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Algorithm 1.
WaldBoost for learning suppression classifiers
Input
: original soft cascade
H
T
(
x
)=
t
=1
h
t
(
x
), its early termination thresholds
θ
(
t
)
and its features
f
t
; desired miss rate
α
; training set
{
(
x
1
,y
1
)
...,
(
x
m
,y
m
)
},x ∈
χ, y ∈{−
1
,
+1
}
,wherethelabels
y
i
are obtained by evaluating the original detector
H
T
at an image position with particular displacement with respect to the position of
corresponding
x
i
Output
: look-up table functions
l
t
and early termination thresholds
θ
(
t
)
of the new
suppression classifier
Initialize
sample weight distribution
D
1
(
i
)=
m
for
t
=1
,...,T
1. estimate new
l
t
such that its
2
ln
Pr
i∼D
(
f
t
(
x
i
)=
j|y
i
=+1)
1
c
(
j
)
t
=
−
Pr
i∼D
(
f
t
(
x
i
)=
j|y
i
=
−
1)
2. add
l
t
to the suppression classifier
t
H
t
(
x
)=
l
r
(
f
r
(
x
))
r
=1
3. find optimal threshold
θ
(
t
)
4. remove from the training set samples for which
≤ θ
(
t
)
5. remove from the training set samples for which
H
t
(
x
)
≤ θ
(
t
)
6. update the sample weight distribution
H
t
(
x
)
D
t
+1
(
i
)
∝
exp(
−y
i
H
t
(
x
i
))
multiple look-up tables
l
t
for a single feature
f
t
can be combined into single wide-
word table such that single word contains
c
(
j
t
values for all the classifiers. In such
case, the required
c
(
j
t
values can be loaded with single memory access, added
to an accumulator register using single instruction and also eciently compared
with the rejection thresholds.
Obviously, such scheme is very well suitable for SIMD architectures, such as
MMX/SSE instruction set extensions found in the contemporary PC processors.
In such architectures, the wide registers can hold 4 32-bit numbers or 8 16-bit
integer numbers. Consequently, the implementation of such scheme can be seen
as nearly free of charge from the computational point of view.
The scheme is also applicable for programmable hardware or other hardware
architectures. In such case, the scheme is beneficial in that addition of the extra
prediction classifiers consumes only very little resources due to nearly unchanged
structure and control subsystems.
On systems with wide enough data words but no SIMD support, the imple-
mentation can be similar to SIMD, except is must be assured that the multi-
accumulator is not overflown (as piecewise addition is not possible in this case).
While this assumption seems to be severe and binding, the reality is such that
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