Atticus never changed throughout the whole novel.  However, through Scout's narration, we find that Atticus was a true gentleman.  He never told them that he was "appointed" to the Tom Robinson case.  He could have, but he did not.  It did not matter to him either way.  He believed in what he was doing and was not about to give excuses for why he was doing it (defending Tom).  That was in part two of the link--summary.

Another topic that is important to point out is that we never knew until he shot that dog that he was the best shot in town.  He kept it to himself, where others may have bragged. (the end of part one of summary in attached link)

Our admiration for the man only grew from the beginning of the novel until the end.

Is what ways do people's perspectives of Atticus change throughout To Kill a Mockingbird?

I agree that you may have a challenging task since I think the characters' perspectives about Atticus change little during the course of the novel. The people of Maycomb already recognize Atticus as one of the town's leaders (he is elected unopposed for the state legislature each term), and they know what to expect from him. Jem and Scout do come to view their father in a different perspective, especially after discovering about his secret marksmanship skills. Jem realizes why Atticus has never bragged about being "the deadest shot in the county" after Miss Maudie explains that "People in their right minds never take pride in their talents." It is a lesson in humility for Jem, and he feels an immense pride in his father, despite his advanced age, feebleness and bad eyesight.

"... I wouldn't care if he couldn't do a blessed thing... Atticus is a gentleman, just like me!"  (Chapter 10)

The lynch mob must have had a change of heart after Atticus made it clear that he would stand in their way--alone if necessary--to prevent them from hanging Tom. A member of the mob proved to be the lone holdout on the jury, proving to Atticus that "once you earned their respect they were for you tooth and nail." Aunt Alexandra seems to have finally given up her desire to take charge of the Finch household after Atticus firmly assures his sister that Calpurnia would remain as the housekeeper for as long as "she wants to." Alexandra comes to recognize that the children are not as desperate for a woman's touch as she had imagined, and that Atticus was providing a solid parental influence. Sheriff Tate catches a rare glimpse of Atticus in a weak moment when Atticus mistakenly believes that it was Jem who had killed Bob; Tate has to assure Atticus that it was not Jem, but Boo who had killed Bob.