Title: FastJAM: a Fast Joint Alignment Model for Images
Venue: NeurIPS 2025
Accepted: yes
Keywords: Computer vision

graph neural network

GNN

image congealing

joint alignment
Abstract: Joint Alignment (JA) of images aims to align a collection of images into a unified coordinate frame, such that semantically-similar features appear at corresponding spatial locations. Most existing approaches often require long training times, large-capacity models,
and extensive hyperparameter tuning. We introduce FastJAM, a rapid, graph-based method that drastically reduces the computational complexity of joint alignment tasks. FastJAM leverages pairwise matches computed by an off-the-shelf image matcher, together with a rapid nonparametric clustering,  to construct a graph representing intra- and inter-image keypoint relations. 
A graph neural network propagates and aggregates these correspondences, efficiently predicting per-image homography parameters via image-level pooling. Utilizing an inverse-compositional loss, that eliminates the need
for a regularization term over the predicted transformations (and thus
also obviates the hyperparameter tuning associated with such terms), FastJAM performs image JA quickly and effectively. Experimental results on several benchmarks demonstrate that FastJAM achieves results better than existing modern JA methods in terms of alignment quality, while reducing computation time from hours or minutes to mere seconds. Our code is available at our project webpage, https://bgu-cs-vil.github.io/FastJAM/.

FastJAM: a Fast Joint Alignment Model for Images

Abstract

Joint Alignment (JA) of images aims to align a collection of images into a unified coordinate frame, such that semantically-similar features appear at corresponding spatial locations. Most existing approaches often require long training times, largecapacity models, and extensive hyperparameter tuning. We introduce FastJAM, a rapid, graph-based method that drastically reduces the computational complexity of joint alignment tasks. FastJAM leverages pairwise matches computed by an off-theshelf image matcher, together with a rapid nonparametric clustering, to construct a graph representing intra- and inter-image keypoint relations. A graph neural network propagates and aggregates these correspondences, efficiently predicting per-image homography parameters via image-level pooling. Utilizing an inversecompositional loss, that eliminates the need for a regularization term over the predicted transformations (and thus also obviates the hyperparameter tuning associated with such terms), FastJAM performs image JA quickly and effectively. Experimental results on several benchmarks demonstrate that FastJAM achieves results better than existing modern JA methods in terms of alignment quality, while reducing computation time from hours or minutes to mere seconds. Our code is available at our project webpage, https://bgu-cs-vil.github.io/FastJAM/ .

1 Introduction

Joint Alignment (JA) is the task of aligning a collection of images by estimating per-image spatial transformations such that, when applied, all images become geometrically consistent in a shared coordinate frame according to certain semantic or geometric criteria (see, e.g ., Figure 1). Unlike pairwise alignment, which aligns each image pair independently and often leads to error accumulation ( i.e ., 'drifting'), JA enforces a global agreement across the entire set, making JA particularly valuable for discovering shared structures between images or building a class atlas. However, achieving JA is inherently challenging: without supervision or a reference image, optimization methods frequently collapse into trivial or inconsistent solutions. Moreover, existing approaches typically require extensive computational resources, taking more than an hour [1, 2] to jointly align as few as 30 images. Recently, we proposed a method called SpaceJAM [3] that, partially by virtue of a new inverse-compositional loss over dense feature maps , significantly mitigated these computational issues, thereby solved the task in only a few minutes. Additionally, SpaceJAM set new state-of-the-art quantitative results. A natural question arises, however: is it possible to do even better in terms of both speed and performance? Fortunately, the answer is positive, as we show in the present paper.

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Here we introduce an even more computationally-efficient method that solves the JA problem in under 50 seconds, dramatically outperforming prior approaches in terms of speed while maintaining, and in fact typically improving, alignment quality.

Traditionally, JA methods relied on classical approaches such as congealing [4, 5], which iteratively align each image towards the remaining set, or centroid-based methods that utilize a reference image or a latent template [3]. Classical techniques employed feature-based methods ( e.g ., SIFT [6]), to establish keypoint (KP) correspondences between images. The rise of deep learning, particularly through Vision Transformers (ViTs) [7] and semantic feature extraction methods like DINO [8], has significantly advanced JA by providing richer representations that alleviate some challenges faced by traditional methods. However, even with ViT features, many difficulties persist, leading recent approaches to depend heavily on high-capacity, computationally-expensive models paired with extensive regularization [1, 2]. This reliance not only increases computational demands but also introduces complexity through the requirement of extensive hyperparameter (HP) tuning, ultimately resulting in methods that are slow and often brittle (as the HP tuning is usually dataset-specific).

Both congealing and atlas-based approaches typically rely on objective functions that fall into two main categories: geometric losses and semantic (feature-based) losses. In the geometric cases, one directly minimizes spatial discrepancies between corresponding KPs across images, leveraging explicit correspondence information. In contrast, semantic losses operate over dense feature representations and provide a smoother, globally-differentiable alignment without requiring explicit KPs. However, such dense (and typically high-dimensional) representations, often derived from high-capacity models like DINO [8], are computationally expensive when used within the JA optimization (even if the features themselves are kept frozen). Therefore, in this work we adopt the geometric loss paradigm, offering a sparse, lightweight, and scalable formulation that achieves typically higher alignment accuracy while significantly reducing the computational overhead.

Concretely, we introduce FastJAM , a graph-based JA framework that achieves fast and scalable alignment. Unlike prior methods that rely on dense feature maps and/or computationally-intensive optimization, FastJAM constructs a KP graph from pairwise correspondences using an off-the-shelf matcher, where nodes represent KPs and edges encode intra- and inter-image relationships. A

Optimization

Keypoint correspondence

Image-Level Pooling &

Linear Projection

GNN

Homography

Prediction

Add intra-image edges

and build a graph

𝐼 1

×𝐿

𝜃1

𝜃2

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Inter-image edge

Corresponding Keypoints Between Images

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Legend:

Figure 2: Overview of the FastJAM architecture. Given a set of images, we extract sparse keypoints (KPs) and pairwise correspondences using an off-the-shelf matcher (left; only red-dot matches are shown for clarity). A graph is built by linking KPs within each image (intra-image edges) and across matched pairs (inter-image edges). A GNN with L layers propagates alignment information through this graph (center). Image-level features are then obtained via mean pooling and used to predict per-image homography parameters ( θ i ) for joint alignment.

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Graph Neural Network (GNN) propagates alignment cues across the graph, and a readout layer produces image-level embeddings used to predict the homography parameters (as shown in Figure 2). Combined with a robust inverse-compositional geometric loss , FastJAM aligns an entire image set in under 50 seconds. Experiments on SPair-71k and CUB-200 show that FastJAM matches or exceeds the accuracy of contemporary JA methods while being significantly more efficient and orders of magnitude faster (see Table 1 for a comparison). Our key contributions are as follows.

We introduce FastJAM, a novel GNN-based framework for JA that significantly accelerates the alignment process (compared with existing methods) from hours/minutes to seconds.

FastJAM graph structure allows for the information from the entire image collection to propagate between images during optimization, unlike previous 'image-by-image' approaches (including SpaceJAM), leading to improvements in JA quality.

The first Inverse-Compositional JA loss that is based on a sparse KP representation.

2 Related Work

Pairwise image alignment. Learning-based correspondence methods have substantially improved the accuracy and robustness of image matching. Sparse approaches like SuperPoint [10] and SuperGlue [11] detect KPs and compute context-aware matches using attention and GNNs, but might struggle in low-texture or repetitive regions due to their reliance on sparse detections. To overcome these limitations, dense methods such as LoFTR [12] compute pixel-wise matches using transformerbased architectures without requiring explicit KPs. Recent advances continue to close the gap between the sparse and dense paradigms. RoMa [13] combines DINOv2 features with hierarchical transformers for robust wide-baseline matching. DIFT [14] introduces efficient descriptor interpolation from diffusion models. Additional types of relevant dense features appeared in the works of Mariotti et al . [15], who propose spherical viewpoint maps that encode rich geometry, and Xu et al . [16], who incorporate directional priors to disambiguate symmetric cases. However, common issues with

dense matching approaches are that they can be computationally demanding and that they require post-processing because the geometry often breaks.

JA by feature matching. Classical JA methods utilize geometric transformations and handcrafted features. The idea of congealing [4, 5] is to iteratively align images by minimizing a global cost, typically entropy or least-squares of pixel values [17, 18, 5] or descriptors like SIFT [19, 20, 21]. Other approaches simultaneously cluster and align images to their class means [22, 23] or use template matching [24, 25, 26]. In any case, such methods are limited by the quality of the extracted features. Another classical approach models image sets as low-rank linear subspaces [27, 28, 29, 30].

Deep learning has substantially advanced image JA. Huang et al . [31] adapted congealing to CNN features, while Spatial Transformer Networks (STNs) [32] introduced a differentiable module for predicting spatial transformations, enabling end-to-end alignment learning. STNs have since been widely adopted in JA tasks, including congealing [33], atlas construction [34, 35, 36, 37, 38], joint clustering [39, 40], moving-camera background modeling [41, 42], and temporal synchronization of multiple videos [43]. STNs have also been combined with GANs [44] to generate high-quality canonical atlases [45, 46], albeit data demanding.

Recent works have increasingly adopted deep features as the basis for JA. DINO features [8], in particular, offer robust and semantically-rich representations well-suited for this task. Neural Congealing [1] employs test-time optimization to build class-specific atlases (e.g., birds) by aligning DINO features using rigid and non-rigid warps, predicted by a ResNet-based STN [47]. ASIC [2] utilizes DINO features, learning dense warps from input images to a canonical space through a U-Net architecture [48]. Both these methods are computationally intensive (often exceeding an hour for 30 images on an RTX 4090), require heavy regularization to avoid degenerate solutions, and are prone to instability. ASIC also typically produces fragmented or globally-incoherent alignments due to the challenges of dense warping. More recently, a previous work from our group introduced SpaceJAM [3], a more efficient solution using a lightweight ConvNet (CNN) and an inverse-compositional loss over refined DINO features, reducing runtime to a few minutes. However, its reliance on high-dimensional feature maps results in substantial memory overhead during the optimization process. In contrast, FastJAM combines sparse KP-based matching with a geometric loss, enabling much faster optimization and better scalability. FastJAM also differs from SpaceJAM in its architecture and the fact that the input to its neural net is based on the entire image collection, as opposed to SpaceJAM's single-image input.

JA by KP correspondence. Several methods tackle JA by explicitly leveraging KP correspondences across the image set and minimizing a geometric loss. Shokrollahi et al . [21] construct a similarity graph from KP matches to select optimal references for alignment. Safdarnejad et al . [49] propose a temporally-aware congealing method for video frames based on tracked KPs. FlowWeb [50] estimates dense correspondences across images and refines them jointly through graph-based optimization. ASIC [2] also incorporates an initial KP matching step, though its primary pipeline relies on dense warping. Dense matching is often computationally demanding and memory intensive, while sparse KPs offer a more efficient alternative. Building on recent successes of GNNs in pairwise alignment tasks [11, 51, 52], FastJAM capitalizes on this sparsity and introduces a GNN to aggregate alignment information across matched KPs. Combined with a fast inverse-compositional loss, this enables high-quality and regularization-free JA in seconds and with a low-memory footprint.

3 Method

In this section, we first formally introduce the JA problem (§ 3.1). We then detail how to construct a correspondence graph from pairwise image matches (§ 3.2), while in § 3.3 we detail the model architecture. Finally, we explain in § 3.4 how to perform image JA with FastJAM.

3.1 The Joint Alignment Problem and the Inverse-Compositional Framework

Given N images, I = ( I i ) N i =1 , depicting different instances from the same semantic class ( e.g ., cars), the task is to facilitate JA by estimating a transformation T θ i ∈ T for each image such that the transformed images ( I i ◦ T θ i ) N i =1 are spatially aligned in a shared coordinate frame C . We assume a parametric family of transformations T ( e.g ., homographies), with T θ i denoting the transformation

Model

Model

Model

Shared Weights

Atlas-based

optimization

Canonical Coordinates

Model

Model

Model

Shared Weights

Inverse-Compositional

Optimization

𝑇 𝜃1

Inverse-Compositional Keypoints-based

Optimization

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Targets

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Model

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T01。

T-02

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for image I i , parameterized by θ i . Atlas-based approaches ( e.g ., [1, 2]) usually optimize for a latent template, I µ , jointly with the transformations. Formally, they solve

where D is a discrepancy measure ( e.g ., the Euclidean distance), R ( T θ i ; λ ) is a regularization term on the predicted transformations with HPs λ , and I µ is the so-called canonical space or atlas. Due to its notion of centrality, I µ is also known as the average or centroid image.

In contrast, FastJAM follows a congealing-inspired approach [4, 5] (particularly, Least-Squares (LS) Congealing [17, 18]) which avoids the need to maintain an explicit reference image, together with the modern Inverse Compositional (IC) approach we proposed in [3]. Concretely, the IC approach can be defined via the following loss:

̸

Of note, the historical roots of the IC approach go back to the pre-DL era [18]. SpaceJAM [3], however, rather than optimizing over the warping of a single image at a time (as was done in traditional LS-congealing) simultaneously optimizes over all transformations.

The IC formulation indicates that the image collection is mapped to a shared space, since

As explained in [3], the IC approach obviates the need for using regularization terms. An important distinction between our work and [3] is that in [3] the optimization is based on the discrepancy between dense feature maps ( e.g ., DINO features), while we adapt it to KPs and rely on geometric measure, as detailed below. Figure 3 illustrates the different JA approaches.

By design, and due to the inverse-compositional nature, IC losses are invariant to a single global homography. That is, for any ( T θ i ) N i =1 and any additional transformation T θ 0 , the ( T θ i ◦ T θ 0 ) N i =1 transformations would give rise to the same value of the loss. The same phenomena happens in not only [3] (and, for slightly-different reasons, [38, 43]) but also many works on synchronization over groups (see, e.g ., [53, 54]). This is a feature, not a bug, as it simplifies the optimization considerably. Importantly: 1) While this means there are infinitely-many solutions, the implied N -fold joint correspondence is unique. 2) After the fact ( i.e ., after the optimization is done), and for visualization purposes, for example, one can pick the value of T θ 0 without affecting the quality of the

Original Image

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solution. Plausible choices include the inverse of the average homography (which can be computed in various ways, including the so-called Karcher mean [55, 56]) or the inverse of, say, T θ 1 . Note that the latter choice does not imply that the first image had any special importance in the optimization.

3.2 Graph Construction

The first stage of FastJAM involves constructing a sparse graph over KPs extracted from the image collection. This graph encodes both intra-image structure and inter-image correspondences and serves as the input to the GNN. The construction process consists of three steps, detailed below.

Object-centric region extraction. We follow [1, 2, 3] and extract object-centric masks for the image collection. We use Grounded-SAM [57], a combination of the Grounding DINO object detector and the Segment Anything Model (SAM) [8, 58]. Given a text prompt corresponding to the object category, Grounded-SAM produces a segmentation mask focusing on the object of interest. This mask is used to restrict the KP extraction and matching to the relevant region, improving robustness to background clutter and occlusions. Mask extraction takes ∼ 0 . 4 seconds per image and can be parallelized over the GPU.

KP detection and matching. For each image I i , we extract a set of sparse KPs X i = { x (1) i , . . . , x ( M i ) i } (where M i is the number KPs in I i ) using an off-the-shelf image matcher inside the objects' mask. We use RoMa [13], but any matcher producing KP correspondences can be used. We chose RoMA due to its robustness and fast inference time ( ∼ 0 . 3 seconds for an image pair on an RTX4090, which can be done in parallel across pairs). For each image pair ( I i , I j ) , RoMa returns a set of KPs, ( X i , X j ) , and correspondences M ij ⊂ X i × X j along with a confidence score for each match. To improve spatial coverage and reduce redundancy, we apply non-maximum suppression (NMS) over the matcher confidence scores using a 30 × 30 window, and retain the top-scoring points. We found that selecting as few as 10 KPs per image is sufficient for our framework.

Intra-image KP clustering. Consider three images, ( I 1 , I 2 , I 3 ) , and recall that RoMa is a pairwise KP extractor and matcher. Running RoMa on ( I 1 , I 2 ) produces 10 KPs on I 1 and 10 on I 2 ; running

it on ( I 1 , I 3 ) produces another 10 KPs on I 1 and 10 on I 3 ; and so on. Consequently, each image (e.g., I 1 ) accumulates multiple sets of KPs obtained from different pairwise runs. Importantly, these sets are not guaranteed to be identical, even though they all refer to the same image, leading to redundancy. For instance, in bird images, most of the N -1 KP sets extracted from I 1 are likely to include a KP near the beak tip, though at slightly different locations. To reduce this redundancy and merge semantically similar KPs within an image, we apply a fast, nonparametric clustering step. Specifically, we use Dinari and Freifeld's parallel DP-Means algorithm [59] (with init_n =3 and δ = 1 ), a highly efficient variant of DP-Means [60], which itself generalizes K -Means to an unknown number of clusters. It takes ∼ 0 . 13 seconds to cluster ∼ 6000 points. After clustering, we discard the original KPs and retain only the cluster means as the representative intra-image KPs.

Graph definition. We define a single graph G = ( V , E ) over the entire image set. Each KP, x ( m ) i , is represented as a node v ∈ V . We add two types of edges: (1) Intra-image edges : In each image I i , we fully connect all KPs in X i to model local spatial structure. (2) Inter-image edges : In each matched KP pair ( x ( m ) i , x ( n ) j ) ∈ M ij , we add an edge between the corresponding nodes. Each node v ∈ V is initialized with a vector h (0) v consisting of the KP's 2D coordinates such that H (0) is the initial nodes coordinates matrix. In addition, each node is tagged with a categorical identifier indicating its source image, which is later used to perform image-level pooling. Unlike traditional graph-level readout layers that summarize the entire graph, FastJAM performs structured readout by pooling node embeddings per image. The edge structure is encoded as a binary adjacency matrix A ∈ { 0 , 1 } |V|×|V| , where A uv = 1 if there is an edge (intra- or inter-image) between nodes u and v . The resulting graph G = ( V , E , H (0) , A ) encodes both local geometric structure and cross-image semantic correspondence, and serves as input to a message-passing GNN that propagates alignment information throughout the image collection.

3.3 Model Architecture

Given the graph G = ( V , E , H (0) , A ) , our objective is to predict a transformation parameter vector θ i ∈ R 8 for each image I i , representing its homography. We treat this as a structured regression task over node features: each node corresponds to a KP, and the GNN must propagate alignment-relevant information across the graph to produce per-image outputs. Formally, let f ( G ) = ( θ i ) N i =1 be a GNN that predicts the warping parameters from the graph. In our setting, where the goal is to regress image-specific transformations from KPs structured within a shared graph, it is essential to preserve the distinction between a node and its neighbors. GraphSAGE [61] achieves this by applying separate transformations to self and neighbor features, enabling more effective modeling of local asymmetries and node-specific roles which is relevant when propagating alignment cues across inter- and intra-image connections. While attention-based models such as GAT [62] offer expressive edge-aware aggregation, we found them to be empirically slower. In contrast, GraphSAGE provided a favorable balance of speed, stability, and alignment accuracy, making it well-suited for FastJAM's test-time optimization regime. The message protocol for GraphSAGE is where h ( l ) v is the embedding of node v at layer l , N ( v ) denotes the neighbors of v , W ( l ) is a learnable weight matrix, and σ is a non-linear activation function. After L = 5 message-passing layers, we perform per-image readout via global average pooling over all nodes belonging to each image:

where V i ⊂ V is the set of nodes from image I i , and z i ∈ R d is the resulting image-level embedding. Finally, we project the embedding of each image to the estimated homography parameters:

3.4 FastJAM Joint Alignment

Lie-algebraic parameterization. To ensure matrix invertibility, which is essential for our IC formulation and for stable optimization [63, 3], we represent homographies using the Special Linear group SL(3) via a Lie-algebraic parameterization as was done in, e.g ., [64, 54, 3]. For details, see our supplemental material ( SupMat ).

Robust inverse-compositional KP loss. Our geometric loss builds upon the IC formulation introduced in [3], adapted to sparse KP correspondences. For each image pair ( I i , I j ) , the forward warp from I i is composed with the inverse warp from I j ( i.e ., T θ i ◦ T -θ j ). We penalize the discrepancy between each matched KP pair ( x ( m ) i , x ( n ) j ) ∈ M ij after applying the IC transformation

̸

where ρ σ ( z ) = z 2 z 2 + σ 2 is the Geman-McClure robust loss function [65] with parameter σ .

This formulation allows alignment to be computed at the original KP locations without any regularization term on the warps or the need to render warped images via expensive interpolation. Compared to dense alignment over high-dimensional DINO feature maps, our sparse formulation is both significantly more efficient and more robust to missing KPs, wrong matches, and outliers.

Handling reflections. We follow [3] and explicitly check for flips every K epochs during optimization (where K = 100 ) and compute the gradient and update the model's weight only for the best configuration. We have found that only checking for horizontal flips is sufficient. This ensures that flipped images can still participate in alignment without requiring a reflection-aware parameterization.

Implementation details. All experiments were conducted on a single NVIDIA RTX 4090 GPU with 24GB of memory. We optimize FastJAM for 600 epochs using Adam [66] with a GemanMcClure robustness parameter σ = 0 . 25 . We use pretrained Grounding-SAM [57] and RoMa [13] with the default HP once, before starting the optimization. For more details, please see our SupMat .

Limitations. Our main limitation is the reliance on an external image matcher to generate initial KP correspondences. While modern matchers like RoMa provide high-quality matches in many scenarios, the overall alignment quality depends on the accuracy of these correspondences. In addition, FastJAM models geometric transformations using homographies, which may be insufficient in cases involving strong non-planar deformations. Extending the model to support more expressive transformation families remains a direction for future work.

4 Results

Datasets, evaluation metrics, and baselines. We evaluate FastJAM under a test-time optimization setting, where the model is optimized independently on each image collection. We use two benchmark datasets: SPair-71k [9] and CUB-200 [67] (classes and subsets). SPair-71k's test set comprises 18 object categories, each with ∼ 30 images, with annotated KPs and large intra-class variation. We report both per-category performance and average results across all categories. Following prior works, we evaluate on the first 3 categories of CUB-200 test set, each containing ∼ 30 images as well. We use the Percentage of Correct Keypoints (PCK) as the evaluation metric. A predicted KP is deemed correct if it falls within a normalized distance threshold α of the ground-truth location. We report mean PCK across all KPs and categories, with α = 0 . 1 . We average the results over 3 runs.

As in prior work [2, 3], we compare FastJAM to several baselines. Neural Best Buddies (NBB) [68] aligns image pairs using mutual nearest neighbors with Moving Least Squares warping [69], using VGG ( VGG-MLS ) or DINO ( DINO-MLS ) features. DINO-NN performs dense nearest-neighbor matching. GANgealing [46] uses GANs but is limited to seen categories. Neural Congealing [1] builds an explicit atlas but requires hyperparameter tuning and reported results on only three SPair-71k classes. ASIC [2] predicts dense warps to a canonical space, and SpaceJAM [3] applies an IC loss over DINO features. FastJAM instead uses sparse KPs and a graph-based model, enabling faster and more scalable alignment. We cite the results reported in [2, 3].

4.1 Qualitative Results

We illustrate the qualitative performance of FastJAM in Figure 1, Figure 4, and Figure 5. Given a collection of category-level images ( e.g ., birds), FastJAM aligns all images within seconds, producing visually coherent and semantically consistent outputs across instances. To interpret the alignment, we

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visualize the canonical space C using a fixed RGB colormap. Each image I i is colored by applying the inverse of its predicted transformation to C , i.e ., C ◦ T -θ i . As shown in Figure 4, semantically similar regions ( e.g ., heads, wings, tails) align to consistent areas in C , indicating robust JA across pose and appearance. As shown in Figure 5 in comparison to [3], FastJAM alignment is visually better. Additional examples and comparisons are available in the SupMat .

4.2 Quantitative Results

Table 2 reports alignment accuracy on the SPair-71k test set, measured by mean PCK@0.10 across 18 object categories. FastJAM achieves the best overall performance with an average PCK of 53.0 , outperforming all competing methods. It ranks first in 11 categories and second in 6 others, with comparable performance across a wide range of object classes and viewpoints. Compared to [1, 2], FastJAM offers on-par or better accuracy while being significantly faster and more memory-efficient, validating the benefits of its sparse, graph-based formulation. While FastJAM performs competitively across most categories, we observe reduced performance on highly-symmetric objects such as bicycles . These cases pose inherent challenges due to visual ambiguity, where the initial matcher struggles to disambiguate symmetric parts ( e.g ., right versus left). In such scenarios, FastJAM can propagate incorrect correspondences. Addressing this remains an interesting direction for future work. Results for the CUB-200 dataset are reported in Table 3 where FastJAM outperforms SpaceJAM and achieves comparable results to ASIC [2] (in a fraction of the computation time) on the categories benchmark and the best results across subsets (results were not reported for [2]).

4.3 Runtime Analysis

Runtime comparison. We evaluate the computational efficiency of FastJAM by comparing its runtime against: NeuCongeal [1]; ASIC [2]; SpaceJAM [3]. As shown in Table 1, FastJAM achieves over an order-of-magnitude speedup (measured over three SPair-71k categories), aligning image collections in under ∼ 50 seconds , compared to 5-6 minutes for SpaceJAM and over an hour for ASIC and NeuCongeal. The reported runtime includes preprocessing ( i.e ., pairwise matches). We also compare FastJAM and SpaceJAM on an increasing number of images ( N = 10 to 100 ). The full experimental setup is available in our SupMat .

Dense vs. KP warping. We analyze the individual warping components of both methods on a set of 30 images (see Table 4, all reported runtime in this table are in seconds) for one epoch. We evaluate how the number of points ( N points ) in the coordinate grid and the feature dimension ( D ) affect the overall warping time. For dense matching, we set N points = 266 × 266 = 70 , 756 (the image resolution used in SpaceJAM) and D = 25 , corresponding to the feature dimension on which the loss is computed. For FastJAM, we set N points = 16 and D = 2 ( i.e ., 8 KPs in 2D). For completeness, we also evaluate D ∈ { 2 , 25 } for both methods. We measure the time required for ( i ) grid warping, ( ii ) interpolation (used only in dense warping), ( iii ) forward and backward warping for the IC loss ( Fwd + Back ), and the total runtime over all batches in a single epoch. For dense warping ( e.g ., SpaceJAM), the maximum batch size is B max = 10 , resulting in a total runtime of 3 × ( Fwd+Back ) . The key observations are: (1) reducing N points is crucial for achieving fast warping, and (2) avoiding interpolation further accelerates computation, making the runtime largely independent of D .

4.4 Ablation Study

Table 5 summarizes our ablation study on CUB-200 (3 categories) and SPair-71k. Replacing RoMa with LoFTR [12] significantly reduces performance, underscoring LoFTR's limitations in crossinstance correspondence. Substituting the Geman-McClure loss [65] with an ℓ 2 loss or removing the object mask also causes notable accuracy drops, confirming the importance of robust error modeling and spatial masking. NMS and intra-image edges provide additional gains. Although removing the Lie-algebraic parameterization has little effect on accuracy, it ensures warp invertibility, essential for the IC loss, as without it about 2% of runs fail due to non-invertible matrices, whereas using it eliminates such failures entirely. Replacing the GNN with a linear projection caused a substantial performance drop, while MLP-based and direct homography optimization models also reduced accuracy, though less severely. Among GNN backbones, GraphSAGE [61] outperforms both GCN [72] and GAT [62] in accuracy and runtime.

5 Conclusion

We introduced FastJAM , a graph-based framework for fast and scalable image JA. By leveraging sparse KP correspondences and a lightweight GNN architecture, FastJAM propagates alignment cues across image collections and regresses per-image transformations. Our method achieves state-of-theart alignment quality while significantly reducing runtime and memory usage.

Acknowledgments

This work was supported by the Lynn and William Frankel Center at BGU CS, by the Israeli Council for Higher Education via the BGU Data Science Research Center, RSW's work was supported by the Kreitman School of Advanced Graduate Studies. Both OH and SI were also supported by the VATAT National excellence scholarship for MSc students in AI and Data Science.

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FastJAM: a Fast Joint Alignment Model for Images ----Supplemental Material

Contents

This document contains the following:

§ A: Visual Comparison

-Additional qualitative comparisons against existing joint alignment methods (Figure 6).

§ B: Additional Visualizations

-Additional joint alignment results on the CUB dataset (Figure 7).

-Full pairwise alignment grids for representative categories (Figure 8 and Figure 9)

§ C: Explaining the Colormap Visualization in More Detail

-Illustration of FastJAM's canonical alignment using a fixed RGB colormap (Figure 10).

§ D: Runtime Analysis

-Scalability runtime assessment for increasing number of images ( N = 10 to 100 ) (Figure 11).

§ E: Model Configuration and Training Setup

-Full architecture summary (Table 5).

-Optimization settings, matcher configuration, and training procedure.

§ F: External Tools and Frameworks

-Summary of third-party tools and libraries used, including RoMa, LoFTR, GroundedSAM, and torch_geometric .

§ G: Lie Group Parameterization

-Full explanation of the Lie group parameterization.

Additionally, key notational conventions used throughout the main paper and this document are summarized in Table 6.

A Additional Visual Comparisons

To qualitatively assess alignment quality, we compare FastJAM against existing joint alignment methods, including SpaceJAM and ASIC. As illustrated in Figure 6, FastJAM produces more coherent and natural-looking alignments, particularly in challenging cases involving pose variation. Unlike ASIC, which applies dense warping and often introduces distortions, FastJAM preserves global structure by relying on sparse keypoints and homographic transformations.

B Additional Visualizations

This section provides supplementary qualitative results that further demonstrate the alignment capabilities of FastJAM across various categories and settings.

Source

Target

ASIC

SpaceJAM

FastJAM (Ours)

B.1 Additional Joint Alignment on CUB Dataset

Figure 7 presents further joint alignment results on additional classes from the CUB-200 dataset. For each class, the original input images are shown in the top row, while the bottom row displays their aligned counterparts. The outputs demonstrate FastJAM's ability to handle fine-grained categories and produce visually coherent canonical views across varying poses and appearances.

B.2 Pairwise Alignment

We visualize full pairwise alignment grids for two representative categories: 'aeroplane' and 'horse.' As shown in Figure 8 and Figure 9, each grid displays how the source images (rows) are aligned to the target images (columns) using the estimated inverse-compositional warps. The diagonal entries, which correspond to self-alignments (i.e., identity transformations), are highlighted with a purple dashed-line frame. These grids illustrate FastJAM's ability to produce consistent, symmetric mappings across image pairs and maintain semantic structure throughout the alignment process.

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C Explaining the Colormap Visualization in More Detail

To provide an intuitive understanding of how FastJAM aligns images to a shared canonical space, we visualize the warped outputs using a predefined RGB colormap. As shown in Figure 10, each input image is first aligned to the canonical frame and blended with the colormap. The result is then inverse-warped back to the original image space, allowing us to visualize how semantic regions are mapped consistently across instances. This process highlights FastJAM's ability to establish meaningful correspondences without relying on dense features or explicit templates.

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As illustrated in Figure 11, FastJAM remains efficient across all tested sizes, completing alignment in under 450 seconds even for 100 images. In contrast, the current implementation of SpaceJAM runs out of RAM after N = 40 images due to the PCA preprocessing step.

E Model Configuration and Training Setup

We train the model for 600 epochs using the Adam optimizer with an initial learning rate of 5 × 10 -3 , multiplied by 0.5 after 200 epochs without improvement. The loss function is based on the GemanMcClure formulation with a robustness parameter σ = 0 . 25 , and no weight decay is applied. The feature extractor within the GNN uses 5 layers of hidden size 128, followed by a linear projection to an 8-dimensional homography parameter vector. A full summary of the model architecture and its 133,256 trainable parameters is provided in Table 5. To encourage geometric stability, the final projection layer is initialized to approximate the identity transformation, and transformations are parameterized using Lie algebra to ensure invertibility. Alignment is applied iteratively using a single pass of the inverse compositional (IC) spatial transformer network. During optimization, horizontal flips are checked every 100 epochs.

For correspondence estimation, we employ the RoMa matcher at a fixed image resolution of 560 × 560 for both coarse and upsampled stages. A maximum of 10 keypoints is retained per image, filtered by

non-maximum suppression (NMS) using a radius of 0.054 in normalized coordinates-corresponding to a 30 × 30 pixel window in the original image space. This ensures spatial coverage while avoiding redundant detections.

F External Tools and Frameworks

We gratefully acknowledge the use of several open-source libraries and resources in this project. Our GNN implementation is based on torch_geometric , primarily using the GraphSAGE [4] architecture, along with other variants for comparison. We used Weights & Biases for experiment tracking and visualization. For keypoint matching, we built upon the official implementation of RoMa [5], and we also incorporated components from the LoFTR framework [6]. Object-centric masks were obtained using Grounded-SAM, which combines Grounding DINO [7, 8] and the Segment Anything Model (SAM) [9]. We thank the authors of all these works for making their code and models publicly available.

G Lie Group Parameterization

A homography has 8 degrees of freedom and corresponds to an equivalence class of invertible matrices, where a representative with unit determinant can be used. Now consider

The space sl (3) is the Lie algebra of trace-zero matrices. The matrix exponential maps sl (3) into SL(3) , yielding a smooth eight-parameter representation of homographies. Our network predicts ( θ i ) N i =1 , where each θ i ∈ R 8 is mapped to Θ i ∈ sl (3) as shown above, and the homography is obtained via T θ i = H i = exp( Θ i ) . This construction guarantees det T θ i = 1 . In particular, θ i = 0 8 × 1 yields the identity matrix, and T -θ i is the inverse of T θ i .

References

Kamal Gupta, Varun Jampani, Carlos Esteves, Abhinav Shrivastava, Ameesh Makadia, Noah Snavely, and Abhishek Kar. ASIC: Aligning sparse in-the-wild image collections. In ICCV , 2023. 2

Nir Barel, Ron Shapira Weber, Nir Mualem, Shahaf E Finder, and Oren Freifeld. Spacejam: a lightweight and regularization-free method for fast joint alignment of images. In European Conference on Computer Vision , pages 180-197. Springer, 2024. 2

Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The caltechucsd birds-200-2011 dataset, 2011. 3

Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. Advances in neural information processing systems , 30, 2017. 8

Johan Edstedt, Qiyu Sun, Georg Bökman, Mårten Wadenbäck, and Michael Felsberg. Roma: Robust dense feature matching. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 19790-19800, 2024. 8

Jiaming Sun, Zehong Shen, Yuang Wang, Hujun Bao, and Xiaowei Zhou. Loftr: Detectorfree local feature matching with transformers. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 8922-8931, 2021. 8

Tianhe Ren, Shilong Liu, Ailing Zeng, Jing Lin, Kunchang Li, He Cao, Jiayu Chen, Xinyu Huang, Yukang Chen, Feng Yan, Zhaoyang Zeng, Hao Zhang, Feng Li, Jie Yang, Hongyang Li, Qing Jiang, and Lei Zhang. Grounded sam: Assembling open-world models for diverse visual tasks, 2024. 8

Shilong Liu, Zhaoyang Zeng, Tianhe Ren, Feng Li, Hao Zhang, Jie Yang, Chunyuan Li, Jianwei Yang, Hang Su, Jun Zhu, et al. Grounding dino: Marrying dino with grounded pre-training for open-set object detection. arXiv preprint arXiv:2303.05499 , 2023. 8

Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C. Berg, Wan-Yen Lo, Piotr Dollár, and Ross Girshick. Segment anything. arXiv:2304.02643 , 2023. 8

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nFastJAM is a method for aligning a small collection of images (typically 10 to 100) into a unified coordinate frame by estimating and applying a homography for each image. The pipeline consists of the following steps:\n1. Object Mask Extraction: For each image, extract object-centric masks using Grounded-SAM.\n2. Keypoint Matching: For each image pair, extract correspondences within the object masks using RoMA and NMS, retaining only 10 keypoints per image.\n3. Graph Construction: Build a graph where:  \n    - Nodes represent keypoints (2D coordinates).  \n    - Each image contributes edges between its keypoints.  \n    - Each image pair contributes edges between matched keypoints.\n4. Graph Neural Network: Apply a 5-layer GraphSAGE model for message passing over the graph. Use average pooling over keypoints per image to obtain an embedding, followed by a linear layer that predicts 8 homography parameters per image.\n5. Optimization: Train the network using Adam to minimize a robust inverse-compositional keypoint alignment loss.\n6. Homography Application: Apply the estimated homographies to align each image.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n1. The paper is well written and easy to follow.\n2. FastJAM builds on well-established methods such as RoMA and Grounded-SAM.\n3. The method is simple and relatively elegant.\n4. FastJAM is an order of magnitude faster than the state-of-the-art SpaceJAM, and achieves slightly better performance in terms of PCK@0.10.\n\n## Weaknesses\n1. JAM (we are talking about aligning 10 to 100 images) seems to be a niche topic. It is unclear whether this problem attracts a wide audience at NeurIPS. It would be helpful for the authors to clarify why JAM is of broad significance to the AI community.\n2. The inverse compositional approach was proposed in SpaceJAM, so the main contribution of FastJAM is to consider a loss over 2D coordinates instead of DINO features.  While this change contributes to the improved efficiency and simplicity of FastJAM, it reduces the overall originality and significance of the contribution.\n3. All the evaluations are performed using PCK@0.10. I understand that a choice had to be made to obtain a quantitative evaluation, but I am wondering if this actually reflects the qualitative results. The only comparative qualitative results that I found are in the supp. mat. Fig.6 and the difference between SpaceJAM and FastJAM is not clear/impressive. \n\nIn summary, the paper's clarity and technical quality are strong points. However, in my opinion, the contributions lack the level of novelty and broader impact typically expected at a conference like NeurIPS.\n\nQUESTIONS:\n1. In Figure 2, it appears that 2D tracks are constructed—e.g., the red 2D point in image I1 is matched across images I2, I3, and I4. Is this correct? If so, applying RoMA + NMS to I1–I2 and I1–I3 would yield two different sets of keypoints for I1. Do you merge these sets? If so, the paper does not describe this process.\n\n2. RoMA is trained for general image matching, not semantic keypoint matching—correct? For example, it is surprising that it can match different instances of the same object class (e.g., different dogs). Could the authors clarify or provide evidence for this behavior?\n\n3. The global parameterization of homographies via the matrix exponential on SL(3) seems inelegant. I assume this choice is numerically stable due to the “small” nature of the estimated homographies. Was the reflection check introduced for numerical stability? Did you consider alternative parameterizations, such as using four corner points?\n\nLIMITATIONS:\nThe method appears to have quadratic complexity in the number of images, which could be a significant limitation when scaling to larger datasets.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-11"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposed FastJAM, a novel GNN-based framework for fast and scalable image JA tasks. It combines the off-the-shelf sparse key point detector/matcher and a lightweight GNN, to propagate alignment cues across image collections and regress per-image transformations, and utilizing an inverse-compositional warping strategy. Extensive experiments show that FastJAM can significantly reduce computation time from hours or minutes to mere seconds, while maintaining similar accuracy compared to other SOTA methods.\n\nSTRENGTHS AND WEAKNESSES:\nStengths:\n1. The method proposed by the author is simple and the experiment proves its huge speed improvement compared to previous works.\n2. Extensive experiments support the author's claim about the speed very well.\n\nWeakness:\n1. The ablation study section is too simple, only showing limited results and lacking a more in-depth analysis.\n2. The authors did not provide enough explanation about why FastJAM is so fast.\n3. Please refer to the \"Questions\" for other weaknesses.\n\nQUESTIONS:\n1. In Line 278, the authors said they replaced the RoMA with LoFTR in the ablation study, but as far as I know, LoFTR is a keypoint-free matching method, how to replace RoMA with it to extract the spare KP sets (as described in Line 147)? Also, both RoMA and LoFTR are not designed for cross-instance matching, why LoFTR show more limitations than RoMA in the JA tasks?\n2. Theoretically, the semantic matching method seems to be more suitable for JA. Have the authors tried to replace RoMA with other cross-instance semantic matching methods?\n3. In Line 210, the author said \"We have found that only checking for horizontal flips is sufficient\". Do you have ablation study results to support it?\n4. In Line 259, can you provide some figures to show the \"ambiguity\" of symmetric object \"bicycles\"?\n5. In Figure 5, it seems that SpaceJAM only uses ~85% of total GPU memory when number of images is 40. Why the authors said \"the PCA preprocessing in SpaceJAM fails to run beyond N = 40 due to memory constraints\" in Line 275.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper considers the joint alignment problem, which is given a collection of images find consistent warps between them. These images might contain objects of the same class, but different instances (e.g. images of different cats), and in different poses. The authors propose to model the warps using homographies and in particular each image is associated with a homography going from the image to a shared canonical space. Following the Inverse Compositional (IC) approach, the relative transformations can then be found by composing a homography for an image with the inverse from another image. Between each pair of images a dense feature matcher is used to find pairwise correspondences which are used to constrain the relative transformations. The homographies themselves are predicted by a GNN that operates on the keypoints in each image, and is trained/fit independently to each image collection. The method is compared to a couple of other alignment approaches and performs well, in particular it is significantly faster compared to previous work.\n\nSTRENGTHS AND WEAKNESSES:\n# Overall\nOverall I like the general setup of splitting the problem into predicting pairwise correspondences, followed by a more global optimization that figures out the warps jointly. I am not an expert in the area, but the experiments seem reasonable and show that the proposed approach achieves similar or better accuracy at much lower runtime.\n\n# Presentation and clarity\nI found the paper easy to read and believe I have a good understanding of how it works. Though some details might be missing, the paper could probably mostly be reproduced.\n\n# Using RoMa matches\nThe paper use RoMa (CVPR'24) for finding pairwise matches between the images. I was a bit surprised that this works, considering RoMa was not specifically trained for this kind of cross-instance matching (e.g. matching different birds etc.), but rather match the same scene under different conditions (viewpoint changes etc.). It would be nice to have some more discussion about this. Though I guess the DINOv2 back-end in RoMa might allow for some more semantic correspondences. \n\n# Missing ablation motivating the GNN\nAs I understood the paper, there is a test-time trained GNN which predicts the homographies. This is trained by minimizing the transfer error between images. It seems that natural baseline here would be to directly optimize for the homographies, i.e. only having $\\theta_1,\\dots,\\theta_n \\in \\mathbb{R}^8$ as the optimizable parameters. Showing that this does not work would motivate the complexity of the GNN.\n\nQUESTIONS:\n1. Did you try optimizing the homographies directly, i.e. without the GNN? If so, how did it work?\n\n2. For the homographies there is a gauge freedom where you can change \"coordinate system\" in the canonical space. Did you try regularizing or fixing this? Does it ever happen that the canonical space is very skewed/distorted?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

comments: SUMMARY:
The paper - FastJam - introduces a rapid, graph-based technique for joint image alignment that relies on pairwise matches and a graph neural network to swiftly predict homography parameters. It surpasses existing methods in alignment quality while drastically cutting down computation time from hours or minutes to seconds. It builds upon extensive prior work in the field, drawing inspiration from early techniques like congealing and least-squares congealing, especially integrating ideas from inverse-composition. The approach achieves state-of-the-art results in joint alignment, with a tenfold speed increase in computation time compared to current leading methods.

STRENGTHS AND WEAKNESSES:
The technical novelty of the approach seems low, as it heavily relies upon ideas from SpaceJam [3] with the exception that they rely on key points (KPs) rather than dense features (e.g. DINO). Further, the approach is dependent upon an external image matcher for the initial correspondences. The big advantage over SpaceJam seems to be the computational speed, which is considerable. This empirical result seems to be the most impressive part of the paper.

QUESTIONS:
Looking at the results in Table 2, there definitely seems to be categories where SpaceJam significantly outperforms FastJam. Some insights into why some categories do well, and others do not would be useful to better understand the utility of the approach? The authors offer up bicycles as a problem category. Is there a way to know ahead of time which categories will struggle with FastJam?
Another question for the authors is what practical applications are now possible thanks to the considerable speedup of FastJam over SpaceJam? Discussion or event some results on this question would be great.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-03