Single Image Super-resolution using Vectorization and Texture Synthesis

Kaoning Hu

, Dongeun Lee

and Tianyang Wang

Department of Computer Science and Information Systems, Texas A&M University - Commerce, Commerce, Texas, U.S.A.

Department of Computer Science and Information Technology, Austin Peay State University, Clarksville, Tennessee, U.S.A.

Keywords:

SISR, Image Vectorization, Texture Synthesis, KS Test.

Abstract:

Image super-resolution is a very useful tool in science and art. In this paper, we propose a novel method for

single image super-resolution that combines image vectorization and texture synthesis. Image vectorization is

the conversion from a raster image to a vector image. While image vectorization algorithms can trace the ﬁne

edges of images, they will sacriﬁce color and texture information. In contrast, texture synthesis techniques,

which have been previously used in image super-resolution, can reasonably create high-resolution color and

texture information, except that they sometimes fail to trace the edges of images correctly. In this work,

we adopt the image vectorization to the edges of the original image, and the texture synthesis based on the

Kolmogorov–Smirnov test (KS test) to the non-edge regions of the original image. The goal is to generate a

plausible, visually pleasing detailed higher resolution version of the original image. In particular, our method

works very well on the images of natural animals.

1 INTRODUCTION

Image super-resolution is a technique that enhances

the resolution of digital images. It has a various

range of applications including medical image pro-

cessing, satellite image processing, art, and entertain-

ment. In this paper, we focus on single image super-

resolution (SISR), which is a classic computer vision

problem to create a visually pleasing high-resolution

image from a single low-resolution input image. In

many situations, a single low-resolution image is the

only source of data when a video sequence or high-

resolution footage does not exist, thus SISR tech-

niques are highly demanded. However, since the

ground truth (i.e. the high-resolution information)

does not exist in the low-resolution image, SISR is

still a challenging problem.

In general, there are four types of super-

resolution methods (Sun et al., 2008): interpolation-

based, learning-based, reconstruction-based, and

edge-directed. The interpolation-based methods, such

as bilinear and bicubic interpolations, are simple

and fast, and have been widely used in commercial

software. However, these methods typically make

the edges of the image blurry. The learning-based

methods ﬁrst learn the correspondences between low-

resolution and high-resolution image patches from the

training dataset, and then apply the learned model

on the test set of low-resolution images to create a

high-resolution image (Yang et al., 2019; Zhang et al.,

2019). With deep neural networks, they can perform

very well on general images. However, these methods

rely largely on the quality of the similarity between

the training set and the test set, and also require a large

training set (Wang et al., 2013). The reconstruction-

based methods assume that the downsampled version

of the target high-resolution image is similar to the

low-resolution image that we have (Wang et al., 2013;

Damkat, 2011). However, it is observed that the re-

constructed edges sometimes are unnaturally sharp

and are often accompanied by undesired artifacts such

as ringing (Wang et al., 2013). The edge-directed

methods place emphasis on processing edges in the

target high-resolution image by tracing the edge with

the gradient of the input low-resolution image (Wang

et al., 2013). While they can create smooth and nat-

ural edges in the target image, these methods can-

not always properly handle certain texture regions

such as grass and animal hair. Therefore, the edge-

directed methods work better in upscaling of video

game pixel arts (Stasik and Balcerek, 2017) and depth

images (Liu and Ling, 2020; Xie et al., 2015), where

there is not much texture information. Since each type

of super-resolution methods has advantages and dis-

advantages, methods that combine two or more types

also exist (Yang et al., 2017; Liu et al., 2019).

512

Hu, K., Lee, D. and Wang, T.

Single Image Super-resolution using Vectorization and Texture Synthesis.

DOI: 10.5220/0010325505120519

In Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2021) - Volume 4: VISAPP, pages

512-519

ISBN: 978-989-758-488-6

Due to the different types of image capturing de-

vices, and objects in the images, there are many dif-

ferent categories of images. As such, SISR methods

have been developed to particularly work on certain

types of images. Besides the previously mentioned

game pixel arts and depth images, there are also meth-

ods that work on remote sensing images (Jiang et al.,

2019), medical images (Chen et al., 2018), and docu-

ment and text images (Wang et al., 2019).

We have observed that most of the previous work

emphasize enhancing edges in the images. Few meth-

ods exist that put emphasis on texture regions (Saj-

jadi et al., 2017). In this paper, we propose a novel

approach that combines texture synthesis and image

vectorization to upscale a single digital image. In par-

ticular, we focus attention on SISR for natural animal

images, as our method works very well in processing

the hair and feather parts of those images.

A digital image of natural animals or objects typ-

ically contains edge regions, where the brightness

changes sharply along contours, and non-edge re-

gions, where there is no signiﬁcant edge. Although

texture regions still have small edges as the colors of

neighboring pixels could be different, these edges are

usually too tiny and irregular to be traced. For this

reason, we consider texture regions as non-edge re-

gions. Edge regions and non-edge regions show sig-

niﬁcantly different visual characteristics. Therefore,

it is reasonable to treat them separately and apply dif-

ferent upscaling operations.

Speciﬁcally, for the edge regions, we will adopt

Potrace (Selinger, 2003), an image vectorization

method, to trace the edge and upscale the regions. Po-

trace approximates the edges in an image ﬁrst with

polygons, and then sharp corners are approximated

with sharp angles, while non-sharp corners are ap-

proximated with B

ezier curves. For the non-edge

regions, we will assume they contain texture infor-

mation, and will exploit the self-similarity of the

texture and apply a texture synthesis method based

on Kolmogorov–Smirnov Test (KS test) (Massey Jr,

1951) to upscale the texture regions. Our work uses

the KS test since it can naturally compare the proba-

bility distributions of an upscaled texture patch and a

low-resolution texture patch whose sizes are different.

The paper is organized as follows. In Section 2,

related work, including conventional algorithms and

deep learning algorithms, is discussed. In Section 3,

we will introduce the proposed method in detail. In

Section 4, we will demonstrate results and evalu-

ate the performance of our image super-resolution

method. The conclusion and future work will be

stated in Section 5.

2 RELATED WORK

In recent years, deep learning has been successfully

applied to SISR, and some non-deep learning meth-

ods have also been successfully implemented in com-

mercial software. Successful commercial software in-

cludes DCCI2x (Zhou et al., 2012) and ON1 Resize.

DCCI2x is an edge-directed interpolation method

that adapts to different edge structures of images.

ON1 Resize uses the technology of the U.S. patent

“Genuine Fractals



” (Faber and Dougherty, 2007),

which exploits the self-similarity of an image to in-

crease its size while preserving its details. Typical

deep learning-based methods include (Zhang et al.,

2019; Zhang et al., 2018), and (Ledig et al., 2017).

In (Zhang et al., 2019), a novel degradation model

for SISR was proposed, leveraging the classical blind

deblurring methods. In (Zhang et al., 2018), the au-

thors aimed to improve framework practicability by

designing a single convolutional network that can take

both blur kernel and noise level as input. Ledig et

al. (Ledig et al., 2017) pioneered to propose a genera-

tive adversarial network (GAN) for SISR, namely SR-

GAN. All these methods achieved competitive quan-

titative results (in PSNR/SSIM) and appealing qual-

itative results. However, most of these methods em-

phasized processing of the edge regions, but not the

texture regions. In 2017, Sajjadi et al. (Sajjadi et al.,

2017) proposed a learning-based method that uses

convolutional neural networks in an adversarial train-

ing setting with a texture loss function. Their goal

was to upscale low-resolution images by a 4 × 4 fac-

tor with synthesized realistic textures.

It is understandable that in many applications, the

primary goal is not to faithfully reconstruct a high-

resolution version of an input low-resolution image,

but to improve its appearance (Damkat, 2011). In

2011, Damkat (Damkat, 2011) proposed an SISR

method using example-based texture synthesis. The

assumption is that even in a low-resolution image,

there are still a number of scale-invariant elements

and self-similarity across scale. For example, animal

hair looks similar at different scales, so upscaling may

be achieved by generating more hairs instead of mak-

ing hairs thicker. Their method achieved relatively

good result in the texture regions except some salt-

and-pepper noises.

The idea of self-similarity can be also explained

by fractals, whose applications include fractal com-

pression (Jacquin et al., 1992; Wohlberg and De Jager,

1999). Fractal compression takes advantage of self-

similarity in images by analyzing and representing

image blocks in terms of parametric models. Since

parts of an image often resemble other parts of the

Single Image Super-resolution using Vectorization and Texture Synthesis

513

same image thanks to the self-similarity, those para-

metric models can signiﬁcantly reduce redundant in-

formation in images. Later, approximation to origi-

nal images can be regenerated by synthesizing from

the parametric models (Sayood, 2012). Our approach

analyzes the low-resolution image to search for self-

similar elements and synthesize new texture regions

from those.

KS test is a popular test for checking similarity

in time series (Lee et al., 2019; Lee et al., 2016) and

images (Khatami et al., 2017; Hatzigiorgaki and Sko-

dras, 2003). It is a statistical tool to measure whether

two underlying one-dimensional probability distribu-

tions follow the same statistical distribution, which

is simple to implement and faster than other non-

parametric statistical hypothesis testing methods.

3 PROPOSED METHOD

The proposed method contains two parts: Image vec-

torization on the edge regions and texture synthesis

on the non-edge regions. The two parts are then fused

to form the ﬁnal result.

Image vectorization, also known as image tracing

or raster-to-vector conversion, has been used in com-

puter graphics to convert a raster image to a vector im-

age. Because vector images only keep the mathemat-

ical expressions of points, lines and curves, they are

scalable. However, real-world photos cannot be rep-

resented as mathematical expressions alone. There-

fore, real-world photos are typically stored as raster

images, whereas vector images are typically used to

store certain art works, such as logos, fonts and some

cartoons. Due to these characteristics, image vector-

ization techniques cannot be directly used in image

super-resolution.

On the other hand, an important aspect of im-

age super-resolution is edge enhancement. To pro-

duce ﬁne and clear edges in high resolution from

a low-resolution image, edge extraction and tracing

have been used in image super-resolution algorithms.

Therefore, edge tracing techniques adopted from im-

age vectorization algorithms can be very useful in

processing the edges for the purpose of image super-

resolution. In our paper, we will apply the algorithm

of Potrace (Selinger, 2003) to scale the edge regions

of the low-resolution image, as Potrace is one of the

most promising image vectorization methods.

Besides the edge regions, an image also con-

tains many non-edge regions. Some of these regions

are plain regions, where color and brightness do not

change very much. Examples are blue sky, white

walls, blackboard, etc. Because there is not much in-

formation in these regions, any image scaling method

can work well. However, there are also many non-

edge regions with important texture information. Ex-

amples are animal hair, bird feather, lawns, wood sur-

face, etc. Since these regions do not have signiﬁ-

cant edges, it is usually impossible to represent them

with mathematical expressions. Therefore, an algo-

rithm that processes the texture should be used in-

stead. With a single low-resolution image, we will as-

sume it contains a considerable amount of self-similar

elements (Damkat, 2011) that can be reused to synthe-

size ﬁne texture for a high-resolution image.

To measure the similarity between pieces of im-

age texture elements, we will combine two measure-

ments. One is the basic Euclidean distance, which

is used to compare the color similarity of two pieces

of image blocks. We consider each image block as

a multi-dimensional vector, where the color of each

pixel in the block is a component, and the Euclidean

distance between two image blocks is computed in

such a hyperspace. The other similarity measurement

is based on the KS test. When we compute the simi-

larity of two image blocks, we use the KS test to mea-

sure the probability distributions of the colors of their

pixels.

With those image vectorization and texture syn-

thesis techniques, the framework of our proposed

algorithm is described as follows. Given a low-

resolution raster image I

, we ﬁrst use a colored vari-

ant of Potrace algorithm (Selinger, 2003), to convert

it to a vector image I

. Then we use a texture synthe-

sis method based on the KS test (Massey Jr, 1951) to

upscale the low resolution raster image I

to a high-

resolution raster image I

by the factor of 2 × 2. We

then fuse I

and I

to get a ﬁnal high-resolution im-

age with ﬁne edges I

. To fuse the two images, we

use edge regions from I

and non-edge regions from

. To distinguish the edge regions and the non-edge

regions, we use a Sobel edge detector on the original

image I

to extract the edge regions from the image.

A ﬂow chart of the proposed method is illustrated in

Figure 1.

The details of image vectorization and texture syn-

thesis will be discussed in the following subsections.

3.1 Image Vectorization using Potrace

Potrace is a robust image vectorization method that

has been successfully used in many programs, includ-

ing some commercial software. The original Potrace

works only with binary images. Its algorithm trans-

forms a black-white bitmap into a vector outline in

three steps (Selinger, 2003).

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

514

Figure 1: Flowchart of the proposed algorithm.

1. The bitmap is decomposed into a number of paths.

A path is a sequence of connected pixels at the

boundaries between black and white areas.

2. Each path is approximated by an optimal poly-

gon. A polygon with fewer segments (edges) is

considered optimal than one with more segments.

Among the polygons with the same number of

segments, a polygon with path points closer to the

segments is considered optimal than one with path

points strayed away from the segments.

3. Each polygon is transformed, so that each sharp

corner is approximated by a sharp angle, while

each non-sharp corners is approximated by a

smooth B

ezier curve.

4. An optional fourth step is to join consecutive

ezier curve segments together when possible.

To make Potrace work with color images, the al-

gorithm is slightly modiﬁed. The edge at the bound-

ary between each pair of different colors should be

traced. However, in a true color image, there are 2

different colors. As a result, it is impractical to trace

the edges of all colors, because the computation will

be too complex, and there will also be a lot of false

and noisy edges. Therefore, the number of colors

must be reduced. In our experiments, we have found

that it is the best to reduce the number of colors to

64. The loss of colors will have little effect to the ﬁ-

nal result, because only signiﬁcant edge regions from

the vectorized image are used in the ﬁnal fused image,

while the rest of the ﬁnal fused image come from the

texture synthesized image.

Figure 2: Comparison after downscale may lead to salt-and-

pepper noise in the texture synthesized image.

3.2 Texture Synthesis based on

Kolmogorov–Smirnov Test

In this step, we upscale the original I

using self-

similarity to obtain image I

. The scaling factor is

2 × 2. The original I

is divided into small blocks of

2 × 2. For example, a 320 × 240 image should be di-

vided into 160 × 120 blocks. To best preserve the ge-

ometrical structure and the texture information of I

in I

, each 2 × 2 block in I

is replaced by a suitable

4 × 4 super block from the same image I

. The self-

similarity of these textures across scale makes their

re-synthesis on a ﬁner scale look plausible (Damkat,

2011). There are two criteria to choose a suitable 4×4

super block S

4×4

that matches a 2 × 2 block B

2×2

1. When S

4×4

is downscaled to 2 × 2, it should look

like B

2×2

2. The color of the pixels in S

4×4

and B

2×2

should

follow the same probability distribution.

The measurement of the ﬁrst criterion is straight-

forward. We can downscale S

4×4

to a 2 × 2 block

2×2

, and compute its Euclidean distance (L2 dis-

tance) Dist

to B

2×2

in terms of pixel intensity (i.e.

color).

However, the above criterion alone cannot guar-

antee that S

4×4

matches B

2×2

. Here we have a spe-

cial case that S

4×4

does not match B

2×2

but the down-

scaled S

2×2

looks like B

2×2

. Given the super block in

Figure 2(a), after it is downscaled, it would look like

the block in Figure 2(b). However, (a) and (b) have

distinctive texture patterns. If (a) is used to replace

(b) in the texture synthesized image I

, it will create

some salt-and-pepper noises.

To avoid the above issue, we must ensure that the

pixel intensity (color) of S

4×4

should have a similar

probability distribution to B

2×2

. Therefore, we apply

the second criterion that requires the comparison of

two blocks whose sizes are different. Here, we should

not downscale S

4×4

, otherwise the above issue may

still appear. We should not upscale B

2×2

either, as

upscaling will modify the probability distribution. To

this end, we take advantage of the KS test, which is

capable of comparing the probability distributions of

Single Image Super-resolution using Vectorization and Texture Synthesis

515

two blocks, even if their sizes are different. In statis-

tics, the KS test is a nonparametric test of the equal-

ity of continuous or discontinuous, one-dimensional

probability distributions. It can be used to compare a

sample with a reference probability distribution, or to

compare two samples.

In our application, we use the two-sample KS test

to test whether two underlying probability distri-

butions of blocks differ or not. Since it is non-

parametric, it can compare two pixel blocks from any

arbitrary distributions without the restriction of para-

metric distribution assumption.

Speciﬁcally, the distance of the KS test is deﬁned

as follows:

Dist

(B, S)

= 1 − D

+ n

, (1)

where n

and n

are the numbers of samples for two

pixel blocks B

2×2

and S

4×4

; D

is the maximum

distributional distance between the two pixel blocks.

This distance, also called the test statistic is deﬁned as

follows:

sup

B,n

(x) − F

S,n

(x)|, (2)

where F

B,n

(·) and F

S,n

(·) are empirical (cumulative)

distribution functions of B

2×2

and S

4×4

; sup is the

supremum.

In addition to the above two criteria, to better pre-

serve the continuity of the brightness of the original

image, it is reasonable to take the surrounding neigh-

borhood of a block into consideration when we search

for a matching super block. However, if too many

neighborhoods are taken, not only the computational

complexity will be increased, but too much irrele-

vant information will be brought into the computa-

tion. Our experiments showed that using a single-

pixel wide neighborhood of a block can effectively

preserve the continuity.

As a result, the algorithm to synthesize the texture

using self-similarity is described as follows.

For each block B

2×2

in I

1. Extract its 4 × 4 neighborhood from I

. Denote it

as N

2. Scan the entire image I

. For each 8 × 8 patch N

whose center is a 4 × 4 super block S

4×4

(a) If Dist

(B, S) is greater than a threshold T ,

disqualify S

4×4

because its distribution is very

different from B

2×2

(b) Otherwise, compute Dist

, N

3. Among the qualiﬁed super blocks, ﬁnd the one

match

whose Dist

is the smallest. Place S

match

on I

at the location where B

2×2

maps to. If there

is no qualiﬁed super block, use bilinear interpola-

tion on B

2×2

to generate a super block and place

it on I

Because the KS test is used to process one-

dimensional probability distributions, in our experi-

ments, when we compute Dist

(B, S), we vectorize

2×2

to a vector of 4 components. In addition, to re-

duce the sensitivity to image variances, we extend the

vector to 16 components with padding 0s. For the

same reason, we also vectorize S

4×4

and extend it to

a vector of 64 components with padding 0s. Then

we compute Dist

between the 16-component vec-

tor and the 64-component vector.

To speed up the algorithm, in the Step (2), instead

of scanning the entire image, we could only scan a

neighborhood of the block B

2×2

. In our experiments,

we found that scanning a neighborhood of 80 × 80

produces very similar results to scanning the whole

image.

After the texture-synthesized image I

and the

vector image I

are generated, the edge regions of I

and the non-edge regions of I

are merged to obtain

the ﬁnal image I

. Anti-aliasing is used on the borders

between the two types of regions to provide a smooth

appearance, and a high threshold is used to extract the

edges, so that only the signiﬁcant edges from I

taken to I

4 EVALUATION

We have tested the effectiveness of the proposed

method using the free and public images from https:

//www.peakpx.com, together with a free turaco pic-

ture by D. Demczuk from Wikipedia and a picture of

a cat taken by ourselves. The process of our algorithm

is illustrated in Figure 3.

We compared our methods with the latest version

of two commercial software packages explained in

Section 2: DCCI2x (2016) (Zhou et al., 2012) and

ON1 Resize 2020 (Faber and Dougherty, 2007). The

results are shown in the following ﬁgures. In our ex-

periments, we downscaled high-resolution images to

low-resolution images, and then used our method as

well as the commercial methods to upscale the low-

resolution images, so that we can compare the up-

scaled results with the ground truth. It should be noted

that our goal is not to faithfully reconstruct the high-

resolution image, but to synthesize visually pleasing

textures.

From the ﬁgures, we can see that our method

is able to provide very sharp and clear textures on

these pictures of natural animals. We have also con-

ducted quantitative comparisons between our method

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516

Figure 3: (a) The original low-resolution image (b) Vector-

ized image I

(d) Edge

regions from I

(e) Non-edge regions from I

(f) Fused

high-resolution image I

- ﬁnal result.

Figure 4: Comparison of results of SISR: (a) Original

HR image (b) Downscaled LR input image (c) Result of

DCCI2x (d) Result of ON1 (e) Result of our method.

Figure 5: Comparison of results of SISR with enlarged de-

tails.

Figure 6: Comparison of results of SISR: (a) Original

HR image (b) Downscaled LR input image (c) Result of

DCCI2x (d) Result of ON1 (e) Result of our method.

Figure 7: Comparison of results of SISR with enlarged de-

tails.

and the two commercial methods. We have chosen to

use two image quality metrics: Blind/Referenceless

Image Spatial Quality Evaluator (BRISQUE) (Mit-

tal et al., 2012) and Perception based Image Qual-

ity Evaluator (PIQE) (Venkatanath et al., 2015). A

BRISQUE model is trained on a database of images

that have subjective quality scores. PIQE is not a

trained model, but it provides local measures of qual-

ity as well as the global quality. Both metrics evalu-

ates the image without any reference, i.e. without the

original high-resolution image. This is reasonable,

because in a real task of super-resolution, the orig-

inal high-resolution image is unknown. We did not

Single Image Super-resolution using Vectorization and Texture Synthesis

517

Figure 8: Comparison of results of SISR: (a) Original

HR image (b) Downscaled LR input image (c) Result of

DCCI2x (d) Result of ON1 (e) Result of our method.

Figure 9: Comparison of results of SISR with enlarged de-

tails.

Figure 10: Comparison of results of SISR: (a) Original

HR image (b) Downscaled LR input image (c) Result of

DCCI2x (d) Result of ON1 (e) Result of our method.

Figure 11: Comparison of results of SISR with enlarged

details.

choose PSNR. As we discussed earlier, PSNR does

not accurately represent the human perception of im-

age quality (Sajjadi et al., 2017), especially when our

images were generated with synthesized texture rather

than reconstructed texture.

The quantitative results are shown in Table 1 and

Table 2. Notice that for both metrics, a smaller score

indicates better perceptual quality.

Table 1: Comparison of results of SISR using BRISQUE.

DCCI2x ON1 Ours

Cat with leaves 26.3153 29.7062 11.0070

Parrot 30.5968 36.7937 31.5079

Humming bird 37.8469 34.6144 23.6938

Turaco 24.4243 21.7355 26.2029

Table 2: Comparison of results of SISR using PIQE.

DCCI2x ON1 Ours

Cat with leaves 39.8146 40.6859 15.0370

Parrot 51.0482 49.8260 23.3640

Humming bird 41.9027 40.1564 34.3446

Turaco 34.5005 29.6453 22.9146

From the tables, we can see that when using

BRISQUE, the two commercial methods outperforms

our method slightly on two of the images, while our

method outperforms them signiﬁcantly on the other

two images. When using PIQE, our method outper-

forms the other two methods signiﬁcantly.

5 CONCLUSION AND FUTURE

WORK

In this paper, we propose a two-phase novel single

image super-resolution method for natural animal im-

ages. Our goal is to synthesize visually pleasing tex-

tures for the hair and feather of animals, as well as

to preserve smooth and ﬁne edges of the images. For

the texture regions of the images, we propose a novel

texture synthesis method based on KS test to produce

ﬁne and sharp textures. For the edge regions, we ap-

ply a traditionally successful image tracing method

Potrace. The two intermediate results are then fused

to produce the ﬁnal result.

Experiments showed that our method outperforms

two popular and successful commercial approaches

in terms of synthesized texture quality. The synthe-

sized texture from our method is sharp and clear, with

little blurring effect. Quantitative comparisons also

showed that our method generally outperforms these

commercial methods.

In the future, we plan to conduct experiments with

more images. We will also focus on the image vector-

ization and improve the performance of edge tracing.

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

518

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