The blind spots are scotomas (areas of degenerated acuity) found in all mammalian eyes, and are due to the way the optic nerve crosses the retina (back of the eye):
Because there are no cells to detect light on the optic disc, the
corresponding part of the field of vision is invisible. Some process
in our brains interpolates the blind spot based on surrounding detail
and information from the other eye, so we do not normally perceive the
Scotomas can result from eye damage as well, and the result is the same:
There is no direct conscious awareness of visual scotomas. They are
simply regions of reduced information within the visual field. Rather
than recognizing an incomplete image, patients with scotomas report
that things "disappear" on them.
As photoreceptor density in our eyes is not evenly distributed, and changes over time due to ageing and cell damage, the way our brain processes the visual field is probably an adaptation, so it is not useful to think of it as "pixelated":
In vision, filling-in phenomena are those responsible for the
completion of missing information across the physiological blind spot,
and across natural and artificial scotomata. There is also evidence
for similar mechanisms of completion in normal visual analysis.
There are three main perspectives on how this happens in the brain. The first is "bottom-up" - called isomorphic filling-in - which is done by early visual systems using information from neighbouring areas. Think of this like the "magic healing brush" in Photoshop. The second is "top-down" - called symbolic filling-in - which is done by downstream areas of the brain filling in the missing parts with higher-level knowledge. The third is that filling-in is a fallacy called the homunculus argument, that is based on the false notion of a Cartesian theatre - that the visual system "projects" an image from the eye onto an observer inside our brain. However this does not make any sense, and so there is no reason to suppose that any kind of "filling-in" process actually needs to happen.
PS: The eye holds an interesting place in the history of evolution, as it has been used to support the case for both intelligent design - due to its amazing complexity - and evolution by chance - due to its flawed design. In mammalian eyes, the optic nerve delivers neurons to photoreceptors from in front, requiring it to pass through the retina. In cephalopod (eg, octopus) eyes, the optic nerve delivers neurons to photoreceptors from behind - a design that results in no blind spots.