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Tissue classification based on 3D local intensity ... - IEEE Xplore

SATO ET AL.: TISSUE CLASSIFICATION BASED ON **3D** LOCAL INTENSITY STRUCTURES FOR VOLUME RENDERING 167 Fig. 5. Guideline 1: Using gradient magnitude to avoid mis**on****on**ds to the value of …p†. The 2D histogram distributi**on** of each edge profile has an arch-shape. In order to keep the same relative relati**on** of S int and S (or M ), all of the 2D histograms shown in this paper were plotted within the domain described as …S int ; S †2‰a; bŠ‰0; 4…b a†=15Š, where ‰a; bŠ depends **on** each applicati**on**. (c) Typical discrete **on****on****on** the arch-shaped distributi**on** observed in the 2D histogram …S int ; S edge † so that, as far as possible, med does not include voxels affected by the partial volume effect (green arch). **on****on** the original **intensity** S int . The specific form given in (26) allows a simple design for the basic **on****on** logic operati**on**s, while it creates the effects inherent in volume rendering by interactive adjustment of 0 …S int † with c**on**tinuous values. Furthermore, this form is suitable for implementati**on** using c**on**venti**on**al volume rendering software packages or hardware renderers (see Secti**on** 4.3 for a detailed descripti**on**). Similarly, the color functi**on** c…p† ˆ …R…p†;G…p†;B…p†† is specified by …R…p†;G…p†;B…p†† ˆ …minfr 0 …S int †; …p†g; minfg 0 …S int †; …p†g; minfb 0 …S int †; …p†g†; …28† where r 0 …S int †, g 0 …S int †, and b 0 …S int † are 1D color functi**on**s whose range is ‰0; 1Š. In summary, the processes of tissue **on****on** c**on**sist of the following steps: 1. Define tissue classes t ˆ…t 1 ;t 2 ; ...;t n †. 2. Design a **on****local** structures to characterize each tissue class t j …j ˆ 1; 2; ...;n† and determine the filter types and widths to define the multidimensi**on**al feature vector p ˆ…p 1 ;p 2 ; ...;p m †. b. Determine j …p†, defining the discrete **on****on**s. The first step is the process of problem definiti**on** **on** the requirements of users such as clinicians and medical researchers. The sec**on**d step includes the analysis of the problem and the design of the multichannel classifier and is performed by the designer. Guidelines for designing a **on****on** **local** structures are given below. The third step is the interactive process of parameter adjustment by the user. 4.2 Guidelines for Choosing Suitable Local Structures for Classificati**on** 4.2.1 Guideline 1: Using Gradient Magnitude to Avoid Mis**on****on**sider two edge models, e 1 …x† ˆ…I 1 I 3 †h edge …x; r †‡I 3 and e 2 …x† ˆ…I 2 I 3 †h edge …x; r †‡I 3 (where I 1 >I 2 >I 3 ) **on** (13) (Fig. 5a). We assume that I 1 , I 2 , and I 3 corresp**on**d to the average **intensity** values of tissue classes, t 1 (ªhighº-**intensity** tissue), t 2 (ªmediumº**intensity** tissue), and t 3 (ªlowº-**intensity** background), respectively. Even if the **intensity** distributi**on**s (histograms) of these tissues are well-separated, ambiguous **intensity** values can exist at the boundaries between two different tissue regi**on**s due to the partial volume effect. Fig. 5a shows the histograms …S int † for these edge models. If the two edges exist in the same volume data, mis**on****intensity** S int **on**ly. Fig. 5b shows histograms plotted in a 2D feature space whose axes are S int and S edge . The 2D histograms …S int ; S edge † are arch-shaped because intermediate **intensity** values occur at the boundaries where the gradient magnitude S edge is high. When the arm of the arch reaches S edge ˆ 0, S int corresp**on**ds to the average **intensity** value of each tissue class. The intermediate intensities with high gradient magnitudes are distributed near the apex of the arch. Based **on** the above observati**on**s, the feature vector p ˆ …S int ; S edge † can be utilized to classify the voxels into two tissue classes, t ˆ (ªhighº, ªmediumº), without mis**on****on****on**s for tissue ªmed,º med …p†, is specified as med …p† ˆminfA med …S int ; L m ;H m †; med …p†g; …29† med …p† ˆminf…S int ;0;T 1 †;…S edge ;0;T 2 †g; where A med is the opacity value for tissue ªmed.º high …p† for tissue ªhighº is specified as

168 **IEEE** TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 6, NO. 2, APRIL-JUNE 2000 Fig. 6. Guideline 2: Using sec**on**d-order **local** structures. (a) 2D histograms …p† for sheet (blue plots), p line (green plots), and blob (red plots) models, where p ˆ…S int ; M 2 † … 2 2fsheet; line; blobg†. For the multiscale filter M 2 , 1 ˆ 1:0, s ˆ 2 , n ˆ 4 in (19). For the **local** structure model h 0 …x; 2 r†; r ˆ 2:0. The sheet and line models had spherical and circular shapes, respectively, whose radii were 64. The unit is voxels. Left: p ˆ…S int ; M sheet †. Middle: p ˆ…S int ; M line †. Right: p ˆ…S int ; M blob †. (b) Typical discrete **on****on**d-order structure. T 2 should be selected so that unwanted structures are removed while the target sec**on**d-order structures are extracted. high …p† ˆminfA high …S int ; L h ;H h †; high …p†g; high …p† ˆ med …p† ˆ maxf…S int ; T 1 ; 1†;…S edge ; T 2 ; 1†g; …30† where med …p† ˆ1 med …p† and A high is the opacity value for tissue ªmedium.º These discrete **on****on****on**d-Order Local Structures We c**on**sider the sec**on**d-order **local** structure model h 0 2 …x† ˆ…I 1 I 2 †h 2 …x; r †‡I 2 , (where 4 2 2fsheet; line; blobg and I 1 >I 2 ) **on** (14), (15), and (16). The **on****intensity** S int **on**ly. Fig. 6a shows histograms for sheet, line, and blob plotted in a 2D feature space whose axes are S int and M 2 . Based **on** the histograms, the feature vector p ˆ …S int ; M 2 † (or …S int ; S 2 †) can be utilized to classify the voxels into two tissue classes, t ˆ… 2 ; 2 †, where 2 represents all other structures different from 2 . Fig. 6b illustrates the discrete **on****on****on****on****intensity** values can be classified into 2 structures and others. Selecting a filter of the type 2 is a simple process. This filter type directly corresp**on**ds to the **local** structure of a tissue to be highlighted or suppressed, as shown in Table 1. The filter width and its multiscale integrati**on** can be determined according to the width resp**on**se curves shown in Fig. 3 if the actual width range of a target tissue can be found. 4.2.3 Summary of Guidelines The two procedures outlined above for improved tissue **on****3D** **local** structures can be summarized as follows: Guideline 1 (dealing with the partial volume effect): At the boundaries of tissues, intermediate **intensity** values often exist that are not inherent to the tissues themselves. When a tissue of interest has **intensity** values similar to such intermediate values, mis**on****on****on****on**d-order features): When a tissue of interest can be characterized by its line, sheet, or blob structure, as well as its **intensity** values, discrete **on****on****on** strategies are designed **on** an interactive analysis of the **local** **intensity** structure of each tissue class by repeating the following processes. First, unwanted tissues that could be c**on**fused with the target tissue when **on**ly the original **intensity** is used are identified Sec**on**d, a **3D** **local** structure filter expected to be effective in disambiguating these tissues is selected **on** the above two guidelines. Finally, the discrete **on****on** a 2D histogram analysis is determined and then checked to see whether the disambiguati**on** power is sufficiently improved when the 2D feature space defined by the original **intensity** and the filter resp**on**se is used. The above procedures are repeated for the remaining tissues until the **on****on****on** represents a nested set of the IF±THEN±ELSE rules.

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