Connect related ideas
An introductory participle clause can add a related action or description: 'Carrying a box, Noor opened the door with her elbow.' The -ing clause describes Noor's action. A past participle clause often has passive meaning: 'Written in large letters, the sign was easy to read.' The sign received the writing.
Make the subject fit
For the introductory clauses practised here, the understood subject must match the subject of the main clause. In 'Walking into the hall, the paintings caught my attention', the wording makes the paintings seem to be walking. Name the walker immediately after the comma, or write a full clause that names both subjects.
Show an earlier action
Having plus a past participle marks an action completed before the main one: 'Having checked the tickets, Noor opened the doors.' Use it when that sequence matters. If the order, reason, or subject is unclear, use a full clause with after, because, or while. Do not compress a sentence at the cost of its meaning.
See it in practice
Starting point
Walking into the hall, the paintings caught my attention.
Using this skill
Walking into the hall, I noticed the paintings.
I is now the subject of both walking and noticed. Another clear option is 'As I walked into the hall, the paintings caught my attention.' That version gives each clause its own subject.