15 ms·

HyperNeRF

288 points by montyanderson 5y ago

themodelplumber 5y ago
Wow. I only get the inner workings at a very basic, intuitive level, but it's really cool to see the progress of this and similar research. Congrats to the researchers. It's awe-inspiring and even frightening at first, in the usual ways, but IMO it has a lot of long-term promise in other ways. Spitballing: I like that this kind of result, which clearly calls into question the role or perception of physical identity, may eventually inform (or even necessitate?) the deconstruction of the physical "I" as a permission broker, and further open a many-to-many interface between the dimensions that underlay what we now think of as "self" and the true depth and variety within what we now think of as "individual humans who are not me". That opening process alone ought to be a huge jump for human development. Right now we're each held, and holding ourselves, way too responsible for maintaining a singular subjective identity, looking at the aggregate. Not only does this compromise our outlook on others based on our subjective perception of the identity match, but it also compromises our ability to reliably consume and metabolize identity-construct-breaking information and experiences. And many of those things, when consumed without so many identity borders--so to speak--will end up being incredibly useful for individuals and group both. Thanks for sharing op.
- walleeee 5y ago
  how in particular do you think this sort of work might inform interpretations of personal identity? what uses do you anticipate for a more [fluid? porous? plural?] self-regard?
  - themodelplumber 5y ago
    Hmm, that would go into specifics, which IMO are kind of tenuous from the start since the point of a spitball is to be open to unknowns. So with that said, some ideas could be started around topics like 1) massive identity theft causing a re-thinking of identity 2) creativity and constraints around the moderation of physical identity and 3) technical-presentational dynamics surrounding physical presence and the moderation of identity presentation in a physical presence context. Any one of these is a great setup for the question: How do we interpret personal identity? And this--again just IMO--would be an amazing point at which to say, "look, if the only word-tool we can use is 'identity' to describe this crisis/opportunity, then maybe all we have is a metaphorical hammer and we have all these endless annoying nails--in the form of identity questions--to hammer down. But if we had maybe some other word-tools to use instead of 'identity', maybe this really would look more like an opportunity to move humanity one more step up the evolutionary ladder." We already moderate our identity every day, either consciously or unconsciously. It's been studied for thousands of years. It's in books you've read, movies you've watched. It's been done for fun, for comic relief, and also it's been done to solve mind-shattering problems. But now we start to really unwind this question of physical identity, the one concrete thing we thought was so much more certain...! and things get _really_ interesting. This is a different level, where there's maybe not such a need to hide or hide from this departure from "this one idea of who I am" which is really just a mess of a complex of ideas. > what uses do you anticipate for a more [fluid? porous? plural?] self-regard? For one: More, and healthier, exposure to alternatives. Your identity is almost synonymous with your subjective past. To that degree, you're screwed in a lot of ways. To give a personal example, I was born into a cult. I was screwed from birth, in that way. One of the best tools I had in removing myself from that environment was the concept of an "online identity" which could be moderated, intentionally, into whatever it needed to be to help me explore alternative perceptions of what it was I was involved in. I could even try on a non-cult identity, and write, online, from the perspective of someone who had freed themselves. And then I could consider how that felt, and reflect on what I learned. Did it kill me? No. Am I in hell now? Nope. etc. Consider the millions of various points of identity just like that. Not just cults, no way! Am I Coke or Pepsi? eh, boring. Am I...which race am I? Is that a tricky question in the future? And from the outside, will I get better treatment from medical professionals if I can moderate my physical presentation at will? Wow so many random questions that can be asked for learning's sake. But again, to emphasize--I love and respect the unknown. I don't have answers, only openness where I don't want to have certainty anymore, because that c-word makes it a little too hard to solve big problems, or a little too easy to avoid them. Don't leave the cult man, you'll lose all your certainty. Hope that helps, a little, or examples, a little.
    - walleeee 5y ago
      thanks for the super thoughtful reply!
  - kingcharles 5y ago
    I think the advent of DeepTomCruise [1] make us rethink the solidity of identity. A majority of those watching the videos appear to believe it is the real Tom Cruise, and really, there is no good way to tell any longer whether it is or not, without reference to external information. There is no reason now that Tom Cruise even needs to exist as a real person, or needs to ever act in a movie ever again. Tom Cruise can just become an abstract concept, no longer a living object. Perhaps it is Tom Cruise himself in these videos. Perhaps the real Tom Cruise no longer exists. Perhaps the whole thing is an elaborate art project. Our certainty of its falsity is tied solely to whether we believe the story of those who claim to have created the videos. Is it easier to create fake videos of Tom Cruise or to create real videos of Tom Cruise and a fake story? What is a Tom Cruise? [1] https://www.tiktok.com/@deeptomcruise https://www.tiktok.com/@deeptomcruise
Namidairo 5y ago
The team photos double as the demo, that's neat. (Mouse over to see the depth colouring.) I presume something along these lines will make it's way to the Pixel 6 camera software, given the origin of the research and the onboard edgeTPU block.
sanxiyn 5y ago
Since neural networks are universal, we can often solve problems we don't know exactly how to solve with neural networks. NeRF is a great example. But once solved, we should try to reverse engineer the solution and optimize. https://arxiv.org/abs/2112.05131 https://arxiv.org/abs/2112.05131 did such work and found you can get NeRF quality without any neural network at all and as a result 100x faster.
- echelon 5y ago
  > But once solved, we should try to reverse engineer the solution and optimize. This is a great point. Does anybody know of any papers that explore non-neural text to speech / voice synthesis that achieve better than parametric quality?
- exikyut 5y ago
  Demo videos and overview: https://alexyu.net/plenoxels/ https://alexyu.net/plenoxels/
- orbital-decay 5y ago
  NeRF triggered the development of a number of improved methods, though. There's DONeRF [1] that is built upon NNs and is currently faster than comparable solutions (the field evolves fast so I may be wrong). [1] https://github.com/facebookresearch/DONERF https://github.com/facebookresearch/DONERF
  - blurbleblurble 5y ago
    Yeah there are dozens of spinoffs inspired by NeRF, it's kind of amazing
  - deleted 5y ago
    [deleted]
- dougabug 5y ago
  Except the plenoxel representation is also 2-3 orders of magnitude larger than an MLP-based NeRF. It’s not very surprising that a sparse voxel representation can capture a plenoptic function. Representation of volumetric video further presses the size disadvantages of voxel based techniques. The reasons for using deep learning function approximators are manifold, for instance in RL, state and state-action spaces quickly become too large for tabular methods. Using grids or tables also basically closes off the opportunities for exploiting meta-learning and analysis-by-synthesis. Plenoxels also rely on explicit specification of a known grid structure, where the HyperNeRF method can learn latent parametric manifolds and handle dynamic objects with changing topologies.
Stevvo 5y ago
What a time to be alive!
- daenz 5y ago
  For those of you who may not get this reference, it's from a popular Youtube channel, Two Minute Papers, run by Dr Károly Zsolnai-Fehér that recently featured OP's link https://www.youtube.com/c/K%C3%A1rolyZsolnai/videos https://www.youtube.com/c/K%C3%A1rolyZsolnai/videos The channel is excellent and I recommend subscribing to it if you like this kind of stuff.
  - Tarks 5y ago
    Which is very likely referencing this : https://youtu.be/qu32fBkiHFE https://youtu.be/qu32fBkiHFE
twoodfin 5y ago
In the right circumstances, the NFL would spend $1E7-$1E8 on this or similar tech. It’s wild to think about how much of what we see on screens in a decade or so will be “computationally inferred”.
- themodelplumber 5y ago
  I'm sure there are also people who would love to computationally infer the preferred ending to an NFL game of their choice, too. Or change the ending to a movie of which they can only tolerate the first hour. It would enable some really cool ideation and modeling, maybe even some of which could be used for psychology work, or sports psychology in the case of the NFL (I'm reminded of those "imagine yourself winning" tricks)
productceo 5y ago
Very interesting. Highly useful for metaverse avatars.
- qwertox 5y ago
  Or YouTube video thumbnails, from the looks of it.
ragmurugesan 5y ago
This is cool
ragmurugesan 5y ago
Thanks for sharing
visarga 5y ago
NeRF's were inveted in 2020 and started an avalanche of papers (637 citations so far). > Original one: "Nerf, Representing scenes as neural radiance fields for view synthesis" > https://scholar.google.com/scholar?cites=9378169911033868166&as_sdt=2005&sciodt=0,5&hl=en https://scholar.google.com/scholar?cites=9378169911033868166... What I find most exciting about it is that a NeRF represents images as neural nets, one neural net for each image (in the OP paper generalised to image + deformations). By evaluating the net at various pixel coordinates it gives the color. Up until now learning to replicate the input exactly was called overfitting and considered a bug, not a feature, but they showed a completely new way to wield neural nets. An interesting detail is that they depend on Fourier encoding for the input coordinates. A variant called SIREN uses `sin` as activation function throughout the net. Maybe neural nets will become the data compressors of tomorrow? Shoot a picture, send a neural net around. Game assets could be NeRFs.
- sbierwagen 5y ago
  >Maybe neural nets will become the data compressors of tomorrow? Long a topic of research, with many interesting ramifications: https://ai.googleblog.com/2016/09/image-compression-with-neural-networks.html https://ai.googleblog.com/2016/09/image-compression-with-neu... In analogy to standard compression techniques, you can think of the neural net as a very large "dictionary". For text compression, there is of course the famous Hutter Prize, launched in 2006: https://en.wikipedia.org/wiki/Hutter_Prize https://en.wikipedia.org/wiki/Hutter_Prize ("Prediction is the golden key that opens all locks". Compressing each byte of wikipedia text is equivalent to predicting it-- to compactly represent its knowledge is to understand it.)
  - vintermann 5y ago
    1. If the first byte is 0, insert the text of Wikipedia, 2. If it isn't, ignore it, and all further bytes are interpreted literally. To avoid these sort of "joke" decompressors, they evaluate compressors on (size of compressed data) + (size of decompressor) in the compression competitions last time I checked. That means we won't get a winner based on GPT3 anytime soon. 350+ GB of weights is a lot to overcome :) Though of course, given enough data to compress, it might well be that full-on neural language models are still worth it.
fartcannon 5y ago
Is there a *Nerf to Blender pipeline?
jcims 5y ago
What’s the difference between this and using photogrammetry to build a 3D model/depthmap and painting it with the images?
- Geee 5y ago
  These contain all the light field information of the scene. See the reflections, refractions etc.
- zcw100 5y ago
  Better in painting and the 3D object can move.
fxtentacle 5y ago
In my opinion, everything nerf related gets a lot of opinion because it's highly graphical and thus easy to present. But there's few practical applications and it tends to be super slow and not work for more challenging scenes where traditional 20-year old methods like global penalty block matching still work reasonably. And for this paper in particular, I fail to see how they improve over other nerf approaches with deformation terms like Nerfies or D-Nerf
- dougabug 5y ago
  Deformation fields would struggle to fundamentally change the topological type, particularly where the transformation would need to “tear” the manifold, such as turning a sphere into a donut or dividing a cell into two child cells. HyperNeRF’s exploit and extend Level Set Methods, which are rooted in Morse Theory. https://en.wikipedia.org/wiki/Level-set_method https://en.wikipedia.org/wiki/Level-set_method https://en.wikipedia.org/wiki/Morse_theory https://en.wikipedia.org/wiki/Morse_theory
dlightlo 5y ago
dlightlo 5y ago
max_ 5y ago
Unfortunately, there is a lot of technical Jargon. I don't seem to understand much. Could someone help me outline what's most interesting here? Maybe applications?
- ibrarmalik 5y ago
  If you have a limited number of images of the same scene, with NeRF you can generate new images from different positions and angles (novel view synthesis). But this only works with rigid scenes: e.g. if you apply NeRF to images of a person, they cannot move between the pictures. This is what HyperNeRF is trying to solve. If there are pictures of a person, and in one of them they are smiling but on another not, 1. this method will not fail, and 2. looks like it will give reasonable new views/images.
bloopernova 5y ago
Is this computational "simple" (efficient?) enough that it could be used to create better interactive graphics in things like games? Or am I understanding this incorrectly? Sorry, this feels very much beyond me.
- visarga 5y ago
  I see two uses: - as a storage format for 3d models - it could become a method to package parametrised game assets, so you can easily customise them. - as a representation for 3d inputs in spatial reasoning tasks, like protein folding and self driving
  - dclowd9901 5y ago
    I was wondering on this. So it _is_ in the photogrammetry space? How soon before I can use my iPhone to take 6 pictures or something and get a perfect 3D model from it?
- Geee 5y ago
  It seems that they're not real-time renderable. There could be a method of converting these to polygons + materials for real-time rendering.

288 points by montyanderson 5y ago

Wow. I only get the inner workings at a very basic, intuitive level, but it's really cool to see the progress of this and similar research. Congrats to the researchers. It's awe-inspiring and even frightening at first, in the usual ways, but IMO it has a lot of long-term promise in other ways. Spitballing: I like that this kind of result, which clearly calls into question the role or perception of physical identity, may eventually inform (or even necessitate?) the deconstruction of the physical "I" as a permission broker, and further open a many-to-many interface between the dimensions that underlay what we now think of as "self" and the true depth and variety within what we now think of as "individual humans who are not me". That opening process alone ought to be a huge jump for human development. Right now we're each held, and holding ourselves, way too responsible for maintaining a singular subjective identity, looking at the aggregate. Not only does this compromise our outlook on others based on our subjective perception of the identity match, but it also compromises our ability to reliably consume and metabolize identity-construct-breaking information and experiences. And many of those things, when consumed without so many identity borders--so to speak--will end up being incredibly useful for individuals and group both. Thanks for sharing op.

walleeee 5y ago
how in particular do you think this sort of work might inform interpretations of personal identity? what uses do you anticipate for a more [fluid? porous? plural?] self-regard?
- themodelplumber 5y ago
  Hmm, that would go into specifics, which IMO are kind of tenuous from the start since the point of a spitball is to be open to unknowns. So with that said, some ideas could be started around topics like 1) massive identity theft causing a re-thinking of identity 2) creativity and constraints around the moderation of physical identity and 3) technical-presentational dynamics surrounding physical presence and the moderation of identity presentation in a physical presence context. Any one of these is a great setup for the question: How do we interpret personal identity? And this--again just IMO--would be an amazing point at which to say, "look, if the only word-tool we can use is 'identity' to describe this crisis/opportunity, then maybe all we have is a metaphorical hammer and we have all these endless annoying nails--in the form of identity questions--to hammer down. But if we had maybe some other word-tools to use instead of 'identity', maybe this really would look more like an opportunity to move humanity one more step up the evolutionary ladder." We already moderate our identity every day, either consciously or unconsciously. It's been studied for thousands of years. It's in books you've read, movies you've watched. It's been done for fun, for comic relief, and also it's been done to solve mind-shattering problems. But now we start to really unwind this question of physical identity, the one concrete thing we thought was so much more certain...! and things get _really_ interesting. This is a different level, where there's maybe not such a need to hide or hide from this departure from "this one idea of who I am" which is really just a mess of a complex of ideas. > what uses do you anticipate for a more [fluid? porous? plural?] self-regard? For one: More, and healthier, exposure to alternatives. Your identity is almost synonymous with your subjective past. To that degree, you're screwed in a lot of ways. To give a personal example, I was born into a cult. I was screwed from birth, in that way. One of the best tools I had in removing myself from that environment was the concept of an "online identity" which could be moderated, intentionally, into whatever it needed to be to help me explore alternative perceptions of what it was I was involved in. I could even try on a non-cult identity, and write, online, from the perspective of someone who had freed themselves. And then I could consider how that felt, and reflect on what I learned. Did it kill me? No. Am I in hell now? Nope. etc. Consider the millions of various points of identity just like that. Not just cults, no way! Am I Coke or Pepsi? eh, boring. Am I...which race am I? Is that a tricky question in the future? And from the outside, will I get better treatment from medical professionals if I can moderate my physical presentation at will? Wow so many random questions that can be asked for learning's sake. But again, to emphasize--I love and respect the unknown. I don't have answers, only openness where I don't want to have certainty anymore, because that c-word makes it a little too hard to solve big problems, or a little too easy to avoid them. Don't leave the cult man, you'll lose all your certainty. Hope that helps, a little, or examples, a little.
  - walleeee 5y ago
    thanks for the super thoughtful reply!
- kingcharles 5y ago
  I think the advent of DeepTomCruise [1] make us rethink the solidity of identity. A majority of those watching the videos appear to believe it is the real Tom Cruise, and really, there is no good way to tell any longer whether it is or not, without reference to external information. There is no reason now that Tom Cruise even needs to exist as a real person, or needs to ever act in a movie ever again. Tom Cruise can just become an abstract concept, no longer a living object. Perhaps it is Tom Cruise himself in these videos. Perhaps the real Tom Cruise no longer exists. Perhaps the whole thing is an elaborate art project. Our certainty of its falsity is tied solely to whether we believe the story of those who claim to have created the videos. Is it easier to create fake videos of Tom Cruise or to create real videos of Tom Cruise and a fake story? What is a Tom Cruise? [1] https://www.tiktok.com/@deeptomcruise https://www.tiktok.com/@deeptomcruise

Namidairo 5y ago

The team photos double as the demo, that's neat. (Mouse over to see the depth colouring.) I presume something along these lines will make it's way to the Pixel 6 camera software, given the origin of the research and the onboard edgeTPU block.

sanxiyn 5y ago

Since neural networks are universal, we can often solve problems we don't know exactly how to solve with neural networks. NeRF is a great example. But once solved, we should try to reverse engineer the solution and optimize. https://arxiv.org/abs/2112.05131 https://arxiv.org/abs/2112.05131 did such work and found you can get NeRF quality without any neural network at all and as a result 100x faster.

echelon 5y ago
> But once solved, we should try to reverse engineer the solution and optimize. This is a great point. Does anybody know of any papers that explore non-neural text to speech / voice synthesis that achieve better than parametric quality?
exikyut 5y ago
Demo videos and overview: https://alexyu.net/plenoxels/ https://alexyu.net/plenoxels/
orbital-decay 5y ago
NeRF triggered the development of a number of improved methods, though. There's DONeRF [1] that is built upon NNs and is currently faster than comparable solutions (the field evolves fast so I may be wrong). [1] https://github.com/facebookresearch/DONERF https://github.com/facebookresearch/DONERF
- blurbleblurble 5y ago
  Yeah there are dozens of spinoffs inspired by NeRF, it's kind of amazing
- deleted 5y ago
  [deleted]
dougabug 5y ago
Except the plenoxel representation is also 2-3 orders of magnitude larger than an MLP-based NeRF. It’s not very surprising that a sparse voxel representation can capture a plenoptic function. Representation of volumetric video further presses the size disadvantages of voxel based techniques. The reasons for using deep learning function approximators are manifold, for instance in RL, state and state-action spaces quickly become too large for tabular methods. Using grids or tables also basically closes off the opportunities for exploiting meta-learning and analysis-by-synthesis. Plenoxels also rely on explicit specification of a known grid structure, where the HyperNeRF method can learn latent parametric manifolds and handle dynamic objects with changing topologies.

Stevvo 5y ago

What a time to be alive!

daenz 5y ago
For those of you who may not get this reference, it's from a popular Youtube channel, Two Minute Papers, run by Dr Károly Zsolnai-Fehér that recently featured OP's link https://www.youtube.com/c/K%C3%A1rolyZsolnai/videos https://www.youtube.com/c/K%C3%A1rolyZsolnai/videos The channel is excellent and I recommend subscribing to it if you like this kind of stuff.
- Tarks 5y ago
  Which is very likely referencing this : https://youtu.be/qu32fBkiHFE https://youtu.be/qu32fBkiHFE

twoodfin 5y ago

In the right circumstances, the NFL would spend $1E7-$1E8 on this or similar tech. It’s wild to think about how much of what we see on screens in a decade or so will be “computationally inferred”.

themodelplumber 5y ago
I'm sure there are also people who would love to computationally infer the preferred ending to an NFL game of their choice, too. Or change the ending to a movie of which they can only tolerate the first hour. It would enable some really cool ideation and modeling, maybe even some of which could be used for psychology work, or sports psychology in the case of the NFL (I'm reminded of those "imagine yourself winning" tricks)

productceo 5y ago

Very interesting. Highly useful for metaverse avatars.

qwertox 5y ago
Or YouTube video thumbnails, from the looks of it.

ragmurugesan 5y ago

This is cool

ragmurugesan 5y ago

Thanks for sharing

visarga 5y ago

NeRF's were inveted in 2020 and started an avalanche of papers (637 citations so far). > Original one: "Nerf, Representing scenes as neural radiance fields for view synthesis" > https://scholar.google.com/scholar?cites=9378169911033868166&as_sdt=2005&sciodt=0,5&hl=en https://scholar.google.com/scholar?cites=9378169911033868166... What I find most exciting about it is that a NeRF represents images as neural nets, one neural net for each image (in the OP paper generalised to image + deformations). By evaluating the net at various pixel coordinates it gives the color. Up until now learning to replicate the input exactly was called overfitting and considered a bug, not a feature, but they showed a completely new way to wield neural nets. An interesting detail is that they depend on Fourier encoding for the input coordinates. A variant called SIREN uses `sin` as activation function throughout the net. Maybe neural nets will become the data compressors of tomorrow? Shoot a picture, send a neural net around. Game assets could be NeRFs.

sbierwagen 5y ago
>Maybe neural nets will become the data compressors of tomorrow? Long a topic of research, with many interesting ramifications: https://ai.googleblog.com/2016/09/image-compression-with-neural-networks.html https://ai.googleblog.com/2016/09/image-compression-with-neu... In analogy to standard compression techniques, you can think of the neural net as a very large "dictionary". For text compression, there is of course the famous Hutter Prize, launched in 2006: https://en.wikipedia.org/wiki/Hutter_Prize https://en.wikipedia.org/wiki/Hutter_Prize ("Prediction is the golden key that opens all locks". Compressing each byte of wikipedia text is equivalent to predicting it-- to compactly represent its knowledge is to understand it.)
- vintermann 5y ago
  1. If the first byte is 0, insert the text of Wikipedia, 2. If it isn't, ignore it, and all further bytes are interpreted literally. To avoid these sort of "joke" decompressors, they evaluate compressors on (size of compressed data) + (size of decompressor) in the compression competitions last time I checked. That means we won't get a winner based on GPT3 anytime soon. 350+ GB of weights is a lot to overcome :) Though of course, given enough data to compress, it might well be that full-on neural language models are still worth it.

fartcannon 5y ago

Is there a *Nerf to Blender pipeline?

jcims 5y ago

What’s the difference between this and using photogrammetry to build a 3D model/depthmap and painting it with the images?

Geee 5y ago
These contain all the light field information of the scene. See the reflections, refractions etc.
zcw100 5y ago
Better in painting and the 3D object can move.

fxtentacle 5y ago

In my opinion, everything nerf related gets a lot of opinion because it's highly graphical and thus easy to present. But there's few practical applications and it tends to be super slow and not work for more challenging scenes where traditional 20-year old methods like global penalty block matching still work reasonably. And for this paper in particular, I fail to see how they improve over other nerf approaches with deformation terms like Nerfies or D-Nerf

dougabug 5y ago
Deformation fields would struggle to fundamentally change the topological type, particularly where the transformation would need to “tear” the manifold, such as turning a sphere into a donut or dividing a cell into two child cells. HyperNeRF’s exploit and extend Level Set Methods, which are rooted in Morse Theory. https://en.wikipedia.org/wiki/Level-set_method https://en.wikipedia.org/wiki/Level-set_method https://en.wikipedia.org/wiki/Morse_theory https://en.wikipedia.org/wiki/Morse_theory

dlightlo 5y ago

max_ 5y ago

Unfortunately, there is a lot of technical Jargon. I don't seem to understand much. Could someone help me outline what's most interesting here? Maybe applications?

ibrarmalik 5y ago
If you have a limited number of images of the same scene, with NeRF you can generate new images from different positions and angles (novel view synthesis). But this only works with rigid scenes: e.g. if you apply NeRF to images of a person, they cannot move between the pictures. This is what HyperNeRF is trying to solve. If there are pictures of a person, and in one of them they are smiling but on another not, 1. this method will not fail, and 2. looks like it will give reasonable new views/images.

bloopernova 5y ago

Is this computational "simple" (efficient?) enough that it could be used to create better interactive graphics in things like games? Or am I understanding this incorrectly? Sorry, this feels very much beyond me.

visarga 5y ago
I see two uses: - as a storage format for 3d models - it could become a method to package parametrised game assets, so you can easily customise them. - as a representation for 3d inputs in spatial reasoning tasks, like protein folding and self driving
- dclowd9901 5y ago
  I was wondering on this. So it _is_ in the photogrammetry space? How soon before I can use my iPhone to take 6 pictures or something and get a perfect 3D model from it?
Geee 5y ago
It seems that they're not real-time renderable. There could be a method of converting these to polygons + materials for real-time rendering.