We have studied ultraviolet images of 40 Green Pea galaxies and 15 local Lyman Break Galaxy Analogs to understand the relation between Ly \alpha photon escape and central UV photometric properties . We measured star formation intensity ( SFI , star formation rate per unit area ) from the central 250 pc region ( S _ { 250 pc } ) using COS/NUV images from the Hubble Space Telescope . The measured S _ { 250 pc } of our sample Green Peas ranges from 2.3–46 M _ { \sun } year ^ { -1 } { kpc ^ { -2 } } , with a geometric mean of 15 M _ { \sun } year ^ { -1 } { kpc ^ { -2 } } and a standard deviation of 0.266 dex , forming a relatively narrow distribution . The Lyman Break Galaxy Analogs show a similarly narrow distribution of S _ { 250 pc } ( 0.271 dex ) , though with a larger mean of 28 M _ { \sun } year ^ { -1 } { kpc ^ { -2 } } . We show that while the Ly \alpha equivalent width ( EW ( Ly \alpha ) ) and the Ly \alpha escape fraction ( f ^ { Ly \alpha } _ { esc } ) are not significantly correlated with the central SFI ( S _ { 250 pc } ) , both are positively correlated with the ratio of surface brightness to galaxy stellar mass ( S _ { 250 pc } / M _ { star } ) , with correlation coefficients ( p -values ) of 0.702 ( 1 \times 10 ^ { -8 } ) and 0.529 ( 5 \times 10 ^ { -4 } ) with EW ( Ly \alpha ) and f ^ { Ly \alpha } _ { esc } , respectively . These correlations suggest a scenario where intense central star formation can drive a galactic wind in galaxies with relatively shallow gravitational potential wells , thus clearing channels for the escape of Ly \alpha photons .