a　variable-rate　image　compression　conditioned　on　a　pixel-wise　quality　map　achieved　an　outstanding　rate-distortion　trade-off　compared　to　the　approaches　based　on　multiple　models.　However,　it　is　hard　to　find　an　appropriate　pixel-wise　quality　map　for　the　target　rate,　and　the　hyperprior　is　only　used　to　capture　the　probability　distribution　of　latent　representation,　which　causes　its　inefficient　utilization.　In　this　paper,　we　propose　a　variable-rate　image　compression　network　with　shallow　to　deep　hyperprior　trained　with　a　uniform　quality　map　generated　by　the　trade-off　parameter　1　of　the　rate-distortion　optimization.　The　shallow　to　deep　hyperprior　structure　enables　the　shallow　hyperprior　to　improve　the　reconstruction　image　quality　by　compensating　the　latent　representation　as　side　information　while　estimating　its　distribution.　Inspired　by　the　fact　that　a　uniform　quality　map　can　continuously　scale　the　latent　representations　with　the　continuous　change　of　1,　we　build　an　individual　R-?　model,　which　characterizes　the　relation　between　R　and　1.　With　this　R-?　model,　we　can　perform　precise　and　continuous　rate　control　in　the　compression.　To　the　best　of　our　knowledge,　this　R-?　model　is　the　first　work　to　propose　a　continuous　rate　control　for　variable-rate　learning-based　image　compression.　Meanwhile,　benefiting　from　the　uniform　values　of　the　map,　our　method　can　handle　various　distortion　metrics,　such　as　MS-SSIM.　Extensive　experimental　results　show　that　the　proposed　model　has　achieved　SOTA　compression　performance　in　variable-rate　learning-based　methods,　achieving　comparable　compression　performance　compared　with　VVC.　Furthermore,　the　rate　control　of　our　scheme　shows　very　high　accuracy.