2 I)$ and the velocity prior $p(V) \propto \exp(-\gamma\|\bar{u}\|^2)\prod_i \mathcal{N}(u_i;\, 0,\, \Sigma_u)$, where the mean-displacement term enforces an unbiased central template and the Laplacian-based covariance encourages smooth deformations. Minimizing the negative log likelihood with stochastic gradients updates template and registration networks jointly, sidestepping expensive iterative pairwise registration.

What would settle it

Train the same model on a cohort that includes focal lesions or large scanner contrast differences and compare per-subject alignment quality, for example Dice overlap or reconstruction error, against a model trained only on homogeneous controls. If the conditional template cannot be deformed to match the atypical images with topology-preserving smooth fields, and those subjects' metrics fall well below the control average, the central modeling assumption is violated.

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Extended reading notes

Core claim

The central claim is that template estimation and image alignment can be cast as a single maximum-likelihood learning problem. For each image $x_i$, the model posits that $x_i$ is generated by warping a conditional template $t = f_{\theta_t}(a_i)$ through a diffeomorphism $\phi_{v_i}$ parameterized by a stationary velocity field $v_i$, with an additive Gaussian or normalized-cross-correlation likelihood and a deformation prior that penalizes the mean displacement and encourages smoothness. A network $g_\theta(x_i, a_i) = (v_i, t)$ is trained end-to-end by minimizing the negative log likelihood, learning at once a template function and a fast registration network; at test time, both the template and the deformation are obtained in a forward pass, and inverse deformations come from integrating the negative velocity field. The experiments claim that this produces central templates requiring smaller deformations than instance-based or decoder-only baselines, and conditional brain templates consistent with known age-related anatomical changes.

Load-bearing premise

The load-bearing assumption is that every image in the dataset can be represented as a single smoothly deformed version of a shared conditional template; images that cannot be diffeomorphically matched to one central shape, such as brains with tumors, lesions, or strong scanner-related contrast differences, would force the template into a compromise and bias the deformation estimates.

Editorial extensions

If this is right

  • A single trained model provides both a template and a deformation field for any new image in one forward pass, making on-demand atlas construction practical in clinical settings where no pre-existing template is available.
  • Conditional templates let the same data support many subpopulation atlases, such as an age- and sex-specific brain template, without subdividing the dataset or arbitrarily thresholding continuous attributes.
  • Because the template is a learned function of attributes, the model can synthesize templates for attribute values that were sparsely observed or held out during training, interpolating age-related anatomy across the whole range.
  • Learning to represent images up to a deformation means the method captures geometric variability aligned with the conditioning attributes, and can reduce confounding effects when those attributes are supplied.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the learned template function could be inverted to estimate attributes such as age from a scan, by finding the attribute value whose template best aligns with the input; the paper mentions this only as future work.
  • The latent-attribute experiment suggests a fully unsupervised version of this framework could build class- or mode-conditional templates without observed labels, effectively discovering geometric factors of variation in a dataset.
  • A testable extension would apply the model to multi-site clinical data with strong scanner or contrast differences; under the current likelihood, such appearance variation might be absorbed into the template and deformations rather than being modeled as noise.
  • If conditional template functions are smooth in the attributes, the framework implicitly yields a generative model of anatomy along those axes, so one could synthesize new population samples by deforming a conditional template with sampled velocity fields.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a probabilistic framework for learning deformable templates from image collections, in which each image is modeled as a diffeomorphic deformation of a template that may itself be a function of observed attributes. The authors derive a maximum-likelihood objective (Eq. 6) combining an image likelihood, a deformation-magnitude prior, and a smoothness prior, and optimize it end-to-end with a template-generation network and a registration network. They present experiments on MNIST and QuickDraw with controlled scaling/rotation attributes, and on a large multi-site brain MRI dataset, where they build unconditional and age/sex-conditioned templates. The paper claims that the learned templates are comparable in quality to a widely used atlas and that conditional templates capture age-related anatomical changes such as ventricle growth and hippocampal shrinkage.

Significance. The maximum-likelihood derivation is clear, the method is general, and the implementation (as part of VoxelMorph) with code and atlases released is a strength. The conditional-template formulation is a useful contribution: it provides a single network that can generate on-demand templates for arbitrary observed attributes without subdividing the population, and the MNIST experiments demonstrate that the model can learn attribute-driven geometric variability and generalize to sparse or held-out attribute values. The neuroimaging results, however, do not yet substantiate the claim that conditional templates improve or match existing atlases in a quantitatively meaningful way, because the only quantitative comparison is explicitly not apples-to-apples and shows no gain over the unconditional template. The value of the contribution therefore rests mainly on the toy experiments and visual/descriptive neuroimaging evidence.

major comments (4)
  1. [Section 4.2, Dice evaluation] The Dice comparison cannot support the abstract-level claim that the learned atlases are 'similar in quality and utility to a widely used atlas.' The authors state that 'these numbers may not be directly compared' because the baseline atlas and segmentations were produced with an external dataset and a different labeling pipeline, while their template labels come from FreeSurfer on their own training images. Moreover, the conditional template achieves Dice 0.795 ± 0.116, numerically below the unconditional template's 0.800 ± 0.110, with no significance test. A matched comparison on the same test subjects, using the same segmentation protocol for all templates, and a conditional-versus-unconditional comparison, is required to support the utility claim.
  2. [Section 4.2, Fig. 13] The age-related volume trends in Figure 13 are computed by warping training segmentations into the model's own conditional templates and measuring volumes of those templates. Because the template network and the deformation network are optimized jointly and the loss in Eq. (6) contains no term that explicitly forces attribute-related geometry into the template, these trends are a description of the learned model's outputs rather than an independent validation that conditional templates capture true anatomical variability. A non-circular test could compare registration accuracy or segmentation accuracy on held-out images when using matched versus mismatched conditional templates (e.g., age-appropriate versus age-inappropriate templates).
  3. [Section 4.1.1, centrality metrics] The centrality metric (mean displacement norm) is directly penalized in the training objective through the term -γ‖ū‖² in Eq. (6), so reporting lower centrality for the proposed method as a success criterion is partly circular. The comparison with the decoder baseline is informative about the objective being optimized, but it does not establish that the templates are better in an independent sense. The more decisive quantitative evidence in this section is the MSE and Jacobian behavior, which should be emphasized, and centrality should be presented as an objective-matching check rather than an external quality measure.
  4. [Section 3.1, generative assumption] The generative model assumes that each image is a spatially deformed version of a single conditional template under a diffeomorphic stationary-velocity-field deformation. In heterogeneous clinical cohorts containing lesions, tumors, or large contrast differences, this assumption is violated and the learned template will be a compromise that cannot be registered accurately to all images. Since the paper motivates clinical applications, the authors should either add a stress test with such images (e.g., synthetic lesions or outlier scans) or explicitly scope the claims to populations that satisfy the mutual-diffeomorphism assumption.
minor comments (5)
  1. [Section 3.2, Eq. (6)] The running-average approximation of ū is introduced only in the text; the notation in Eq. (6) treats ū as if it were the full dataset mean. The approximation should be made explicit in the equation or immediately after it.
  2. [Section 4.2] The text says the conditional model was trained 'using only the ADNI and ABIDE datasets' but the overall dataset includes many sources; clarify which splits were used for the unconditional and conditional models and how the 250 test subjects were selected.
  3. [Section 4.2, Figure 13] No error bars or confidence intervals are given for the volume-age trends, and the y-axis units ('x1000 voxels') are potentially confusing; specify whether these are raw voxel counts and report variability across subjects or templates.
  4. [Sections 2.2 and 3.1] The term 'unbiased population templates' is used for a template whose mean deformation is small; this is not the same as statistical unbiasedness of an estimator. Consider rewording to 'central' templates.
  5. [Throughout] There are several typos and notation issues: 'levarges' should be 'leverages' in Section 2.2, and in Section 4.1.1 the expression '|Jφ(p)|≤0' should be clarified to mean Jacobian determinants at or below zero, with the intended interpretation of non-topology-preserving pixels.

Circularity Check

1 steps flagged · score 3.0 of 10

Centrality metrics duplicate the training-loss regularizers, but the core conditional-template learning chain is self-contained.

  1. self definitional [Section 4.1.1, 'Evaluation criteria' (and Fig. 6), vs. Eq. (6) in Section 3.2 and Section 1's template definition.]
    "Our first two quantitative evaluation criteria relate to centrality, for which we computed the norm of the mean displacement field ‖¯u‖2 and the average displacement size 1 n ∑ i‖ui‖2."

    Section 1 defines template quality as minimizing geometric distance: 'A good template therefore minimizes the geometric distance to all images in a dataset.' Equation (6) instantiates this with the loss L = −(1/2σ²)‖x_i − g_t(a_i)∘φ_v_i‖² − γ‖u_bar‖² − (λ_d d/2)Σ_i‖u_i‖² + (λ_a/2)Σ_i‖∇u_i‖² + const. The two 'centrality' evaluation metrics in Section 4.1.1, ‖u_bar‖² and (1/n)Σ_i‖u_i‖², are exactly the second and third terms being minimized. Reporting them as evidence that the method yields 'more central templates requiring smaller deformations' therefore evaluates the training objective itself. This is a partial self-evaluation; the comparison against differently trained baselines remains informative, but the metric is definitionally aligned with the method's objective.

full rationale

The main derivation is self-contained: Eq. (1) poses a maximum-likelihood problem, the network in Section 3.2 minimizes the resulting negative log-likelihood in Eq. (6), and the MNIST/QuickDraw experiments evaluate on held-out images against instance and decoder baselines, so the core claim of jointly learning conditional templates and fast diffeomorphic alignment is not circular. The only concrete circular step I found is the centrality evaluation in Section 4.1.1, which uses the same displacement norms the loss is built to minimize. This is a minor, evaluation-level circularity and does not force the central result. The age-conditioned brain templates are not hard-coded by the loss; conditioning enters only through the input attribute vector and the observed age trends emerge from the joint optimization, so Figure 13 is descriptive output rather than a definitional tautology. Section 4.2 explicitly disclaims the Dice comparison: 'We emphasize that these numbers may not be directly compared, since the baseline atlas (and segmentations) were obtained using a different process involving an external dataset and manual labeling, while our template was built with our training images (and their FreeSurfer segmentations to obtain template labels).' That is a support limitation for the atlas-quality claim, not a circularity. No load-bearing self-citation chain or imported uniqueness theorem appears; prior VoxelMorph work is cited for architectures and integration layers, which are technical building blocks rather than the paper's central claim.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The method's core is the generative model of images as deformed templates; all listed axioms are either standard domain assumptions or implementation choices that the paper does not independently validate. The free parameters are regularization weights tuned on validation data, and the network weights themselves are estimated from data.

free parameters (5)
  • gamma (mean-deformation prior weight) = 0.01 (initial, tuned on validation)
    Controls the prior on the average displacement to enforce template centrality; tuned by visual assessment of deformations.
  • lambda_d (deformation-size prior weight) = 0.001 (initial, tuned)
    Penalizes the per-image deformation norm; tuned on validation data.
  • lambda_a (deformation-smoothness prior weight) = 0.01 (initial, tuned)
    Penalizes the spatial gradient of the deformation field to encourage smoothness; tuned on validation data.
  • sigma (image noise standard deviation) = 1
    Noise level in the Gaussian data likelihood used for toy experiments; set to 1 and kept fixed.
  • c (running-average window) = 100
    Number of recent displacement fields used to approximate the dataset-wide mean deformation in the loss function.
assumptions (5)
  • domain assumption Each image is a diffeomorphic deformation of a conditional template plus noise.
    Eq. (5) models p(x_i|v_i;a_i) = N(x_i; f_theta_t(a_i) composed with phi_{v_i}, sigma^2 I), which is the generative core of the method.
  • domain assumption Deformation prior enforces smoothness and unbiasedness.
    Eq. (3) assumes small average displacement and Laplacian-regularized smooth fields, a standard computational anatomy prior that is not validated for the datasets.
  • domain assumption Likelihood models (Gaussian for 2D images, normalized cross-correlation for MRI) are appropriate.
    Section 4.2 adopts an NCC loss for MRI based on prior literature; the paper does not compare alternative likelihood choices.
  • ad hoc to paper The running average over the last c displacements approximates the true mean deformation.
    Section 3.2 approximates the mean displacement with a weighted running average over c=100 iterations, an implementation choice that could bias early optimization.
  • ad hoc to paper The registration network has sufficient capacity to predict the optimal velocity field for every image-template pair.
    The U-Net is assumed to solve the per-image optimization; no convergence or optimality guarantee is provided.

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Cite this review

Pith. "Pith review of Learning Conditional Deformable Templates with Convolutional Networks." pith.science (2026). https://pith.science/paper/AKIAJJUB

@misc{pith2026190802738,
  author       = {Pith},
  title        = {Pith review of: Learning Conditional Deformable Templates with Convolutional Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AKIAJJUB}},
  note         = {Machine review of arXiv:1908.02738}
}
read the original abstract

We develop a learning framework for building deformable templates, which play a fundamental role in many image analysis and computational anatomy tasks. Conventional methods for template creation and image alignment to the template have undergone decades of rich technical development. In these frameworks, templates are constructed using an iterative process of template estimation and alignment, which is often computationally very expensive. Due in part to this shortcoming, most methods compute a single template for the entire population of images, or a few templates for specific sub-groups of the data. In this work, we present a probabilistic model and efficient learning strategy that yields either universal or conditional templates, jointly with a neural network that provides efficient alignment of the images to these templates. We demonstrate the usefulness of this method on a variety of domains, with a special focus on neuroimaging. This is particularly useful for clinical applications where a pre-existing template does not exist, or creating a new one with traditional methods can be prohibitively expensive. Our code and atlases are available online as part of the VoxelMorph library at http://voxelmorph.csail.mit.edu.

Figures

Figures reproduced from arXiv: 1908.02738 by the authors.

Figure 1
Figure 1. Conditional deformable templates generated by our method. Left: slices from 3D brain [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Overview. The network takes as input an image and an optional attribute vector. The upper network gt,θt (·) outputs a template, which is then registered with the input image by the second network gv,θv (·). The loss function, derived from the negative log likelihood of the generative model, leverages the template warped into t ◦ φvi . 3.2 Neural Network Model To solve the maximum likelihood formulation (1) given the… view at source ↗
Figure 3
Figure 3. MNIST examples (1) MNIST digits from D-scale-rot; (2) templates conditioned on class (vertical axis) and scale (horizontal axis) on MNIST D-scale, learned with our model, and (3) with a decoder-only baseline model; (4) conditional templates learned with our model on the MNIST D-class-scale-rot dataset for the digit 3 and a variety of scaling and rotation values [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (10 more)
Figure 5
Figure 5. Figure 5: Example deforma￾tions. Each row shows: class template, example class im￾age, template warped to this instance, instance warped to match the template, and the de￾formation field. intrinsic properties of the templates. They need to be evaluated together - otherwise, defo…
Figure 6
Figure 6. Figure 6: Quantitative measures. Top: Centrality and average deformation norm for templates generated by our model and the baselines on the D-class variant of MNIST. We find that our models yield more central templates. Bottom: Both MSE and Jacobians determinants measures indica…
Figure 7
Figure 7. Figure 7: Variability. Left: Images are synthesized by warping a learned template from the D-class dataset along the main two axes found by applying PCA to test deformation fields. Right: Images are synthesized by warping learned template using the D-class-scale along the main t…
Figure 8
Figure 8. Figure 8: Missing attributes. Left: during training, digits 3-5 are not synthesized using scaling 0.9− 1.1. Right: during training, only 5 examples of digit 5 are given. Red boxes highlight templates build with attributes where data was held out [PITH_FULL_IMAGE:figures/full_fi…
Figure 9
Figure 9. Figure 9: Latent attribute results. The top row shows sample input digits. The middle row shows our reconstruction for those input images, highlighting that the model learns a template for each digit type even when the digit attribute is not explicitly given. The bottom row show…
Figure 10
Figure 10. Figure 10: Slices from Learned 3D Brain MRI templates. Left: single unconditional template representing the entire population. Right: conditional age templates for brain MRI for ages 15 to 90, illustrating, for example, growth of the ventricles, also evident in a supplementary v…
Figure 11
Figure 11. Figure 11: Segmentations. Example segmentations overlayed with different brain views for our unconditional template (left) and conditional templates (right) varying by age [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: Example 3D neuroimaging deformations. Frames include: coronal slices for age￾conditional template, subject scan, warped template onto subject, warped subject onto template (using inverse field), and the first two directions of the 3D forward and inverse warps, and vel…
Figure 13
Figure 13. Figure 13: Volume trends. Change in volume of ventricles and hippocampi of the age-conditional brain templates. 4.2 Experiment 2: Neuroimaging In this section, we illustrate unconditional and conditional 3D brain MRI templates learned by our method, with the goal of showing its …
Figure 14
Figure 14. Figure 14: Quickdraw example templates. Left: example and learned atlases for the D-class QuickDraw dataset, and below variability examples similar to [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]

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