Texture analysis is the process of highlighting key characteristics thus providing an exhaustive and unambiguous mathematical description of any object represented in a digital image. Each characteristic is connected to a specific property of the object. In some cases the mentioned properties represent aspects visually perceptible which can be detected by developing operators based on Computer Vision techniques. In other cases these properties are not visually perceptible and their computation is obtained by developing operators based on Image Understanding approaches. Pixels composing high quality medical images can be considered the result of a stochastic process since they represent morphological or physiological processes. Empirical observations have shown that these images have visually perceptible and hidden significant aspects. For these reasons, the operators can be developed by means of a statistical approach. In this paper we present a set of customized first and second order statistics based operators to perform advanced texture analysis of Magnetic Resonance Imaging (MRI) images. In particular, we specify the main rules defining the role of an operator and its relationship with other operators. Extensive experiments carried out on a wide dataset of MRI images of different body regions demonstrating usefulness and accuracy of the proposed approach are also reported.
As it is well known, there is no univocal definition of texture [
The operators applied on a wide dataset containing
Different works in the literature concerning the description of the natural domain by texture analysis processes [
The paper is structured as follows. Section
This section details the designed texture analysis process. The mentioned process is the same on each established type of image (i.e., brain, heart, liver, and bones), where only the definition of some parameters has to be adjusted depending on both the specific type of image (e.g., brain or heart) and the fixed targets (e.g., brain mass or heart lesions identification). Being different targets heterogeneous and hugely numerous, our purpose is to provide a guideline on
Each image is entirely browsed by a window (recognition window, RW) of fixed size (i.e.,
Each RW contains a set of pixels (i.e.,
As shown in Figure
The source image is browsed by the operator
This section shows the CV and IU textural operators customized after our investigative experience regarding the established domains: brain, heart, liver, and bones. Since the browsing process determines the
The first two operators we consider are based on the first order statistic, specifically,
The following constraints must hold:
Actually, they are not properly textural operators, since their task is only to measure the informative content of different image zones. In particular, the first operator (
The rest of the operators introduced in this section are fully texture based since they work both on spatial disposition and amplitude value of the pixels contained within the RW. They are based on the Haralick et al. studies [
Variation of the Haralick et al. approach which considers all the possible directions and not only the cardinal ones. In the example the RW contains 9 pixels; each circumference provides 16 pair of pixels; therefore the current RW provides 144 values to the co-occurrence matrix.
The first two textural operators belonging to the second order statistic are customized to emulate two main visual perceptions related to the CV field [
The following constraints must hold:
In our context,
The other two textural operators belonging to the second order statistics are customized to determine two hidden significant features useful to identify both the period and the size of the involved patterns, specifically,
In our context,
Empirical experiences have allowed us to consider two other textural operators to support the working of the previous ones. These operators do not have a specific meaning: they are utilized to increase the detail and the reliability of the proposed second order statistics based operators, specifically,
In this context, it is important to note that the whole set of operators have different degrees of dependence. This means that the results of each operator have to be considered jointly with those provided from the others. A single operator is only able to describe the general features of a complex texture. To identify more patterns, different textural aspects have to be adopted within the same mathematical model. Table
Relationship between the customized first and second order statistics based operators. The value from 1 (low) to 4 (high) points out the dependence level between two operators.
Operators |
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In order to define qualitative and technical aspects of the proposed approach, experimental results were obtained from a wide dataset containing images of brain, heart, liver, and bones. In particular, the experimental phase was divided into three sessions: basic parameter definition, model parameter definition, and qualitative response. The first served to identify the basic parameters through which the source images had to be browsed; the second focused on the parameter definition of each first and second order statistics based operator according to a specific natural domain; finally, the third focused on the qualitative aspects of the approach with respect to a specific basic task (i.e., segmentation). All the experimental sessions were performed using MRI transversal
Table
I° experimental session: basic parameter definition.
Basic parameter definition | |||||||||
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Body regions | Training patients | Training images | Task | Recognition window (RW) | Image scanning process | Pyramid level | |||
Shape | Size | Mode | Type | Levels |
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Brain | 15 | 35 | Segmentation | Square |
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Top-to-down |
Without overlapping |
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Very high |
Heart | 10 | 30 | Segmentation | Square |
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Top-to-down |
Without overlapping |
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High |
Liver | 8 | 25 | Segmentation | Square |
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Top-to-down |
Without overlapping |
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Middle |
Bone | 8 | 20 | Segmentation | Square |
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Top-to-down |
With and without overlapping |
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Low |
Table
II° experimental session: model parameter definition.
Model parameter definition | ||||||||||
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Body regions | Training patients | Training images | First and second order statistics based operators | |||||||
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Brain | 55 | 135 |
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Heart | 45 | 105 |
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Liver | 35 | 85 |
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Bone | 25 | 55 |
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Figure
Qualitative response on (a) brain, (b) heart, (c) liver, and (d) bone.
Texture analysis of MRI images supports their exhaustive and unambiguous mathematical description. The base of this process is composed of a set of feature extractors to detect the key characteristics related to the objects contained within the image layout. These characteristics change depending on the established task (e.g., volume evaluation, lesions identification); despite this, our parametric approach designed for specific MRI images (i.e., brain, heart, liver, and bones) and the developed set of customizable textural operators can jointly provide a numerical interpretation of the images according to the specific task. This numerical interpretation represents a tool to describe different models to implement heterogeneous CAD functionalities (e.g., mass identification). To prove the usefulness and the accuracy of the proposed approach, we have fixed and tested the segmentation task on the analyzed domains; these experimental sessions allowed providing a set of information (i.e., roles, rules, and dependences) on the developed operators which can be used as guidelines to implement new tasks and CAD functionalities.
The authors are grateful to Mrs. Carmelita Marinelli for the technical assistance.