## 1 Introduction  
The lifetime risk of developing breast cancer among American women is 12.7% (one in eight, [[http://www.cancer.gov/cancertopics/factsheet/Detection/probability-breast-cancer](http://www.cancer.gov/cancertopics/factsheet/Detection/probability-breast-cancer)]([http://www.cancer.gov/cancertopics/factsheet/Detection/probability-breast-cancer](http://www.cancer.gov/cancertopics/factsheet/Detection/probability-breast-cancer)), from the National Cancer Institute), exceeded only by lung cancer. Mammography is considered the most effective technology presently available for breast cancer screening. With digital or digitized mammograms computer-aided detection (CAD) has proven to be a very useful tool for radiologists. A successful CAD system will eventually facilitate a computer-aided diagnosis (CADx) system development that may greatly save radiologists' work and benefit patients. There are three types of breast lesions according to the ACR Bi-RADS (r) lexicon, which are mass, calcification and architecture distortion. In this paper, all discussions focus on mass detection and calcification detection, which are briefly reviewed as follows. A _mass_ is defined as a space-occupying lesion seen in at least two different projections [1]. Masses are described by their _shape_ (Round, Oval, Lobulated, Irregular) and _margin_ characteristics (Circumscribed, Microlobulated, Obscured, Ill-Defined, Spiculated). On mammograms, mass areas usually appear brighter than healthy tissues. However, the patterns of mass lesion are hard to be defined by simple features such as intensities or gradients because of huge variations among individuals. For example, masses are quite difficult to be recognized from dense breasts. Therefore, many advanced features are proposed to identify mass lesions from screening mammograms in the literature. In general, neighborhood or region texture features are generated by jointly considering differences of orientations and correlation of scales. [PERSON] _et al_. [2] developed a method to detect _spiculated_ masses using a set of five features for each pixel. They used the standard deviation of a local edge orientation histogram (_i.e._, analysis of local oriented edges, ALOE) and a subset of _[PERSON]'s texture_ features (of four dimensions). To address the variant mass size problem, [PERSON] _et al_. [3] proposed a multi-resolution algorithm by using the discrete wavelet transform based on [PERSON] _et al_. 's work. [PERSON] _et al_. [4] presented an adaptive thresholding technique for the detection of masses. [PERSON] _et al_. [5] developed a multi-resolution and multi-orientation wavelet transform for the detection of masses and _spiculation_ analysis. They observed that traditional wavelet transforms cannot extract directional information which is crucial for a spiculation detection task. _Calcifications_ are small calcium deposits that form in the breast as a result of benign or malignant processes. Mammographically, they appear as bright white spots of various sizes and shapes. The important characteristics of calcifications are their size, shape or morphology, number, and distribution. Malignant calcifications tend to be numerous, clustered, small, varying in size and shape, angular, irregularly shaped, and branching in orientation [6, 7]. On the other hand, calcifications associated with benign diseases are generally larger, more rounded, smaller in number, more diffusely distributed, and more homogeneous in size and shape. [PERSON] _et al_. [8] used a wavelet filter for the detection of microcalcifications, and a Markov random field (MRF) model to obtain textural features from the neighborhood of every detected calcification. The MRF-based textural features and three statisticaltextural features (the mean, variance, and a measure of edge density), were used to reject false positives. [PERSON] _et al._[9] compared four groups of features: multi-wavelet-based features, wavelet-based features, Haralick's texture features [10], and shape features.