AMICO: Multi-Domain Research Frameworks

• AMICO is a research acronym with multiple definitions across astrophysics, computer vision, and AI, each employing distinct technical methodologies.
• In astrophysics, it models galaxy distributions using probabilistic membership assignment and optimal matched filters to detect clusters with high purity and calibrated amplitudes.
• In computer vision and autonomous systems, AMICO supports amodal instance composition, event-driven autonomy, and AI-enabled pedagogy with state-of-the-art performance.

AMICO is a research acronym used for several technically unrelated systems. In astrophysics and cosmology it most often denotes the Adaptive Matched Identifier of Clustered Objects, a matched-filter framework for detecting galaxy clusters and groups in photometric surveys and assigning probabilistic galaxy memberships (Bellagamba et al., 2017). In computer vision it denotes Amodal Instance Composition, a pipeline for composing incomplete or coarsely segmented objects into scenes through amodal shape prediction, content completion, and neural blending (Zhuang et al., 2022). More recent work also uses Amico for an event-driven Rust/WebAssembly framework for persistent autonomous agents (Yang et al., 19 Jul 2025) and for an AI-enabled pedagogical accompaniment system organized around bounded “micro-mediations” and the dual modes AmicoMio and AmicoTuo (Benedetti, 20 May 2026).

1. Terminological scope

The acronym has acquired distinct meanings across different research communities. The following usages are explicitly documented in the cited literature.

Expansion	Domain	Representative source
Adaptive Matched Identifier of Clustered Objects	Galaxy-cluster detection and cosmology	(Bellagamba et al., 2017)
Amodal Instance Composition	Computer vision and image composition	(Zhuang et al., 2022)
Amico	Persistent and embedded autonomy	(Yang et al., 19 Jul 2025)
Amico	AI-enabled pedagogical accompaniment	(Benedetti, 20 May 2026)

Within the astrophysical literature, AMICO forms a coherent methodological lineage. It begins with the optimal-filter cluster finder itself (Bellagamba et al., 2017), then extends to survey catalog production and calibration in KiDS, COSMOS, miniJPAS, and COSMOS-Web (Maturi et al., 2018). It is further specialized for weak-lensing detection in AMICO-WL, which ports the matched-filter logic from galaxy counts to shear data (Trobbiani et al., 27 Jan 2025).

Outside astronomy, the acronym does not designate a common platform or shared codebase. The computer-vision, autonomous-agent, and educational uses are independent constructions with different objectives, architectures, and evaluation protocols (Zhuang et al., 2022).

2. Adaptive Matched Identifier of Clustered Objects

In its original and most extensively developed sense, AMICO is an optimal matched-filter algorithm for cluster detection in photometric surveys. It models the observed galaxy distribution as a cluster signal plus a field component, and estimates a detection amplitude on a grid in sky position and redshift. In the 2017 formulation, the amplitude is the minimum-variance unbiased linear estimator of the cluster template normalization, and the signal-to-noise ratio is defined by the corresponding estimator variance (Bellagamba et al., 2017).

For survey applications, the discrete estimator is written as

$$A(\vec{\theta}_c, z_c) = \alpha^{-1}(z_c)\, \sum_{i=1}^{N_\text{gal}} \frac{C(z_c;\,\vec{\theta}_i-\vec{\theta}_c, m_i)\,p_i(z_c)}{N(m_i, z_c)} - B(z_c),$$

where $C$ is the cluster model, $N$ the field distribution, and $p_i(z_c)$ the photometric-redshift posterior evaluated at the trial redshift (Maturi et al., 2018). The formalism incorporates full photometric-redshift PDFs rather than hard redshift assignments, and the filter normalization and variance are explicitly corrected for photo-$z$ statistics through the $q_1$ and $q_2$ kernels in later implementations (Maturi et al., 2018).

A distinctive feature of AMICO is the explicit probabilistic treatment of membership. For a detection $j$, galaxy $i$ is assigned

$$P_i(j) = P_{f,i}\,\frac{A_j\,C(\vec{\theta}_i-\vec{\theta}_j, m_i)\,p_i(z_j)}{A_j\,C(\vec{\theta}_i-\vec{\theta}_j, m_i)\,p_i(z_j) + N(m_i, z_j)},$$

with $C$0 the residual field probability after previous assignments (Maturi et al., 2018). These probabilities support both cluster characterization and iterative deblending: once a candidate is identified, its imprint is removed from the amplitude map, allowing lower-significance or partially aligned structures to emerge (Bellagamba et al., 2017).

AMICO’s cluster observables include the amplitude $C$1, the apparent richness $C$2, and the intrinsic richness

$C$3

which is constructed to be nearly redshift independent under the adopted model (Maturi et al., 2018). In the original validation on simulations, the mass–amplitude relation was consistent across $C$4, with logarithmic slope $C$5 and logarithmic scatter $C$6, while false detections became negligible at $C$7 (Bellagamba et al., 2017).

A notable methodological choice in KiDS applications is the deliberate avoidance of explicit color cuts or red-sequence priors. AMICO instead uses positions, magnitudes, and photometric-redshift posteriors, thereby aiming for a selection function less sensitive to cluster color composition (Maturi et al., 2018). This design choice remains central to later wide-field and deep-field deployments.

3. Survey catalogs, selection functions, and high-redshift deployments

AMICO has been used to build large optical cluster and group catalogs with explicit purity, completeness, and observable-error calibration from data-driven mocks. In KiDS-DR3, the first AMICO catalog contained 7988 candidate galaxy clusters over an effective area of 377 deg$C$8 in the range $C$9, selected at $N$0, with purity approaching 95% over the full redshift range (Maturi et al., 2018). The catalog included a companion galaxy-membership table with probabilistic associations.

The KiDS-DR4/KiDS-1000 cosmological catalog substantially enlarged the sample. Using a homogeneous galaxy selection $N$1, AMICO identified 23965 clusters over about 839 deg$N$2 in $N$3 with $N$4, and calibrated the cluster redshift bias against GAMA spectroscopy, obtaining $N$5 after correction (Maturi et al., 18 Jul 2025). The same work introduced border-handling modifications, detection-level redshift PDFs, ODDS values, and blinded variants of the selection function to support cosmological analyses (Maturi et al., 18 Jul 2025).

Deep-field applications pushed the algorithm into lower-mass and higher-redshift regimes. In AMICO-COSMOS, three independent single-band runs in $N$6, $N$7, and $N$8 produced 1269 candidates with $N$9 and 666 with $p_i(z_c)$0, extending to $p_i(z_c)$1; 622 candidates were assigned X-ray properties, enabling calibration of AMICO mass proxies against X-ray-inferred masses (Toni et al., 2023). In COSMOS-Web, AMICO was applied to JWST-based photometry over an effective area of about 0.45 deg$p_i(z_c)$2, yielding 1678 groups up to $p_i(z_c)$3, with 756 detections at 80% purity and more than 500 groups with spectroscopic confirmation (Toni et al., 15 Jan 2025). At $p_i(z_c)$4, the detections are interpreted as protocluster cores or virialized substructures rather than complete extended protoclusters (Toni et al., 15 Jan 2025).

Narrow-band photometric data in miniJPAS provided a different operating regime. There, AMICO detected 80, 30, and 11 systems at $p_i(z_c)$5, $p_i(z_c)$6, and $p_i(z_c)$7, respectively, in $p_i(z_c)$8, down to $p_i(z_c)$9, and the cluster redshift uncertainty improved to $z$0 when using the median redshift of high-probability members (Maturi et al., 2023). The miniJPAS study also introduced a stellar-mass-weighted proxy $z$1 made possible by J-PAS SED fitting (Maturi et al., 2023).

A common feature across these deployments is the use of SinFoniA or related data-driven mock-generation schemes to estimate purity, completeness, and observable scatter directly from survey data rather than from fully synthetic cosmological realizations (Maturi et al., 2018). This approach is intended to preserve masks, photo-$z$2 uncertainties, depth variations, and galaxy clustering in the estimated selection function.

4. Cosmological exploitation and weak-lensing extensions

AMICO catalogs have been used in multiple cosmological analyses based on counts, clustering, stacked weak lensing, halo bias, and splashback. A joint counts-plus-weak-lensing study of the KiDS-DR3 catalog modeled 3652 clusters with $z$3 over 377 deg$z$4 and obtained

$z$5

while simultaneously constraining the mass–richness relation and intrinsic scatter (Lesci et al., 2020). A complementary clustering analysis of 4934 clusters with $z$6 in $z$7 yielded

$z$8

and, with Planck-fixed cosmology, constrained the mass–richness normalization to $z$9 (Lesci et al., 2022).

The KiDS-1000 counts-plus-lensing analysis increased statistical power and systematic control. Using about 8000 clusters over 839 deg$q_1$0 up to $q_1$1, and explicitly marginalizing over impurities, photo-$q_1$2 biases, projection, orientation, baryons, miscentring, halo-mass-function uncertainty, and super-sample covariance, it obtained

$q_1$3

with intrinsic scatter $q_1$4 in the $q_1$5 relation, corresponding to an average mass precision of 8% (Lesci et al., 18 Jul 2025).

Weak-lensing studies have also been used to interrogate more specific aspects of AMICO-selected halos. For 6925 KiDS-DR3 clusters, the comparison between the weighted-mean $q_1$6 shear estimator and an $q_1$7 regression estimator found a small but significant estimator-dependent bias in the excess surface density, with full-stack proportional difference parameter $q_1$8; the inferred $q_1$9–$q_2$0 scaling had slope $q_2$1 for both estimators, but different normalizations (Smit et al., 2021). Another analysis of 6962 AMICO clusters modeled the splashback feature with the DK14 profile and found $q_2$2, smaller than low-accretion-rate predictions for mass-selected halos, which the authors interpret as evidence for selection effects in optically selected samples (Giocoli et al., 2024). A halo-bias analysis over 6961 weak-lensing stacks measured the mean values

$q_2$3

and, with a Tinker et al. prior on the bias–mass relation and fixed $q_2$4, inferred $q_2$5 (Ingoglia et al., 2022).

The most direct weak-lensing generalization is AMICO-WL, which replaces galaxy-count filtering with a shear matched filter. Its Fourier-space kernel is

$q_2$6

where $q_2$7 is an NFW shear template and $q_2$8 is the total noise power spectrum, including shape noise and large-scale-structure shear (Trobbiani et al., 27 Jan 2025). AMICO-WL adds purity-targeted thresholding by comparing positive and negative E-mode peaks and uses iterative subtraction to clean blended detections. On a Euclid-like $q_2$9 mock, and at a target purity of about 70%, a foreground-removal cut $j$0 doubled completeness from 6.5% to 13.0% relative to the full source catalog and significantly reduced spurious detections (Trobbiani et al., 27 Jan 2025).

5. Amodal Instance Composition and the autonomous-agent framework

In computer vision, AMICO stands for Amodal Instance Composition. It addresses image composition when source objects are partially occluded, incompletely observed, or only coarsely segmented. The framework combines three modules: an amodal shape predictor $j$1, a content completion network $j$2, and a neural composition model $j$3 that takes separate foreground and background inputs and predicts RGBA layers with an explicit alpha mask (Zhuang et al., 2022).

The key technical idea is the separation of foreground and background representations. Rather than pre-compositing the object into the scene and predicting only RGB corrections, AMICO predicts a harmonized foreground image $j$4 and a blending mask $j$5, with final composite

$j$6

This design is intended to repair coarse boundaries, remove stray pixels, and harmonize color and illumination (Zhuang et al., 2022). The content-completion module uses only visible object pixels and masks, with a two-stage coarse-to-refine generator using gated convolutions and contextual attention, while the composition module is trained self-supervised through background inpainting and photorealistic color transfer (Zhuang et al., 2022).

Quantitatively, the method reported state-of-the-art results on COCOA and KINS. For object completion on 500 test images, the COCOA results were L1 37.11, PSNR 31.91, and SSIM 0.985, while the KINS results were L1 34.99, PSNR 26.93, and SSIM 0.965 (Zhuang et al., 2022). In composition with coarse masks, the KINS benchmark showed PSNR/SSIM/LPIPS of (38.60, 0.996, 0.004), (37.44, 0.996, 0.007), and (37.28, 0.996, 0.008) across the three object-area-ratio buckets, outperforming Poisson Blending, Deep Image Blending, and DoveNet (Zhuang et al., 2022). On COCOA amodal mask prediction, the method achieved mIoU 0.820 (Zhuang et al., 2022).

A separate 2025 work uses Amico for an event-driven framework for persistent and embedded autonomy. This system is implemented in Rust, deployable through WebAssembly, and organized into Environment, Interaction, AI Agent, and Engine layers (Yang et al., 19 Jul 2025). It decouples event production from action selection through a central event queue and supports plugin-based LLM and RAG integration. The WebShop evaluation reported average reward 0.61 for event-driven Amico, compared with **0.47