Local LUT Upsampling for Acceleration of Edge-preserving Filtering

Hiroshi Tajima, Teppei Tsubokawa, Yoshihiro Maeda and Norishige Fukushima

∗

Nagoya Institute of Technology, Japan

∗

https://fukushima.web.nitech.ac.jp/en/

Keywords:

Edge-preserving Filtering, Local LUT Upsampling, Acceleration, Bilateral Filtering, L

Smoothing.

Abstract:

Edge-preserving ﬁlters have been used in various applications in image processing. As the number of pixels

of digital cameras has been increasing, the computational cost becomes higher, since the order of the ﬁlters

depends on the image size. There are several acceleration approaches for the edge-preserving ﬁltering; howe-

ver, most approaches reduce the dependency of ﬁltering kernel size to the processing time. In this paper, we

propose a method to accelerate the edge-preserving ﬁlters for high-resolution images. The method subsam-

ples an input image and then performs the edge-preserving ﬁltering on the subsampled image. Our method

then upsamples the subsampled image with the guidance, which is the high-resolution input images. For this

upsampling, we generate per-pixel LUTs for high-precision upsampling. Experimental results show that the

proposed method has higher performance than the conventional approaches.

1 INTRODUCTION

Edge-preserving ﬁltering smooths images while

maintaining the outline in the images. There are

various edge-preserving ﬁlters for various purposes

of image processing, such as bilateral ﬁltering (To-

masi and Manduchi, 1998), non-local means ﬁlte-

ring (Buades et al., 2005), DCT ﬁltering (Yu and

Sapiro, 2011), BM3D (Dabov et al., 2007), guided

image ﬁltering (He et al., 2010), domain transform

ﬁltering (Gastal and Oliveira, 2011), adaptive mani-

fold ﬁltering (Gastal and Oliveira, 2012), local Lapla-

cian ﬁltering (Paris et al., 2011), weighted least square

ﬁltering (Levin et al., 2004), and L

smoothing (Xu

et al., 2011). The applications of the edge-preserving

ﬁlters include noise removal (Buades et al., 2005),

outline emphasis (Bae et al., 2006), high dynamic

range imaging (Durand and Dorsey, 2002), haze re-

moving (He et al., 2009), stereo matching (Hosni

et al., 2013; Matsuo et al., 2015), free viewpoint

imaging (Kodera et al., 2013), depth map enhance-

ment (Matsuo et al., 2013).

The computational cost of edge-preserving ﬁlte-

ring is the main issue. There are several accelera-

tion approaches for each ﬁlter, such as bilateral ﬁl-

tering (Durand and Dorsey, 2002; Yang et al., 2009;

Adams et al., 2010; Chaudhury et al., 2011; Chaud-

hury, 2011; Chaudhury, 2013; Sugimoto and Kamata,

2015; Sugimoto et al., 2016; Ghosh et al., 2018; Ma-

eda et al., 2018b; Maeda et al., 2018a), non-local me-

Subsampling

Edge-preserving

smoothing filter

Reference

Output

Generating

Local LUT

Low-resolution

Input

Low-resolution

Output

Input Image Output Image

Local LUT

Figure 1: Local LUT upsampling: an input image is do-

wnsampled and then the image is smoothed by arbitrary

edge-preserving ﬁltering. Next, we create per-pixel LUT

by using the correspondence between subsampled input and

output images. Finally, we convert the input image into the

approximated image by the LUT.

ans ﬁltering (Adams et al., 2010; Fukushima et al.,

2015), local Laplacian ﬁltering (Aubry et al., 2014),

DCT ﬁltering (Fujita et al., 2015), guided image ﬁlte-

ring (Murooka et al., 2018; Fukushima et al., 2018b)

and weighted least square ﬁltering (Min et al., 2014).

The computational time of each ﬁlter, however, de-

pends on image resolution, and it is rapidly incre-

asing, e.g., smartphone’s cameras even have 12M

pixels. For such a high-resolution image, we require

more acceleration techniques.

Processing with subsampling and then upsam-

pling is the most straightforward approach to acce-

lerate image processing. This approach dramatically

reduces processing time; however, the accuracy of the

Tajima, H., Tsubokawa, T., Maeda, Y. and Fukushima, N.

Local LUT Upsampling for Acceleration of Edge-preserving Filtering.

DOI: 10.5220/0007364601310138

In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019), pages 131-138

ISBN: 978-989-758-354-4

131

approximation is also signiﬁcantly decreased. Subs-

ampling loses high-frequency and large edges in ima-

ges; hence, the resulting images also lose the infor-

mation. Different from super-resolution problems,

subsampling/upsampling for acceleration can utilize

a high-resolution input image as a guidance signal.

Joint bilateral upsampling (Kopf et al., 2007) and gui-

ded image upsampling (He and Sun, 2015) utilize the

high-resolution image for high-quality upsampling as

extensions of joint bilateral ﬁltering (Petschnigg et al.,

2004; Eisemann and Durand, 2004). However, both

upsampling are speciﬁc for accelerating bilateral ﬁlte-

ring and guided image ﬁltering. Note that More spe-

ciﬁc upsampling, e.g., depth map upsampling (Fukus-

hima et al., 2016), improve the upsampling quality.

In this paper, we propose a method to accelerate

arbitrary edge-preserving ﬁlters by using subsampling

and upsampling with guidance high-resolution ima-

ges. We named the proposed method local LUT ups-

ampling. Figure 1 indicates the overview of the pro-

posed method. In the proposed, edge-preserving ﬁlte-

ring, which has the highest cost in the processing, is

performed in the downsampled domain for accelera-

tion. Then our method utilizes high-resolution infor-

mation for accurate upsampling.

2 RELATED WORK

In this section, we review two edge-preserving ﬁlters

used in the section of experimental results, i.e., bila-

teral ﬁltering and L

smoothing. Also, we introduce

guided image upsampling, which is an acceleration

method for edge-preserving ﬁltering.

2.1 Bilateral Filtering

Bilateral ﬁltering is a standard edge-preserving ﬁlte-

ring, and it is one of the ﬁnite impulse response (FIR)

ﬁlters. The processing of the bilateral ﬁlter for an in-

put image I

I can be expressed as:

∑

q∈N

p,q

q)I

∑

q∈N

p,q

, (1)

where J

J is an output image of the bilateral ﬁlter, p

p and

q are target and reference pixels, respectively. N

is a

set of the neighboring pixel of the target pixel p

p. f

represents a weight function, and it is deﬁned as:

p,q

q)=exp



p−q

−2σ



exp



−I

−2σ



, (2)

where kp

p − q

and kI

− I

show the difference

of the spatial distance and luminance value between

the target pixel and the reference pixel, respectively.

and σ

are smoothing parameters for the Gaussian

distributions of the spatial distance and luminance dif-

ference, respectively. The bilateral ﬁlter smooths ima-

ges with the range weight in addition to the spatial

weight. As a result, a large weight is given to a refe-

rence pixel whose distance and luminance from target

pixel is close.

2.2 L

Smoothing

smoothing can emphasize rough edges and can re-

duce ﬁne edges. The L

smoothing smooths weak

edge-parts in images more strongly than the bilateral

ﬁltering. Therefore, it is useful for extracting edges

and generating non-photorealistic effects. An output

is obtained by solving the following equation:

min

J,h,v

(

∑

−I

)

+λC(h,v)

+β((∂

−h

)

+(∂

−v

)



, (3)

where I

I and J

J are input and output images, respecti-

vely. h

, v

are auxiliary variables corresponding

to ∂

and ∂

, where p

p is a target pixel coordi-

nate, respectively. C(h, v) is the number of p

p that

| + |v

| 6= 0, and β is determined from the gradient

of (h,v). In order to solve Eq. (3), it is divided into

two sub-problems. The ﬁrst is computing J

J. Exclu-

ding the term not including J

J from Eq. (3), the follo-

wing equation is obtained:

E =

∑



−I

)

+β((∂

−h

)

+(∂

−v

)



. (4)

J is obtained by minimizing equation (4). In this met-

hod, derivative operators are diagonalized after the

fast Fourier transform (FFT) for speedup:

J =F

−1



F (I

I)+β(F (∂

)

∗

F (h) + F (∂

)

∗

F (v))

F (I

I)+β(F (∂

)

∗

F (∂

)+F (∂

)

∗

F (∂

))



, (5)

where F is the FFT operator and

∗

denotes the com-

plex conjugate. The second is computing (h,v). The

objective function for (h,v) is deﬁned as follows:

∑

min

{(h

−∂

)

+(v

−∂

)

H(|h

|+|v

|)}, (6)

where H

H(|h

| + |v

|) is a binary function returning 1,

if |h

| + |v

| 6= 0 and 0 otherwise. When Eq. (6) is

rewritten to the function E

of each pixel p

p, the follo-

wing expression is obtained.

= (h

−∂

)

+(v

−∂

)

H(|h

|+|v

|), (7)

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

132

Algorithm 1: L

Gradient Minimization.

Input: image I, smoothing weight λ, parameters β

max

, and rate κ

Initialization: J ← I,β ← β

,i ← 0

repeat

With J

(i)

, solve for h

(i)

and v

(i)

in Eq. (8)

With h

(i)

and v

(i)

, solver for J

(i+1)

with Eq. (5)

β ← κβ,i + +

until β ≥ β

max

Output: result image J

which reaches its minimum E

∗

under the condition:

(

(0,0) ((∂

)

+(∂

)

≤λ/β)

(∂

,∂

) (otherwise.)

(8)

After computing the minimum energy E

∗

for each

pixel p

p, calculating

∑

∗

becomes the global opti-

mum for Eq. (6). The alternating minimization al-

gorithm is sketched in Algorithm 1. Parameter β is

automatically adapted for each iteration. β is starting

from a small value β

, and then it is multiplied by κ

each time.

2.3 Guided Image Upsampling

We now summarize guided image upsampling. The

upsampling is an extension of the guided image ﬁl-

tering. The ﬁltering converts local patches in an in-

put image by a linear transformation of a guidance

image. Let the guide signal be G, and it is possible to

be G = I, where I is an input image. The output patch

should be satisﬁed for the following relation:

= a

+ b

,∀p

p ∈ ω

, (9)

where k

k indicates a center position of a rectangular

patch ω

, and p

p indicates a position of a pixel in the

patch. a

and b

are coefﬁcients for the linear trans-

formation. The equation represents the coefﬁcients

linearly convert the guide signals in a patch.

The coefﬁcients are calculated by a linear regres-

sion of the input signal I and Eq. (9),

arg min

∑

p∈ω

((a

+ b

− I

)

+ εa

). (10)

The coefﬁcients are estimated as follows:

cov

(G,I)

var

(G) + ε

, b

− a

, (11)

where ε indicates a parameter of smoothing degree.

¯·

, cov

and var

indicate the mean, variance, and co-

variance values of the patch k

k. The coefﬁcients are

overlapping in the output signals; thus, these coefﬁ-

cients are averaged;

¯a

|ω|

∑

k∈ω

|ω|

∑

k∈ω

, (12)

where | · | indicates the number of elements in the set.

Finally, the output is calculated as follows:

= ¯a

. (13)

For color ﬁltering, let input, output and guidance

signals be I

I = {I

}, J

(n = 1, 2, 3), and G

G, re-

spectively. The per-channel output is deﬁned as:

, (14)

|ω|

∑

k∈ω

|ω|

∑

k∈ω

. (15)

The coefﬁcients a

, b

are obtained as follows:

cov

G,I

)

var

G) + εE

, b

− a

, (16)

where E

E is an identity matrix. When the output sig-

nal is a color image, cov

is the covariance matrix of

the patch in I and G

G. Also, var

is the variance of

the R, G, and B components, which will be covari-

ance matrix, in the patch of G

G. The division of the

matrix is calculated by multiplying the inverse matrix

of the denominator from the left. We use box ﬁlte-

ring for the calculation of per pixel mean, variance,

and covariance. The fast implementation of the box

ﬁltering (Fukushima et al., 2018a) accelerates the ﬁl-

tering.

The guided image upsampling is an extension of

guided image ﬁltering and the upsampling is expres-

sed as:

= S

−1

(

)

+ S

−1

(

)), (17)

where S(·) and S

−1

(·) indicate subsampling and ups-

ampling operators, respectively. The upsampling

computes coefﬁcients of

and

in the subsampled

domain, and then upsamples the coefﬁcients. Notice

that we should keep high-resolution signal of G

The coefﬁcients in the downsampled domain is

computed as follows:

↓

:= S(

↓

:= S(

), (18)

↓

|ω

∑

↓

∈ω

↓

|ω

∑

↓

∈ω

↓

, (19)

↓

cov

↓

)

var

↓

) + εE

, b

↓

− a

↓

(20)

Local LUT Upsampling for Acceleration of Edge-preserving Filtering

133

where p

↓

indicates pixel coordinate in the downsam-

pled domain. Also, a

and b

are coefﬁcients in the

downsampled domain, respectively G

:= S(G

G) and

:= S(I) represent downsampled input and guidance

images, respectively. The ﬁltering radius is reduced

according to the rate of subsampling; thus, ω

indica-

tes a small rectangular patch, which is reshaped to ﬁt

the rate of subsampling.

3 PROPOSED METHOD

We propose an upsampling method guided by a high-

resolution image for various edge-preserving ﬁlte-

ring. The proposed method generates a per-pixel

look-up table (LUT), which maps pixel values of the

input image to that of the output image of the edge-

preserving ﬁltering. If we have the result of edge-

preserving ﬁltering, we can easily transform the in-

put image into the edge-preserving result by one-to-

one mapping. We generate the mapping function in

the subsampled image domain for acceleration. The

proposed method generates per-pixel LUTs for the

function from the correspondence between a subsam-

pled input and its ﬁltering result.

Luminance values are highly correlated between

pixels and its neighboring region in the image. Also,

the correlation between the output of edge-preserving

ﬁltering and the input image becomes high. There-

fore, in this method, a LUT for each pixel is created

from a pair of low-resolution input and output ima-

ges. Then, we refer the subsampled LUT to generate

the high-resolution edge-preserving image. Initially,

an input image I

I is subsampled to generate a low-

resolution input image I

↓

= S

I), (21)

where S

is a subsampling operator. Then, edge-

preserving ﬁlter is applied for I

↓

and the output J

↓

is obtained as follows:

↓

= F(I

↓

), (22)

where F is an operator of arbitrary edge-preserving

ﬁltering. Then, we count frequency of one-to-one

mapping between the images J

↓

and I

↓

. Let f

(s,t)

be a frequency map on a pixel p

p, where s and t are an

intensity value on image I

↓

and J

↓

, respectively. The

frequency is counted by gathering around a pixel. The

map f is deﬁned as follows:

(s,t) =

∑

q∈W

δ(S

q↓

),s)δ(S

q↓

),t), (23)

(x) = bx/lc (24)

128

Output

Input

(a) Frequency map

128

Output

Input

(b) Winner-takes-all

128

Output

Input

Figure 2: Frequency map f

(s,t) and its results of winner-

takes-all and dynamic programming approaches for local

LUT on p

p. The number of bins is 128, i.e., quantization

level is l = 2. The radius is r = 20 for visibility of this

ﬁgure. In the experiment, small radius setting, e.g., r = 2, 3

have better performance.

where δ(a,b) indicates the Kronecker delta function.

p = (x,y) indicates a pixel position in the images of

↓

and J

↓

. q

q is a neighboring pixel around p

p. W

indicates the set including q

q. S

(x) is a quantization

function, which is divided by l. The output values

have 256/l candidates. The redaction also accelera-

tes the processing. We call the number of intensity

candidates as the number of bins.

Next, we determine a local LUT on a pixel p

With the simplest solution, we select the maximum

frequency argument from the f by the winner-takes-

all approach (WTA). The LUT under the downsam-

pled domain is deﬁned as follows:

p↓

[s] = arg max

f (s,t) (25)

The operator [·] is an array operator in programming

languages, such as C programming language. We

cannot determine the value where f (s,t) = 0|

∀t

. In

this case, we linearly interpolate the values by the ne-

arest non-zero values around s. For boundary con-

dition, we set T

p↓

[0] = 0 and T

p↓

[255] = 255, when

f (s,t) = 0|

∀t

. The solution cannot keep monotonicity

for the LUT. The fact sometimes generates negative

edges.

To keep the monotonicity, we can solve the pro-

blem by using dynamic programming (DP). We as-

sume that T

[0] = 0 and T

[n] >= T

[n]. We deﬁne a

cost function C(s,t) for the DP under this condition:

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

134

(a) artiﬁcial (3072 × 2048) (b) tree (6088 × 4550) (c) bridge (2749× 4049)

(d) cathedral (2000 × 3008) (e) ﬁreworks (3136 × 2352)

Figure 3: High-resolution test images.

C(s,t)= max



C(s−1,t−1) + O,C(s−1,t)),C(s,t−1)



+ f (s,t)

(26)

where C(0, 0) = f (0,0), C(s,t) = 0 (s < 0 ∨ t < 0).

The parameter O represent an offset value to enforce

diagonal matching. The cost function can be recursi-

vely updated. After ﬁlling the cost function, then we

trace back the function to determine a solid pass.

p↓

= arg DP

C(s,t), (27)

where p

s shows the tracing back pass of the cost

matrix C by using DP. Figure 2 shows the frequency

map and the resulting LUTs obtained by WTA and

DP. After WTA and DP, the matrix indicates one-to-

one mapping. We call this per-pixel LUT T

as local

LUT.

The LUT has three-dimensional information, such

as n, p

p = (x, y); however, all elements are subsampled.

It has not enough to map an input image into a high-

resolution image. Therefore, we upsample the LUT

by using tri-linear upsampling. The upsampling is de-

ﬁned as follows:

= S

−1

p↓

)), (28)

where S

−1

and S

−1

is upsampling operator for the in-

tensity and spatial domain, respectively. p

p indicates

the image coordinate of pixel in the upsampled dom-

ain.

Finally, the output image is referred from the local

LUT and input intensity I

. The output is deﬁned by:

= T

]. (29)

4 EXPERIMENTAL RESULTS

We approximated two edge-preserving ﬁlters, such as

iterative bilateral ﬁltering and L

smoothing by subs-

ampling based acceleration methods. These ﬁlters can

mostly smooth images; however, the computational

cost is high. We compared the proposed method of

the local LUT upsampling with the conventional met-

hod of the cubic upsampling and guided image ups-

ampling by approximation accuracy and computatio-

nal time. Also, we compared the proposed method

with na

ıve implementation, which does not subsam-

ple images, in computational time. We utilized high-

resolution test images, which are shown in Fig. 3

We used two metrics of PSNR and SSIM (Wang

et al., 2004) for accuracy evaluation, and we regar-

ded the results of the na

ıve ﬁltering as ground truth

http://imagecompression.info

Local LUT Upsampling for Acceleration of Edge-preserving Filtering

135

results. We implemented the proposed method by

C++ with OpenMP parallelization. We also used In-

tel IPP for the cubic upsampling, which is optimized

by AVX/AVX2. For guided image upsampling, we

also optimized by AVX/AVX2 with OpenCV functi-

ons. For downsampling in the proposed method, we

use the nearest neighbor downsampling. This downs-

ampling has better performance than the cubic inter-

polation for our method. We used OpenCV and In-

tel IPP for the operation with cv::INTER NN option.

The used computer was Intel Core i7 6700 (3.40 GHz)

and compiled by Visual Studio 2017. We used r = 3

for local LUT upsampling, r = 10, iteration = 10,

= 10,σ

= 20 for iterative bilateral ﬁltering, and

λ = 0.01 and κ = 1.5 for L

smoothing.

Figures 4, 5, and 6 show the PSNR/SSIM accu-

racy and computational time of iterative bilateral ﬁl-

tering and L

smoothing for large images. The para-

meters of the proposed method are l = 2 and downs-

ampling ratio is 8 × 8. The computational time is an

average of 10 trails. The local LUT upsampling has

drastically higher PSNR than the cubic interpolation

for each image. Guided image upsampling is slower

and lower PSNR than the proposed method. The com-

putation time of the local LUT is ×100 faster than the

ıve implementation; however, the cubic upsampling

artificial

tree

bridge

cathedral

fireworks

PSNR [dB]

cubic upsampling

guided upsampling

local LUT

(a) Bilateral ﬁltering

artificial

tree

bridge

cathedral

fireworks

PSNR [dB]

cubic upsampling

guided upsampling

local LUT

(b) L

smoothing

Figure 4: Approximation accuracy of PSNR for each image

and method.

0.7

0.8

0.9

1.0

artificial

tree

bridge

cathedral

fireworks

SSIM

cubic upsampling

guided upsampling

local LUT

(a) Bilateral ﬁltering

0.7

0.8

0.9

1.0

artificial

tree

bridge

cathedral

fireworks

SSIM

cubic upsampling

guided upsampling

local LUT

(b) L

smoothing

Figure 5: Approximation accuracy of SSIM for each image

and method.

100

1000

10000

100000

1000000

artificial

tree

bridge

cathedral

fireworks

Time [ms]

cubic upsampling

guided upsampling

local LUT

naive

(a) Bilateral ﬁltering

100

1000

10000

100000

artificial

tree

bridge

cathedral

fireworks

Time [ms]

cubic upsampling

guided upsampling

local LUT

naive

(b) L

smoothing

Figure 6: Computational time for each image and method.

is ×10000 faster. Notice that the code of the proposed

method is not vectorized, such as AVX/AVX2; thus,

the proposed can speed up by programming, while In-

tel’s code fully optimizes the cubic upsampling. We

now optimize the code for the proposed method while

reviewing period.

Figures 7 and 8 show the relationship between

spatial/range subsampling ratio and PSNR for itera-

tive bilateral ﬁltering and L

smoothing. The result

shows that 1/4 range downsampling (64 bin) and

8 × 8 spatial downsampling do not notable decrease

the PSNR quality.

Figures 9 and 10 show the trade-off between the

PSNR accuracy and computational time by changing

the resizing ratio from 1/16 to 1/1024. We also

change the number of bins for local LUT upsampling.

These results show that the proposed method has the

best trade-off than the cubic interpolation and guided

image upsampling.

Figures 11 and 12 depict input image and results

of each upsampling method for iterative bilateral ﬁl-

tering and L

smoothing, respectively.

128

PSNR [dB]

number of bins

subsampling rate : 1024

subsampling rate : 256

subsampling rate : 64

subsampling rate : 16

Figure 7: Bilateral ﬁltering result: PSNR w.r.t. the number

of bins with changing resizing ratio.

128

PSNR [dB]

number of bins

subsampling rate : 1024

subsampling rate : 256

subsampling rate : 64

subsampling rate : 16

Figure 8: L

smoothing result: PSNR w.r.t. the number of

bins with changing resizing ratio.

5 CONCLUSIONS

In this paper, we proposed an acceleration method for

edge-preserving ﬁltering with image upsampling. We

call the upsampling as local LUT upsampling. The lo-

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

136

(a) Input (b) Na

ıve (c) Cubic (d) Guided Upsampling (e) Local LUT

Figure 11: Results of iterative bilateral ﬁltering.

(a) Input (b) Na

ıve (c) Cubic (d) Guided Upsampling (e) Local LUT

Figure 12: Results of L

smoothing.

1000

2000

3000

4000

5000

6000

7000

PSNR [dB]

Time [ms]

cubic upsampling

guided upsampling

number of bins : 32

number of bins : 64

number of bins : 128

Figure 9: Resizing and changing the number of bins perfor-

mance in PSNR w.r.t. computational time (bilateral ﬁlter).

Local LUT samples 32, 64, and 128 bins, respectively.

5000

10000

15000

20000

PSNR [dB]

Time [ms]

cubic upsampling

guided upsampling

number of bins : 32

number of bins : 64

number of bins : 128

Figure 10: Resizing and changing the number of bins per-

formance in PSNR w.r.t. computational time (L

smoo-

thing). Local LUT samples 32, 64, and 128 bins, respecti-

vely.

cal LUT upsampling has higher approximation accu-

racy than the conventional approaches of cubic and

guided image upsampling. Also, the local LUT ups-

ampling accelerates ×100 faster than the na

ıve imple-

mentation.

ACKNOWLEDGEMENTS

This work was supported by JSPS KAKENHI

(JP17H01764, 18K18076).

REFERENCES

Adams, A., Baek, J., and Davis, M. A. (2010). Fast high-

dimensional ﬁltering using the permutohedral lattice.

Computer Graphics Forum, 29(2):753–762.

Aubry, M., Paris, S., Hasinoff, S. W., Kautz, J., and Durand,

F. (2014). Fast local laplacian ﬁlters: Theory and ap-

plications. ACM Transactions on Graphics, 33(5).

Bae, S., Paris, S., and Durand, F. (2006). Two-scale tone

management for photographic look. ACM Transacti-

ons on Graphics, pages 637–645.

Buades, A., Coll, B., and Morel, J. M. (2005). A non-local

algorithm for image denoising. In Proc. Computer Vi-

sion and Pattern Recognition (CVPR).

Chaudhury, K. N. (2011). Constant-time ﬁltering using

shiftable kernels. IEEE Signal Processing Letters,

18(11):651–654.

Chaudhury, K. N. (2013). Acceleration of the shiftable o(1)

algorithm for bilateral ﬁltering and nonlocal means.

IEEE Transactions on Image Processing, 22(4):1291–

1300.

Chaudhury, K. N., Sage, D., and Unser, M. (2011).

Fast o(1) bilateral ﬁltering using trigonometric range

Local LUT Upsampling for Acceleration of Edge-preserving Filtering

137

kernels. IEEE Transactions on Image Processing,

20(12):3376–3382.

Dabov, K., Foi, A., Katkovnik, V., and Egiazarian, K.

(2007). Image denoising by sparse 3-d transform-

domain collaborative ﬁltering. IEEE Transactions on

image processing, 16(8):2080–2095.

Durand, F. and Dorsey, J. (2002). Fast bilateral ﬁltering

for the display of high-dynamic-range images. ACM

Transactions on Graphics, 21(3):257–266.

Eisemann, E. and Durand, F. (2004). Flash photography en-

hancement via intrinsic relighting. ACM Transactions

on Graphics, 23(3):673–678.

Fujita, S., Fukushima, N., Kimura, M., and Ishibashi, Y.

(2015). Randomized redundant dct: Efﬁcient denoi-

sing by using random subsampling of dct patches. In

Proc. ACM SIGGRAPH Asia 2015 Technical Briefs.

Fukushima, N., Fujita, S., and Ishibashi, Y. (2015). Swit-

ching dual kernels for separable edge-preserving ﬁl-

tering. In Proc. IEEE International Conference on

Acoustics, Speech and Signal Processing (ICASSP).

Fukushima, N., Maeda, Y., Kawasaki, Y., Nakamura, M.,

Tsumura, T., Sugimoto, K., and Kamata, S. (2018a).

Efﬁcient computational scheduling of box and gaus-

sian ﬁr ﬁltering for cpu microarchitecture. In Proc.

Asia-Paciﬁc Signal and Information Processing As-

sociation Annual Summit and Conference (APSIPA),

2018.

Fukushima, N., Sugimoto, K., and Kamata, S. (2018b).

Guided image ﬁltering with arbitrary window

function. In Proc. IEEE International Conference on

Acoustics, Speech and Signal Processing (ICASSP).

Fukushima, N., Takeuchi, K., and Kojima, A. (2016). Self-

similarity matching with predictive linear upsampling

for depth map. In Proc. 3DTV-Conference.

Gastal, E. S. L. and Oliveira, M. M. (2011). Domain

transform for edge-aware image and video processing.

ACM Transactions on Graphics, 30(4).

Gastal, E. S. L. and Oliveira, M. M. (2012). Adaptive ma-

nifolds for real-time high-dimensional ﬁltering. ACM

Transactions on Graphics, 31(4).

Ghosh, S., Nair, P., and Chaudhury, K. N. (2018). Optimi-

zed fourier bilateral ﬁltering. IEEE Signal Processing

Letters, 25(10):1555–1559.

He, K. and Sun, J. (2015). Fast guided ﬁlter. CoRR,

abs/1505.00996.

He, K., Sun, J., and Tang, X. (2009). Single image haze

removal using dark channel prior. In Proc. Computer

Vision and Pattern Recognition (CVPR).

He, K., Sun, J., and Tang, X. (2010). Guided image ﬁl-

tering. In Proc. European Conference on Computer

Vision (ECCV).

Hosni, A., Rhemann, C., Bleyer, M., Rother, C., and Ge-

lautz, M. (2013). Fast cost-volume ﬁltering for vi-

sual correspondence and beyond. IEEE Transacti-

ons on Pattern Analysis and Machine Intelligence,

35(2):504–511.

Kodera, N., Fukushima, N., and Ishibashi, Y. (2013). Fil-

ter based alpha matting for depth image based ren-

dering. In Proc. IEEE Visual Communications and

Image Processing (VCIP).

Kopf, J., Cohen, M. F., Lischinski, D., and Uyttendaele, M.

(2007). Joint bilateral upsampling. ACM Transactions

on Graphics, 26(3).

Levin, A., Lischinski, D., and Weiss, Y. (2004). Colo-

rization using optimization. ACM Transactions on

Graphics, 23(3):689–694.

Maeda, Y., Fukushima, N., and Matsuo, H. (2018a). Ef-

fective implementation of edge-preserving ﬁltering on

cpu microarchitectures. Applied Sciences, 8(10).

Maeda, Y., Fukushima, N., and Matsuo, H. (2018b). Taxo-

nomy of vectorization patterns of programming for ﬁr

image ﬁlters using kernel subsampling and new one.

Applied Sciences, 8(8).

Matsuo, T., Fujita, S., Fukushima, N., and Ishibashi, Y.

(2015). Efﬁcient edge-awareness propagation via

single-map ﬁltering for edge-preserving stereo mat-

ching. In Proc. SPIE, volume 9393.

Matsuo, T., Fukushima, N., and Ishibashi, Y. (2013). Weig-

hted joint bilateral ﬁlter with slope depth compensa-

tion ﬁlter for depth map reﬁnement. In Proc. Inter-

national Conference on Computer Vision Theory and

Applications (VISAPP).

Min, D., Choi, S., Lu, J., Ham, B., Sohn, K., and Do, M. N.

(2014). Fast global image smoothing based on weig-

hted least squares. IEEE Transactions on Image Pro-

cessing, 23(12):5638–5653.

Murooka, Y., Maeda, Y., Nakamura, M., Sasaki, T., and Fu-

kushima, N. (2018). Principal component analysis for

acceleration of color guided image ﬁltering. In Proc.

International Workshop on Frontiers of Computer Vi-

sion (IW-FCV).

Paris, S., Hasinoff, S. W., and Kautz, J. (2011). Local lapla-

cian ﬁlters: Edge-aware image processing with a lap-

lacian pyramid. pages 68:1–68:12.

Petschnigg, G., Agrawala, M., Hoppe, H., Szeliski, R., Co-

hen, M., and Toyama, K. (2004). Digital photography

with ﬂash and no-ﬂash image pairs. ACM Transacti-

ons on Graphics, 23(3):664–672.

Sugimoto, K., Fukushima, N., and Kamata, S. (2016).

Fast bilateral ﬁlter for multichannel images via soft-

assignment coding. In Proc. Asia-Paciﬁc Signal and

Information Processing Association Annual Summit

and Conference (APSIPA).

Sugimoto, K. and Kamata, S. (2015). Compressive bilate-

ral ﬁltering. IEEE Transactions on Image Processing,

24(11):3357–3369.

Tomasi, C. and Manduchi, R. (1998). Bilateral ﬁltering for

gray and color images. In Proc. International Confe-

rence on Computer Vision (ICCV), pages 839–846.

Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P.

(2004). Image quality assessment: from error visi-

bility to structural similarity. IEEE Transactions on

Image Processing, 13(4):600–612.

Xu, L., Lu, C., Xu, Y., and Jia, J. (2011). Image smoothing

via l0 gradient minimization. ACM Transactions on

Graphics.

Yang, Q., Tan, K. H., and Ahuja, N. (2009). Real-time o

(1) bilateral ﬁltering. In Proc. Computer Vision and

Pattern Recognition (CVPR), pages 557–564.

Yu, G. and Sapiro, G. (2011). Dct image denoising: A sim-

ple and effective image denoising algorithm. Image

Processing On Line, 1:1.

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

138