First you have to put on your mathematical hat. Which shouldn't be hard for you, should it?
"spatially video resizing"?
You need to decide which it is that you want
- you want spatially to describe video = use adjective spatial instead
- you want spatially to describe resizing = use adverb spatially
Now, perform your equation factorization. Which of the following is it?
1.1
completed task improving seam merging, which temporally & spatially resizes videos.
{Improved {seam merging}}
for
{
{{temporally and spatially} resizing}
videos
}
using
{{structure and motion} preservation}
1.2
completed task improving seam merging, for a single video whose resizing is characterised by its temporal & spatial dimensions.
{Improved {seam merging}}
for
{
{{temporally and spatially} resizing}
video
}
using
{{structure and motion} preservation}
2.
{Improved {seam merging}}
for
{{temporally and spatially} resizing}
{
videos
that have
{{structure and motion} preservation}
}
3.
{Improved {seam merging}}
for
{
resizing
{temporal and spatial}
videos
}
using
{{structure and motion} preservation}
4.0.
{Improved {seam merging}}
for
{
resizing
{
{
{temporal and spatial}
videos
}
that have
{{structure and motion} preservation}
}
}
4.1.
Improved
{
{seam merging}
for
{
resizing
{
{
{temporal and spatial}
videos
}
that have
{{structure and motion} preservation}
}
}
}
5.
{Improved {seam merging}}
for
{
resizing
{temporal and spatial}
videos
}
by preserving
{structure and motion}
6.
{Improved {seam merging}}
for
{
resizing
{temporal and spatial}
videos
that preserves
{structure and motion}
}
If your intention is none of the above, then factorize the structure until it does convey your intention.
Also note that 4.0 and 4.1 convey the same message, using the same order of words, but with different structures. Such alternative structures is also available for the other points 1 - 3, 5 - 6.
Appendix
To answer a further question ...
Principle of proximity in the use of English compels placing related words as close as is beneficial towards showing their relationship.
Use either
- Temporally and spatially resizing of videos
- Temporal and spatial video-resizing
Resizing in video-resizing is a gerund, no longer a verb or a participle.
Pls refer to my write-up at Gerund ending in -ings? for an explanation between present participles, gerunds and verbal nouns.
A gerund is a noun form, the name of an action. A noun requires its descriptor to be an adjective rather than an adverb.
- Her noisy complaining is abruptly annoying our patrons.
- Her abrupt annoying of our patrons occurs when she is complaining noisily.
A participle is still a verb form. A verb requires its descriptor to be an adverb.
- Her noisy complaining is abruptly annoying our patrons.
- Her abrupt annoying of our patrons occurs when she is complaining noisily.