We explore the structure of the spin-1/2 flavor-octet baryons (hyperons) through their electromagnetic transverse densities. The transverse densities describe the distribution of charge and magnetization at fixed light-front time and enable a spatial representation of the baryons as relativistic systems. At peripheral distances b~1/M_pi the transverse densities are computed using a new method that combines chiral effective field theory and dispersion analysis. The peripheral isovector densities arise from two-pion exchange, which includes the rho-meson resonance through elastic unitarity. The isoscalar densities are estimated from vector meson exchange (omega, phi). We find that the pion cloud in the charged Sigma hyperons is comparable to the nucleon, while in the Xi it is suppressed. The Lambda-Sigma^0 transition density is pure isovector and represents a clear manifestiation of peripheral two-pion dynamics.
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