Intracranial hemorrhage (ICH) is associated with pathologies such as hemorrhagic stroke and traumatic brain injury. Multi-detector CT is the current front-line imaging modality for detecting ICH (fresh blood contrast 40-80 HU, down to 1 mm). Flat-panel detector (FPD) cone-beam CT (CBCT) offers a potential alternative with a smaller scanner footprint, greater portability, and lower cost potentially well suited to deployment at the point of care outside standard diagnostic radiology and emergency room settings. Previous studies have suggested reliable detection of ICH down to 3 mm in CBCT using high-fidelity artifact correction and penalized weighted least-squared (PWLS) image reconstruction with a post-artifact-correction noise model. However, ICH reconstructed by traditional image regularization exhibits nonuniform spatial resolution and noise due to interaction between the statistical weights and regularization, which potentially degrades the detectability of ICH. In this work, we propose three regularization methods designed to overcome these challenges. The first two compute spatially varying certainty for uniform spatial resolution and noise, respectively. The third computes spatially varying regularization strength to achieve uniform "detectability," combining both spatial resolution and noise in a manner analogous to a delta-function detection task. Experiments were conducted on a CBCT test-bench, and image quality was evaluated for simulated ICH in different regions of an anthropomorphic head. The first two methods improved the uniformity in spatial resolution and noise compared to traditional regularization. The third exhibited the highest uniformity in detectability among all methods and best overall image quality. The proposed regularization provides a valuable means to achieve uniform image quality in CBCT of ICH and is being incorporated in a CBCT prototype for ICH imaging.