压缩灰度图像快速区域分割：非对称反打包与扩展阴影表示法

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"该资源是一篇研究论文，探讨了一种基于非对称反打包模型(Non-symmetry and Anti-packing Model, NAMES)和扩展阴影表示(Extended Shading, ES)的压缩灰度图像快速区域分割算法。由中山大学、宾夕法尼亚大学放射学系和华中科技大学软件工程学院的研究人员共同完成。文章于2015年4月提交，11月接受，并在网上发布。关键词包括图像表示、图像分割、四叉树阴影表示(QS)、层次表示模型、非对称反打包模型与扩展阴影表示、二元分区树(BPT)、同质块以及区域分割和压缩灰度图像。" 本文的主要研究内容是图像分割技术，特别是在压缩灰度图像上的应用。图像分割在图像分析中扮演着关键角色，其目的是识别并区分图像中的同质区域，将它们归类为不同的对象或类别。传统的图像分割方法可能在处理压缩图像时效率低下，因为需要先解压再进行处理，这会增加计算时间和内存需求。论文提出了一种新的快速区域分割算法，该算法结合了非对称反打包模型和扩展阴影表示。非对称反打包模型是一种优化的数据结构，用于高效地存储和处理图像信息，尤其是在压缩状态下。这种模型能够减少解压过程中的计算复杂性，提高处理速度。扩展阴影表示则是一种增强图像细节的方法，通过改进原有的四叉树阴影表示（Quadtree Shading, QS）来提供更精确的图像区域边界描述。此外，论文还提到了层次表示模型，如二元分区树(BPT)，这是一种用于图像分割的树状结构，可以递归地将图像划分为较小的同质块。这种结构有助于快速定位和分割图像中的不同区域。同质块的概念是指在特定特征（如颜色、纹理或亮度）上相似的像素集合，是图像分割中的基本单元。论文的贡献在于提出了一种能够在不完全解压图像的情况下进行有效分割的新方法，这对于处理大体积的压缩图像数据尤其有用。这种方法减少了对内存的需求，提高了实时性和效率，对于医疗成像、遥感图像分析和其他领域有着重要的应用价值。这篇论文深入研究了压缩图像处理的挑战，并提出了一种创新的、基于NAMES和ES的快速区域分割算法，为图像分析领域的研究和实践提供了新的思路和技术支持。

In fact, previously, considering a map image, Dillencourt and

Samet [43] presented a pioneering region segmentation algorithm

on the quadtree representation, where each leaf node represented

a block with constant color. On the gray image of size N  N, Fiorio

and Gustedt [44] presented two linear-time, i.e., OðN

Þ-time, algo-

rithms for performing the region segmentation. With the same

time complexity, Chung et al. [45] extended the pioneering results

by Dillencourt and Samet from the map image to the gray image

and presented an efﬁcient OðB

ðBÞÞ-time algorithm for performing

region segmentation on the compressed image directly by using

quadtree and shading representation, which was called the QS-

based algorithm, where B was the number of homogenous blocks

and

ðBÞ was the inverse of the Ackerman’s function. In addition,

with four real images, their experimental results showed that the

QS-based algorithm had about 55.4% execution time improvement

ratio when compared to the previous fastest region segmentation

algorithm by Fiorio and Gustedt whose OðN

Þ-time algorithm

was run on the original N  N gray image.

However, in this paper, with the same experimental condition

and the same time complexity as the QS-based algorithm, the

experimental results presented show that our proposed

NAMES-based algorithm has about 86.75% and 89.47% average exe-

cution time improvement ratio when compared to the BPT-based

algorithm and the QS-based algorithm, respectively. To the best of

our knowledge, this is the ﬁrst time to propose a region segmenta-

tion algorithm on compressed gray images using Non-symmetry

and Anti-packing Model and Extended Shading representation.

The main contributes of this paper lie in: Firstly, we put forward

four extended Lemmas and two extended Theorems which could

be considered as the bases of our proposed NAMES-based segmen-

tation algorithm. Secondly, unlike the data structures used to merge

two regions in the QS-based algorithm, we propose some novel

NAMES-based data structures in our algorithm. Thirdly, we present

a new scanning method used to process each NAMES block, which

is totally different from the traditional scanning method. Fourthly,

we extend the popular hierarchical representation model to a

new non-hierarchical representation model. Finally, by comparing

our NAMES-based algorithm with the QS-based algorithm and the

BPT-based algorithm, the experimental results show that the for-

mer has not only higher compression ratio and less number of

homogenous blocks than the latter whereas maintaining the satis-

factory image quality, but also it can signiﬁcantly improve the exe-

cution speed for image segmentation.

2. Principium of proposed NAMES-based segmentation

algorithm

Inspired by the concept of the packing problem, a novel Non-

symmetry and Anti-packing Model (NAM) was proposed in our

previous work [26] in order to represent the pattern more effec-

tively. In this paper, our proposed novel segmentation algorithm

uses the NAM and the extended Gouraud shading approach which

were introduced in [26–28].

2.1. Theoretical bases of our proposed algorithm

We ﬁrst present and prove four extended Lemmas and two

extended Theorems which are considered as the bases of our

NAMES-based algorithm. A formal deﬁnition of a NAMES block B

is shown in Fig. 1 where g

; g

, and g

are gray values of the

four corners.

By using our proposed extended Gouraud shading approach, the

estimated gray value at the coordinate (x; yÞ, i.e., g

est

ðx; yÞ, in the

block is calculated by the following four cases:

est

ðx; yÞ¼

þðg

 g

Þi

< x

; y

< y

þðg

 g

Þi

– x

; y

¼ y

þðg

 g

Þi

¼ x

; y

– y

¼ x

; y

¼ y

where g

¼ g

þðg

 g

Þi

; g

¼ g

þðg

 g

Þi

; i

¼ðy  y

Þ/

ðy

 y

Þ; i

¼ðx  x

Þ=ðx

 x

Þ.

In the encoding phase and the decoding phase, the extended

Gouraud shading approach is used to control the image quality

under a speciﬁed error tolerance. Given a speciﬁed error tolerance

, a NAMES block is called a homogeneous block if the condition

jgðx; yÞg

est

ðx; yÞj 6

holds for all the pixels in the block, where

gðx; yÞ is the gray value at the coordinate (x; yÞ; x

6 x 6 x

and

6 y 6 y

The following steps present how to search and locate the gray

values g

, g

, and g

of each NAMES block for a given gray image

Step 1. Find out an unmarked start point ðx

; y

Þ from the ﬁrst

entrance of the gray image I according to the raster scanning

order.

Step 2. Let the point ðx

; y

Þ be an upper-left coordinate of the

block and ﬁnd out the biggest block in terms of the speciﬁed

error tolerance

Step 3. Mark the found block in the gray image I.

Step 4. Record the parameters of the found block, i.e., the coor-

dinate of the top left vertex ðx

; y

Þ, the coordinate of the bot-

tom right vertex ðx

; y

Þ, and the gray values of the four

corners g

, g

, and g

Step 5. Repeat Step 1 to Step 4 until there is no unmarked block

in the gray image I.

According to the deﬁnition of the NAMES block, we can easily

know that a new block is still a NAMES block after it is rotated in

an integral multiple of 90 degrees. However, if a NAMES block is

rotated in any degree except an integral multiple of 90 degrees,

then the new block may or may not be a NAMES block since the

size of the new block will be changed due to the rotation. Also, if

we resize a NAMES block by a function B = imresize(A; M, METHOD)

which returns a new block that is M times the size of A, then we

can easily know that if M is between 0 and 1.0, the new block is still

a NAMES block; otherwise, the new block may or may not be a

NAMES block since the size of the new block will be changed into

a bigger size than its original size. The variable METHOD herein

represents an interpolation method, such as the nearest neighbor

interpolation, the bilinear interpolation, and the bicubic

interpolation.

As far as the NAMES block B is concerned, suppose that the size

of the homogenous block is w  h, and that gðx; yÞ is the gray value

at the coordinate (x; yÞ where x

6 x 6 x

and y

6 y 6 y

. In the

following Lemmas and Theorems, let

g

x

g

w1

g

x

g

w1

g

y

g

h1

g

y

g

h1

, C

2w1

6 w1ðÞ

2h1

6 h1ðÞ

, and D

g

þg

w1ðÞh1ðÞ

In the case of the NAMES block B, the estimated gray value

est

ðx; yÞ at position ðx; yÞ where x

6 x 6 x

and y

6 y 6 y

can

be calculated as follows:

Y. Zheng, M. Sarem / J. Vis. Commun. Image R. 34 (2016) 153–166

155

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