Future Work.

7.3.1. Wavelets

The aim of this stu d y w as to exam ine the perform ance of the W avelet

T ransform based analysis an d classification on digital m am m ogram s, an d in

partic u la r to answ er the question if w e can w ith confidence distin g u ish

b etw een the general classes of norm al and abnorm al m am m ographie im ages.

Since the A d ap tiv e W avelet Splitting scheme, p ro d u ced the best classification

accuracy results it can be used, as the backbone, for fu rth er investigations.

O ne p ro p o sitio n is to "tu n e" the adaptive algorithm for each subclass of bo th

th e n o rm al an d abnorm al categories. This, if successful, w ill lead to the

creation of different decom position-tree p atterns, w hich m ig h t be u sed to

characterise the im ages n o t only as norm al or abnorm al, b u t into their

subclasses as well.

A nother p o in t of im provem ent is the selection of the criterion u sed into the

ad ap tiv e w avelet transform algorithm . The criterion u sed here is the n u m b er

of zerocrossings, w hich w as em pirically tuned. H ow ever, it is of in terest to

em ploy som e of the statistical features used into the p a tte rn recognition

schem e, as possible candidates, since some of those m easures h av e sh o w n

their discrim inatory ability.

There are tw o m ain considerations w hen one applies the discrete w avelet

transform : firstly, is the lack of shift invariance, w hich m eans th a t sm all

shifts in the in p u t signal can cause variations in the distrib u tio n of energy

p o o r directional selectivity for diagonal features. It is fou n d th a t b o th the

p rev io u sly m entioned problem s can be solved by the C om plex W avelet

T ransform (CWT). The structure of the com plex w avelet tran sfo rm is the

sam e as the discrete w avelet transform schem es, expect th at the CWT filters

h av e com plex coefficients an d generate com plex o u tp u t sam ples. H ow ever,

the design of filters w hich have the p ro p erties of shift invariance, good

directional selectivity, an d perfect reconstruction, w as h am p ered by several

p roblem s (especially the conditions for perfect reconstruction), an d only

recently such a fam ily of filters w as rep o rted [75] [76]. Therefore this is a very

active an d n ew area of w avelet theory, w hich w ill find applications into

im age denoising, restoration, and texture m odelling, b u t d u e to the com plex

n a tu re of the w avelet transform coefficients it produces, its application into

s ig n a l/im a g e com pression is questionable.

7.3.2. Pattern Recognition

In this stu d y w e tried to classify the w avelet transform coefficients p ro d u ced

after decom posing the m am m ography im ages into 8 levels of decom position

u sin g several w avelet analysis schemes. A lth o u g h there are som e

publications exploring the idea of try in g to classify either th e w avelet

tran sfo rm coefficients of specific decom position levels, or the reconstructed

im ages w hich w ere synthesised using the w avelet transform coefficients of

certain decom position levels, those publications w ere u sin g the Logarithm ic

architectures like the U niform an d the A d ap tiv e m ig h t p ro d u c e b etter

results.

• As discussed earlier into o u r feature selection step of o u r p a tte rn recognition

schem e, w e com bine features, w hich belong to the sam e set of features (i.e. V*

an d 2"^^ O rd er Statistics, an d G ray Level R un Lengths). H ow ever, it m ig h t be

w o rth exam ining th e o p tion of com bining the features of those th ree subsets.

• D uring the classification p ro ced u re the decision space is restricted to three-

dim ensions, it is im p o rtan t to increase to the n u m b er of dim ensions taking

into account o u r prev io u s p ro p o sal in hope of an im p ro v em en t to th e overall

classification accuracy.