{
  "abstract": "Astronomical maps made with different tracers are not expected to have identical morphology. Excitation, optical depth, chemistry, radiation, and ISM phase alter the response of a tracer, and the resulting differences can depend on both position and spatial scale. We propose scale-vector alignment, a scale-aware method based on Constrained Diffusion Decomposition (CDD). CDD decomposes an image into localized scale components; at each position, their amplitudes define a scale vector that describes how the measured intensity is distributed over spatial scale. We define the pixel-wise similarity $\\Spix(x,y)$ as the normalized alignment of two local scale vectors. The normalization removes the overall amplitude, so $\\Spix$ compares relative scale composition rather than absolute flux. We also define the scale-wise similarity $\\Sscale(l)$ by comparing the two CDD component maps at each spatial scale. Spatial shifts are used to construct an empirical shifted reference distribution for $\\Spix$. In Orion~A, the tracer with the highest similarity to the dust-derived column-density map changes from $^{12}$CO to $^{13}$CO to C$^{18}$O toward higher column density. In NGC~6334I(N), the line--continuum similarity decreases locally around the brightest compact structures, where radiative-transfer effects can alter the observed line morphology. In NGC~3627, CO is most similar to 21~$μ$m emission, and $\\Sscale$ reaches its maximum at an intermediate sub-kpc scale. The method measures where two tracers have similar multiscale structure and at which scales their spatial distributions agree. The implementation is publicly available at https://github.com/meng-ke/Scale-Vector-Alignment.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24304",
  "author_total": 4,
  "authors": [
    {
      "name": "Mengke Zhao"
    },
    {
      "name": "Guang-Xing Li"
    },
    {
      "name": "Keping Qiu"
    },
    {
      "name": "Shanghuo Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9qt5hgcmmg7gq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24304",
  "fulltext_url": null,
  "id": "9qt5hgcmmg7gq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24304",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.GA"
    ],
    [
      "arxiv",
      "astro-ph.IM"
    ],
    [
      "arxiv",
      "cs.CV"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3103|Astrophysics and Star Formation Studies"
    ]
  ],
  "openalex": "W7213996125",
  "pdf_url": "https://arxiv.org/pdf/2609.24304",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9qt5hgcmmg7gq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24304",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24304"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Scale-Vector Alignment: A Scale-Aware Framework for Spatially Resolved Morphological Similarity in Astronomical Images",
  "title_text": "Scale-Vector Alignment: A Scale-Aware Framework for Spatially Resolved Morphological Similarity in Astronomical Images",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/9qt5hgcmmg7gq",
  "venue": "arXiv",
  "versions": []
}