The two separate incidents took place on Sunday in Bishop Crispian Way in Portsmouth.
The first incident took place at around 5.55am and the second at around 11.40pm.
A statement from Hampshire Constabulary said: ‘We have been making a number of enquiries as part of this investigation and are now in a position to release this image and ask for the public’s help. We want to identify the person pictured as they may have vital information that could assist us.
‘Officers will continue to patrol and conduct enquiries in this area in the evenings and early mornings while the investigation continues.’
Anyone who recognises the man is urged to call 101 and quote reference 44200268631.