Beyond Colors: Probing Redshifts from Galaxy Morphology in Single-band Images with ViT-MDNz

Abstract To address the challenge of estimating redshifts when only single-band images are available, this study introduces a deep learning model named Vision Transformer (ViT)-MDNz. Leveraging robust statistical priors learned from large-scale data concerning the correlation between redshift and morphology, the model can directly estimate redshifts and their associated uncertainties from single-band galaxy images. It integrates a ViT to extract deep morphological features and a mixture density network (MDN) to predict the full redshift probability density function (PDF). Trained and evaluated on approximately 300,000 single-band images from the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys (DESI-LS), the model achieves a normalized median absolute deviation σ NMAD = 0.034 and an outlier fraction f out = 2.6% in the r band for redshifts up to z ≲ 1. Evaluations using probability integral transform and continuous ranked probability score confirm that the predicted PDFs are well calibrated and closely match the true distribution. These results demonstrate that competitive redshift estimates can be obtained using morphological features alone, and that incorporating color information further enhances the accuracy and robustness of the estimation. Therefore, ViT-MDNz provides a practical approach for redshift estimation of galaxy samples with limited photometric band coverage, contributing to improved completeness and usability of redshift catalogs for future large-scale surveys such as DESI and Legacy Survey of Space and Time.