# bbNms

## PURPOSE

Bounding box (bb) non-maximal suppression (nms).

## SYNOPSIS

function bbs = bbNms( bbs, varargin )

## DESCRIPTION

``` Bounding box (bb) non-maximal suppression (nms).

type=='max': nms of bbs using area of overlap criteria. For each pair of
bbs, if their overlap, defined by:
overlap(bb1,bb2) = area(intersect(bb1,bb2))/area(union(bb1,bb2))
is greater than overlap, then the bb with the lower score is suppressed.
In the Pascal critieria two bbs are considered a match if overlap>=.5. If
ovrDnm='min', the 'union' in the above formula is replaced with 'min'.

type=='maxg': Similar to 'max', except performs the nms in a greedy
fashion. Bbs are processed in order of decreasing score, and, unlike in
'max' nms, once a bb is suppressed it can no longer suppress other bbs.

type='cover': Perform nms by attempting to choose the smallest subset of
the bbs such that each remaining bb is within overlap of one of the
chosen bbs. The above reduces to the weighted set cover problem which is
NP but greedy optimization yields provably good solutions. The score of
each bb is set to the sum of the scores of the bbs it covers (the max can
also be used). In practice similar to 'maxg'.

type=='ms': Mean shift nms of bbs with a variable width kernel. radii is
a 4 element vector (x,y,w,h) that controls the amount of suppression
along each dim. Typically the first two elements should be the same, as
should the last two. Distance between w/h are computed in log2 space (ie
w and w*2 are 1 unit apart), and the radii should be set accordingly.
radii may need to change depending on spatial and scale stride of bbs.

Although efficient, nms is O(n^2). To speed things up for large n, can
divide data into two parts (according to x or y coordinate), run nms on
each part, combine and run nms on the result. If maxn is specified, will
split the data in half if n>maxn. Note that this is a heuristic and can
change the results of nms. Moreover, setting maxn too small will cause an
increase in overall performance time.

Finally, the bbs are optionally resized before performing nms. The
resizing is important as some detectors return bbs that are padded. For
example, if a detector returns a bounding box of size 128x64 around
objects of size 100x43 (as is typical for some pedestrian detectors on
the INRIA pedestrian database), the resize parameters should be {100/128,

USAGE
bbs = bbNms( bbs, [varargin] )

INPUTS
bbs        - original bbs (must be of form [x y w h wt bbType])
varargin   - additional params (struct or name/value pairs)
.type       - ['max'] 'max', 'maxg', 'ms', 'cover', or 'none'
.thr        - [-inf] threshold below which to discard (0 for 'ms')
.maxn       - [inf] if n>maxn split and run recursively (see above)
.radii      - [.15 .15 1 1] supression radii ('ms' only, see above)
.overlap    - [.5] area of overlap for bbs
.ovrDnm     - ['union'] area of overlap denominator ('union' or 'min')
.resize     - {} parameters for bbApply('resize')
.separate   - [0] run nms separately on each bb type (bbType)

OUTPUTS
bbs      - suppressed bbs

EXAMPLE
bbs=[0 0 1 1 1; .1 .1 1 1 1.1; 2 2 1 1 1];
bbs1 = bbNms(bbs, 'type','max' )
bbs2 = bbNms(bbs, 'thr',.5, 'type','ms')