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We present a solution to image-based cell counting with dot annotations for both 2D and 3D cases. Current approaches have two major limitations: 1) inability to provide precise locations when cells overlap; and 2) reliance on costly labeled data. To address these two issues, we first adopt the inverse distance kernel, which yields separable density maps for better localization. Second, we take advantage of unlabeled data by self-supervised learning with focal consistency loss, which we propose for our pixel-wise task. These two contributions complement each other. Together, our framework compares favorably against stateof- the-art methods, including methods using full annotations on 2D and 3D benchmarks, while significantly reducing the amount of labeled data needed for training. In addition, we provide a tool to expedite the labeling process for dot annotations. Finally, we make the source code and labeling tool publicly available. 

ABSTRACT Standard stellar evolution theory poorly predicts the surface abundances of chemical species in low-mass, red giant branch (RGB) stars. Observations show an enhancement of p–p chain and CNO cycle products in red giant envelopes, which suggests the existence of non-canonical mixing that brings interior burning products to the surface of these stars. The 12C/13C ratio is a highly sensitive abundance metric used to probe this mixing. We investigate extra RGB mixing by examining: (1) how 12C/13C is altered along the RGB, and (2) how 12C/13C changes for stars of varying age and mass. Our sample consists of 43 red giants, spread over 15 open clusters from the Sloan Digital Sky Survey’s APOGEE DR17, that have reliable 12C/13C ratios derived from their APOGEE spectra. We vetted these 12C/13C ratios and compared them as a function of evolution and age/mass to the standard mixing model of stellar evolution, and to a model that includes prescriptions for RGB thermohaline mixing and stellar rotation. We find that the observations deviate from standard mixing models, implying the need for extra mixing. Additionally, some of the abundance patterns depart from the thermohaline model, and it is unclear whether these differences are due to incomplete observations, issues inherent to the model, our assumption of the cause of extra mixing, or any combination of these factors. Nevertheless, the surface abundances across our age/mass range clearly deviate from the standard model, agreeing with the notion of a universal mechanism for RGB extra mixing in low-mass stars.