Mystic Eyes of Death Perception

The Mystic Eyes of Death Perception (直死の魔眼) are an ability in the Nasuverse. Only two characters are known to possess them: Ryougi Shiki and Tohno Shiki.

Description
The eyes are not really different set of eyes but are a circuit (possibly similar to a Magic Circuit) that opens up in the users brain and normal eyes, allowing them to "perceive death" in the form of lines and dots. The user in question is the only one who can touch or use these lines and dots (i.e. no one can interact with the lines/dots even if the user of the eyes were to point out their location on something).

These lines can then be traced with a sharp object such as a knife or a sword. Cutting the line “breaks” the object along that line and damage inflicted this way can not be healed or repaired in any way. Healing is possible if cutting the line doesn't completely separate a part of the object from the object itself. Also of note is how Arcueid was cut into a multitude of individual pieces as a result of having her lines traced but was able to survive anyway despite not being able to regenerate. She was able to accomplish this by completely reinventing the conceptual structure of her body, abandoning the conceptual structure that had been traced.

Dots can be pierced by sharp objects. Piercing a dot effectively “erases” that object from existence, in a sense that the object loses even its inherent properties such as momentum, toxicity, and generally any effect it may impose on it's surrounding. Living things whose dot was pierced get “stopped” and, as a consequence, die. While this death may not be instant, it is absolutely permanent, and can't be reversed or bypassed, even by reincarnation.

Note that Tohno Shiki shows signs of mental/physical strain when using this ability extensively, manifested as headaches and even temporary loss of sight. Arcueid noted that this is due him having to “connect” to the perspective of an object he wishes to see the death of and that perceiving things in a way not meant for humans is putting a strain on his brain.

Mystic Eyes of Death Perception are categorized as Blue under the Noble Colors system. Additionally, Tohno Shiki's eyes glow with blue and it is the dominant color of Ryougi Shiki's irises (see image) when her eyes are activated.

Acquiring the eyes
The only way to acquire the eyes is by having a near-death experience. It is possible it has do with the user in question getting close to Akasha (the root of all things) due to this experience. However, this ability is extremely rare, to the point of being thought of being no more than a myth.

Tohno Shiki acquired the eyes after nearly dying in a fight with his "brother". Shiki already had a form of jougan (Pure Eyes) from his genetic family, this may have helped him get the eyes. Shiki did not accept the eyes and later acquired Magangoroshi (魔眼殺し) glasses (made by Aozaki Touko and reinforced by Aozaki Aoko) that removed them from his sight.

Ryogi Shiki acquired the eyes after a two year coma. Her eyes are much more advanced than Tohno Shiki's allowing her to see lines on objects more distant from human perception without any notable strain.

Levels of Perception
So far, four levels of perception have been observed by various users, in order of least advanced to most advanced. All of these users are capable of seeing both points and lines.
 * Tohno SHIKI (Roa): Technically speaking, these are not "true" mystic eyes of death perception; his ability is to see the life force, and it is because he sees the life force, and not actually the death, that these Mystic Eyes of Death Perception are not considered true MEoDP. Consequently, these eyes are limited to killing living things and can be used to directly damage or annihilate someone's life force. Because the flow of one's life is the same as the flow of one's death, the lines overlap, but their origins are different, and therefore the dots don't. His mystic eyes can't actually "kill" like real MEoDP users. Instead, it would just inflict critical damage on someone's life force. So, rather than dying because their "death" has been directly activated, SHIKI (Roa)'s victims die simply because they can no longer live, which leads to their death.
 * Nanaya Shiki: His MEoDP allows him to perceive the death of any concrete, physical existence. So he can kill people, animals, walls, locks, Nero's Soil of Genesis, etc. Basically Nanaya Shiki's Mystic Eyes attack the "point of death" and not the "point of life," so people killed by his mystic eyes die directly. What happens is that as soon as a death is triggered, the object's existence unravels and whatever made the object what it is (like, what makes a living person a living person or a hallway a hallway) immediately ends in the simplest way (Death for the person, and collapsing for the hallway). Those who have accumulated an exceptionally large weight of existence, like Roa or Araya Souren, take longer to die because there is more of their existence that needs to unravel. Also, some things possess death that is too far from human perception to be understood by Shiki, such as a True Ancestor under the full moon. On a side note, Shiki has been known to kill things that have not yet fully assumed physical form, such as when he killed the Tatari in Melty Blood before he had true form in the world or even Arcueid's link to the world. He could also see and kill Akiha's "Plundering" or "Caging Hair" in Tsukihime, but this has been retroactively explained as being a Pure Eyes ability he already possessed.
 * Ryougi Shiki: Her MEoDP allows her to perceive the death of more or less anything that exists. Whether it is a person, an object, a ghost, a disease, a thought lingering in someone's mind, magecraft, a ward, a psychic attack, etc., so long as it exists, she can kill it. (In fact, she claims that if god exists, she could kill him.) So, she basically kills whatever she pleases, although she had some difficulty with killing Araya Souren. Nevertheless, Araya Souren himself infers that ultimately she could perceive the death of anything, without exception, if she searched deeply enough. Contrary to what the OVAs may lead one to conclude, her eyes are permanently active, but she doesn't suffer any strain from this.
 * Ryougi Shiki (Void): The hidden, third personality of Ryougi Shiki. In fact, it is this personality that is directly connected to the root of all things. Her mystic eyes are much the same as the normal Ryougi Shiki's, only much, much more powerful. This is the personality that faces Araya Souren with the katana in the novels. At her rank, she can see Araya Souren's death with ease while the regular Shiki needs to focus intently. She can also kill a concept such as the distance between her and an enemy, allowing her to move in a way that we're not entirely certain if she was merely incredibly fast or genuinely warping through space. Beyond that, she can kill multiple things within a single motion. She also claims that it would be trivially easy for her to annihilate reality.