Classification Results from the Logarithmic Splitting.

In this section the classification accuracy results obtained from the

features collected from the Logarithm ic Splitting analysis algorithm , w ill be

p resen ted an d discussed. All the im ages w ere decom posed to seven (7)

decom position levels, in other w o rd s a fram e length of 256 elem ents w as

analysed to length of tw o (2) elem ents. The sam e d e p th of decom position w as

u sed for all the w avelet-based analysis architectures u sed in this stu d y . The

overall classification accuracy of all the classifiers an d features for the

n o rm a l/ abnorm al classes is show n at Figure 6.16. Figure 6.16, is the su m m ary

of Table A p p B l at the A ppendix B section, w ere the read er can v iew all the

feature com binations an d their perform ance w h en u sed u n d e r different

discrim ination regim es.

A s w e can see from Figure 6.16, the m axim um classification accuracy for the

n o rm a l class im ages is 83%, and for the abnorm al 93%. H ow ever, as w e can

exam ine from the sp read in g of the classification scores, for b o th the n o rm al an d

the abnorm al im age classes, only a m inority m akes it to the h igher classification

rates (13 o u t of the 113 feature com binations exceeded 80% of classification

accuracy for the n orm al class, and 24 o u t of the 113 com binations exceeded 90%

classification accuracy for the abnorm al class). The perform ance of each

in d iv id u al classifier is given at Table 6.17, an d their overall perform ance is

35 30 _{0 NORMAL} □ ABNORMAL 25 CD CO 00 o CO CO CT) (J) Classification Accuracy (%)

F ig u re 6 .1 6 : C la ss ific a tio n A cc u r a c y fo r th e N orm al - A b n o rm a l c la s se s u sin g fea tu res from th e L o g a rith m ic S p littin g W a v e le t T r a n sfo r m D o m a in .

M DC k -N N LSMDC QC Bayes (%) N orm al A bnor m al N orm al Abnor m al N orm al A bnor m al N orm al A bnor m al N orm al A bnor m al 70 2 5 71 6 1 72 5 2 73 10 3 74 1 6 1 75 12 3 76 1 5 10 77 6 78 14 79 7 80 3 10 6 5 81 1 1 8 3 3 82 1 9 2 2 83 21 2 84 1 85 2 1 86 1 87 5 88 4 89 1 10 90 6 91 9 92 5 93 3 1

Table 6.17: The number of feature combinations and their classification accuracy score, using the M DC, k-NN, LSM DC, QC and BC for the normal and abnormal images, using features from the Logarithm ic Splitting W avelet Transform domain.

Overall (%) M DC k -N N LSMDC QC Bayes 75 2 76 8 77 1 8 1 78 25 1 79 1 6 2 80 2 3 81 7 82 2 11 1 83 11 84 11 85 6 86 4 Total 3 1 51 57 1

Table 6.18: The number of feature combinations and their overall classification accuracy score, using the M DC, k-NN, LSM DC, QC, and BC, using features from the Logarithmic Splitting W avelet Transform domain.

A nalytically, from Table 6.17, w e can see th at the perform ance of the M DC is

rath er p o o r w ith only 3 com binations just b eyond the classification thresh o ld s

as th ey are p resen ted at the previous parag rap h . The k-N N classifier p ro d u c e d

only one com bination, again w ith a low score. The LSMDC's classification

accuracy is relatively poor, since the m ajority of its scores are in the ran g e of the

classification thresholds (70% for the norm al an d 80% for the abnorm al), the

h ig h est score for the n orm al class is 82% and for the abnorm al class 89%.

The QC perfo rm ed better com pared to all the other classifiers, since for the

n o rm a l category eleven (11) classification scores w ere above 80% w ith the

m axim um of 82%, an d for the abnorm al category tw en ty th ree (23) scores w ere

above 90%, w ith the m axim um of 93%. Finally, the QC achieved just one score

above the specified requirem ents, w ith seventy tw o (72%) classification

accuracy for the n orm al class, and for the abnorm al class the accuracy achieved

w as 93%

Table 6.18, presents the overall classification accuracy of all the classifiers. We

can see th at the classifiers LSMD and QC achieved to classify 51 an d 57 feature

com binations, respectively. H ow ever, the perform ance of the QC is superior,

because it p ro v id e d the highest classification score, an d the m ajority of th em are

w ith in the range of 82% an d 86%.

In this section the perform ance of the three different sets of statistical features

(i.e. 1®‘ O rd er Statistics, 2"'^ O rder Statistics, an d G ray Level R un Lengths),

collected from the Logarithm ic Splitting W avelet Transform coefficients do m ain

w ill be p resen ted and discussed. The n u m b er of feature com binations, from

classifiers), are show n in Table 6.19. This table is a su m m ary of Table A p pB l

from the A ppendix B section, em phasising on the features rath er th a n the

classification accuracy scores, as in the previous tables.

MDC k-NN LSMDC QC BC Total

1*‘ Order 0 0 3 4 1 8

2"“^ Order 3 1 44 48 0 96

GLRL 0 0 4 5 0 9

Total 3 1 51 57 1 113

Table 6.19: The number o f feature combinations from the sets o f 1st Order Statistics, 2nd Order Statistics, and the Gray Level Run Lenghts, collected from the Logarithmic Splitting W avelet Transform domain, as were used by different classification schemes.

A s w e can see from Table 6.19 all the classifiers succeeded in classifying feature

com binations above the criteria set. All the com binations w hich co n trib u ted to

the above p resen ted results come from the 1®‘ an d the O rd er Statistics, as w ell

as from the G ray Level R un Lengths. Analytically, the MDC classified th ree (3)

o u t of the tw o h u n d re d tw enty (220) feature com binations of the O rd er

Statistics. The k-N N classified one o u t the tw o h u n d re d tw en ty (220) feature

com binations of the 2""^ O rd er Statistics. The LSMDC classified three (3) o u t of

th e ten (10) com binations of the 1*‘ O rd er Statistics, forty four (44) the tw o

h u n d re d tw en ty (220) com binations of the 2"*^ O rd er Statistics, an d four (4) o ut

of the tw en ty (20) com binations of the G ray Level R un Lengths. The QC

classified four (4) o u t of the ten (10) com binations of the 1®‘ O rd er Statistics,

fo rty eight (48) the tw o h u n d re d tw enty (220) com binations of the 2"^^ O rd er

Statistics, an d five (5) o u t of the tw enty (20) com binations of the G ray Level R un

Lengths. Finally the BC classified one o u t of the ten (10) com binations of the 1®‘

Quadrature Classifîer 2™* Order Statistics

Sum of Squares: Variance - Sum Entropy - Entropy

Normal TRUE 108 FALSE 30 78.26

Abnormal TRUE 129 FALSE 9 93.48

Overall 85.87

Sum Average - Sum Entropy - Entropy

Normal TRUE 110 FALSE 28 79.71

Abnormal TRUE 127 FALSE 11 92.03

Overall 85.87

Gray Level Run Lengths

Short Run Emphasis - Run Percentage - Gray Level Nonuniformity

Normal TRUE 109 FALSE 29 78.99

Abnormal TRUE 127 FALSE 11 92.03

Overall 85.51

Short Run Emphasis - Run Percentage - Run Length Nonuniformity

Normal TRUE 109 FALSE 29 78.99

Abnormal TRUE 127 FALSE 11 92.03

Overall 85.51

Table 6.20: The best classification accuracy scores obtained from features collected from the the Logarithmic Splitting W avelet Transform domain.

The feature com binations, w hich p ro d u ced the best overall classification

accuracy results, are show ed in Table 6.20. As w e can see, the QC achieved its

b est overall classification accuracy score using tw o (2) feature com binations

from the 2"^^ O rd er Statistics and tw o (2) feature com binations from the G ray

Level R un Lengths. It is w o rth stating th at the h ighest overall classification

accuracy result, 85.87%, w as m anaged b y the QC usin g the feature

com binations of: Sum of Squares: Variance - Sum E ntropy - Entropy, a n d Sum