The Woman in Black is a mysterious figure in House's hallucinations in the Season 4 episode House's Head. She was portrayed by actress Ivana Miličević.
While House is hallucinating about being on the bus and trying to figure out whose life is in danger, the Woman in Black usually appears just across the aisle from him. House notices right away she looks completely out of place on the bus, wearing expensive clothes and shoes.
The Woman in Black speaks to him and keeps asking him who she is. House keeps claiming he doesn't know.
House recreates the scene on the bus and takes Alzheimer's drugs to boost his memory. He sees the Woman, who asks him what kind of jewelry she's wearing. He answers that it's some type of resin, then finally realizes it's Amber. When he awakens from his hallucination, he asks James Wilson where Amber Volakis is, and he realizes he hasn't heard from her since the previous evening. They realize she was on the bus and was one of the few people who was transferred to Princeton General and was only identified as a Jane Doe.
Later in the Season 5 episode titled Adverse Events, Lucas shows a picture to Cuddy of House from his college days at Hopkins, the picture shows young House carrying a woman very similar to the Woman in Black that House saw in his hallucinations in the Season 4 episode titled House's Head, both House and the woman appear to be cheerleaders of the lacrosse team, House at the end of the episode says to Lucas that "there was a girl" suggesting that House had a relationship in college or at least a crush on this woman, which explains why he hallucinated her in Season 4 as a placeholder figure instead of Amber. The way he saw her in detail in his hallucinations suggest that he knew the woman in black from memory, House probably forgot her as he graduated college a long time ago, but his subconscious planted her in his hallucination, furthermore the woman looks about the same age in the picture as she did in House's hallucinations, while House looks significantly younger in the picture, supporting the theory that she is the same woman, as this means House hallucinated her as a young woman as he remembered her from his college days because he doesn't know what she looks like today.
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Woman in Black Season 4 Episode 15 (House's Head)
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Woman in Black Season 5 Episode 3 (Adverse Events)
Lastly, this picture was brought up in the story and shown to us early in Season 5, not so far from the hallucination's episode at the end of Season 4, suggesting that after the hallucinations House probably became obsessed with trying to find out who is the woman he hallucinated instead of Amber, why her? because House is House and he has to solve the mystery, so he probably went looking through his old pictures and finally found the connection.