DeepAP: Deep Learning for Aperture Photometry

• The paper introduces DeepAP, a two-stage deep learning framework that uses a Vision Transformer for feasibility assessment and a ResNet-18 regressor for optimal aperture size prediction.
• DeepAP enhances signal-to-noise ratios and reduces computational load by automating aperture photometry in crowded fields where traditional methods are unreliable.
• Experiments demonstrate that DeepAP achieves near-exhaustive enumeration performance with a dramatic speed-up, making it highly suitable for large-scale time-domain surveys.

DeepAP is a two-stage deep learning framework for aperture photometry that targets automatic light-curve extraction under conditions where classical procedures become inefficient or unreliable, particularly in crowded fields and large survey pipelines. It addresses two operational questions: whether aperture photometry is feasible for a given source at all, and, if so, which three radii should be used for the source aperture and sky-background annuli. The method combines a Vision Transformer for feasibility assessment with a ResNet-18 regressor for aperture size prediction, with the stated objective of improving photometric quality, especially signal-to-noise ratio, while reducing the computational burden of exhaustive aperture enumeration (Du et al., 5 Aug 2025).

1. Problem formulation and motivation

Aperture photometry is described as a fundamental technique for obtaining high-precision light curves in optical survey projects such as Tianyu, but its effectiveness is limited in crowded fields. The paper identifies several specific deficiencies in traditional practice. The growth curve method optimizes only the inner source aperture rather than the full three-aperture configuration used here; it is typically applied per image, so the selected aperture may not generalize across the night; nearby stars can cause the aperture to expand and contaminate the target flux; and, in crowded regions, no uncontaminated aperture may exist within the tested range, making aperture photometry effectively infeasible (Du et al., 5 Aug 2025).

These constraints are especially consequential for large robotic and time-domain surveys, where manual parameter tuning is not operationally viable and throughput is a first-order requirement. DeepAP is therefore framed not merely as an aperture optimizer but as a pipeline-level automation mechanism that performs feasibility screening before regression. This design reflects the practical observation that aperture selection is meaningful only after contamination risk has been adjudicated.

2. Two-stage architecture

DeepAP is organized into two sequential stages. The first stage is a ViT-based feasibility classifier operating on a $128\times128$ source cutout. It assigns a binary label: $1$ for sources feasible for aperture photometry and $0$ for sources deemed infeasible because of crowding, severe occlusion, or contamination. The second stage is a ResNet-18-based regression model that predicts three real-valued radii, $(r_1,r_2,r_3)$, corresponding to the inner aperture radius, middle aperture radius, and outer aperture radius (Du et al., 5 Aug 2025).

These three radii define the source aperture and the two boundaries of the sky-background annulus. The paper emphasizes that the regression stage is intended to predict apertures that maximize photometric quality, particularly the signal-to-noise ratio. This division of labor is central to the framework: the transformer handles a discrete feasibility decision, while the convolutional regressor addresses continuous aperture estimation.

The feasibility stage uses a ViT with a $128\times128\times1$ input, patch size $P=16$, and $N=64$ patches. A learnable $[CLS]$ token and positional embeddings are added, and the resulting sequence is processed through Transformer encoder blocks with multi-head self-attention, MLP feed-forward layers, residual connections, and layer normalization. The final classification token is mapped to two class probabilities through a softmax head (Du et al., 5 Aug 2025).

The regression stage uses a standard ResNet-18 backbone configured for three-output regression. Its architecture consists of an initial $7\times7$ convolution and max pooling, several residual blocks with skip connections, global average pooling, and a final fully connected layer with three outputs. The regression loss is mean squared error (Du et al., 5 Aug 2025).

3. Dataset construction and labeling protocol

The authors collected 522 images from Muguang Observatory and retained 506 high-quality images for analysis. For every detected source, the model input is a $128\times128$ pixel cutout centered on that source. The labels for the aperture-size task were produced by brute-force enumeration over candidate aperture triples, whereas the feasibility labels were derived from whether an uncontaminated aperture configuration exists (Du et al., 5 Aug 2025).

The aperture search space is explicitly defined. For the $1$0-th source, the inner aperture radius satisfies

$1$1

The middle aperture radius satisfies

$1$2

The outer aperture radius satisfies

$1$3

For each triple $1$4, a light curve is extracted and its SNR is computed (Du et al., 5 Aug 2025).

The SNR of the light curve is defined as

$1$5

where $1$6 and $1$7 are the weighted mean and weighted standard deviation of the light curve for the $1$8-th source, and the weights are inversely proportional to the squared photometric uncertainty from sep (Du et al., 5 Aug 2025).

Feasibility is defined geometrically by the existence of an uncontaminated aperture configuration. A source is feasible if there exists a set of apertures such that no neighboring source contaminates the photometric apertures, using a $1$9-FWHM margin intended to make contamination negligible. This explicit criterion is important because it makes the classifier’s target operational rather than subjective: feasibility is tied to the existence of a contamination-free three-aperture configuration in the prescribed search space.

4. Training behavior and quantitative performance

For feasibility assessment, the ViT is trained with binary cross-entropy. On the test set, it achieves an ROC AUC of $0$0, precision $0$1, recall $0$2, F1 $0$3, and average precision $0$4. The reported confusion matrix is $0$5, $0$6, $0$7, and $0$8. Inference speed for this stage is $0$9 ms per batch of $(r_1,r_2,r_3)$0 images, or about $(r_1,r_2,r_3)$1 ms per image (Du et al., 5 Aug 2025).

For aperture-size prediction, the ResNet-18 regressor is trained for $(r_1,r_2,r_3)$2 epochs with batch size $(r_1,r_2,r_3)$3, Adam optimizer, and learning rate $(r_1,r_2,r_3)$4. The test loss converges to about $(r_1,r_2,r_3)$5, which the authors interpret as an average aperture prediction error of approximately

$(r_1,r_2,r_3)$6

They further note that this test loss is better than a simple discretization bound from the exhaustive grid, estimated as

$(r_1,r_2,r_3)$7

and use this to argue that the model predicts with finer granularity than the brute-force search grid (Du et al., 5 Aug 2025).

This finer-granularity point is methodologically significant. The labels are generated by enumeration over a discretized aperture grid, but the regressor outputs continuous radii. A plausible implication is that the regression model is not constrained to reproduce the coarseness of the labeling grid and can, in some cases, interpolate to aperture choices that improve downstream SNR.

5. Comparison with growth-curve baselines and exhaustive enumeration

The paper compares the regression stage against three reference procedures: GCS, defined as growth curve on the stacked image; GCF, defined as growth curve on the first calibrated image; and exhaustive enumeration, which is also the labeling procedure. On the common sample of 587 sources, the reported median SNRs are $(r_1,r_2,r_3)$8 for ResNet-18, $(r_1,r_2,r_3)$9 for GCS, $128\times128\times1$0 for GCF, and $128\times128\times1$1 for exhaustive enumeration (Du et al., 5 Aug 2025).

These results imply that exhaustive enumeration remains the strongest median-SNR baseline overall, but the learned regressor is close while being dramatically cheaper computationally. Relative to classical growth-curve methods, the regressor is substantially more adaptive. It outperforms GCS for $128\times128\times1$2 of sources and GCF for $128\times128\times1$3 of sources. The paper further states that the model behaves adaptively: for bright sources, it tends to resemble stacked-image growth-curve behavior, while for faint sources it tends to resemble the smaller apertures selected by first-image growth curves (Du et al., 5 Aug 2025).

A particularly notable result is that for 13 targets, ResNet-18 produces a higher SNR than the exhaustive-enumeration labels. The paper attributes this to finer output granularity than the enumeration step size and to limitations in the enumeration range, especially for faint stars where the optimal outer radius can lie beyond the search range. This directly counters a common misconception that DeepAP is only a fast surrogate for brute-force search. The reported result suggests that, under the defined search procedure, the learned regressor can surpass the label generator in some cases.

6. Runtime, deployment setting, and limitations

A central empirical claim is the runtime reduction achieved by integrating ResNet with the ViT network. DeepAP has a median total processing time of $128\times128\times1$4 ms for a batch of $128\times128\times1$5 images, corresponding to a speed-up of approximately $128\times128\times1$6 times relative to exhaustive aperture size enumeration (Du et al., 5 Aug 2025).

This speed profile is the basis for the framework’s positioning in large automated survey pipelines, particularly Tianyu and LSST. The method is presented as especially useful in crowded fields, under variable seeing and background conditions, in high-throughput transient or time-domain processing, and in settings where manual aperture tuning is impossible. The paper argues that DeepAP can extend the applicability of aperture photometry to cases that are usually considered too crowded or too messy for conventional methods (Du et al., 5 Aug 2025).

The paper also delineates several caveats. The training data come from one telescope-camera setup under specific observing conditions, so retraining or fine-tuning will likely be necessary for other telescopes or observing regimes. The method depends on the chosen threshold for the ViT feasibility classifier, making false-positive control important. A ViT false positive does not necessarily mean the labels are wrong, because some such cases still fail in the aperture-prediction stage. For relative photometry, aperture sizes should ideally remain consistent within a group of stars. The authors suggest transfer learning or domain adaptation, GPU acceleration to expand the exhaustive-search range and improve labels, and the use of ensemble images as input so the model can jointly decide grouping and apertures for relative photometry (Du et al., 5 Aug 2025).

Taken together, these points place DeepAP in a specific methodological niche. It is neither a universal replacement for all photometric workflows nor a purely heuristic accelerator. Rather, it is a learned decision-and-regression pipeline whose main contribution is the combination of feasibility assessment and aperture optimization under survey-scale throughput constraints.