In the following sentence, Who is the direct object and who is the indirect object?
I know the woman in the blue dress.
A direct object is a noun or a noun phrase denoting a person or thing that is the recipient of the action of a transitive verb. For example, the book in John gave the book to him is a direct object because it is directly affected by the action of the transitive verb gave.
An indirect object, on the other hand, is a noun or a noun phrase referring to someone or something that is affected by the action of a transitive verb typically as a recipient, but is not the primary object. For instance, him in John gave the book to him is an indirect object because it is indirectly affected by the action of the transitive verb gave.
Applying all that knowledge to your example, we can see that there is only a direct object in your sentence which is represented by the noun phrase the women in the blue dress because the women in the blue dress is directly affected by the transitive verb know.