Image processing techniques are bringing new insights to biomedical research. The automatic recognition and classification of biomedical objects can enhance work efficiency while identifying new inter-relationships among biological features. In this work, a simple rule-based decision tree classifier is developed to classify typical features of mixed cell types investigated by atomic force microscopy (AFM). A combination of continuous wavelet transform (CWT) and moment-based features are extracted from the AFM data to represent that shape information of different cellular objects at multiple resolution levels. The features are shown to be invariant under operations of translation, rotation, and scaling. The features are then used in a simple rule-based classifier to discriminate between anucleate versus nucleate cell types or to distinguish cells from a fibrous environment such as a tissue scaffold or stint. Since each feature has clear physical meaning, the decision rule of this tree classifier is simple, which makes it very suitable for online processing. Experimental results on AFM data confirm that the performance of this classifier is robust and reliable.
Atomic force microscopy (AFM) has recently found widespread use in cellular investigations because of its ability to provide active and high resolution probing of specimens with minimal sample preparation and under nearly lifelike conditions. Recent studies include investigations of cell surfaces (Frankel et al 2006) and subsurfaces (Pelling et al 2004) , active response to environmental change (Canetta et al 2006) , healthy and pathological cell determination by elasticity variation (Dulinska et al 2006; Rosenbluth et al 2006) and local macromolecular probing of individual receptor sites (Hinterdorfer and Dufrêne 2006) .
The large amounts of newly available AFM-based cellular structure-function information drives a need to systematize both the experimental approach and interpretation of the results across multiple scales. To aid interpretation, image processing techniques are bringing new insights to biomedical research. Recent studies include investigations of supervised learning-based cell image segmentation (Mao et al 2006) and automated tracking of cancer cell nuclei (Chen et al 2006) . The automatic recognition and classifi cation of biomedical objects can enhance work effi ciency while identifying new inter-relationships among biological features.
In the present work we develop a combined AFM and image processing approach for use in cellular investigations. Our example is recognition of major structure-function relationships across multiple scales in blood cells. We set a further goal of maintaining translation, rotation, and scale invariance as important for both correct biological interpretation and real-time automated investigation. We fi nd that a combination of moment-based invariant features with continuous wavelet transform (CWT) analysis can provide recognition of major features across multiple scales while retaining translation, rotation, and scale invariance for accurate interpretation of data.
Blood samples (about 3 ml), from male Wistar rats (Charles River Laboratories, Inc, Wilmington, MA), were centrifuged at 300 RPM at 4 °C for 15 minutes. Small volumes (<1 ml) containing mainly neutrophilic leukocytes (white blood cells) and a small amount of erythrocytes (red blood cells) on top of the centrifuged samples were extracted with a pipette and placed on a glass cover slide. Further details are provided by Goolsby and colleagues (2003) .
Afm Experimental Parameters
Atomic force microscope images of the mixed cell types, as shown in Figure 1 , were obtained using a Veeco Instruments Nanoscope IIIa (Woodbury, NY) operated in Tapping Mode ® in ambient air as shown in Figure 1 . Other experimental parameters included: use of a J scanner with a maximum 125 × 125 square micron x-y scan range, silicon tips with a nominal 10 nm tip radius of curvature, and a scan rate of approximately 1 Hz. The cells adhered readily to the glass slides and there was no evidence of tip-induced damage to the samples. Each image was a 512 × 512 pixel raster scan with 3 x-y-z points per pixel.
Moment-based features and continuous wavelet transformbased analysis were integrated to realize a robust and reliable classifi er for blood cell types. The overall analysis procedure consists of three steps as depicted in Figure 2 .
Moment-based methods have been successfully used to extract the shape, more accurately the shape feature of the object under investigation (Prokop and Reeves 1992) . In pattern recognition (Grimson 1991) , a feature (Jain and Zongker 1997) is an individual property of the phenomena being observed. The choice of discriminating properties as features is key to any classifi er being successful. For a method appropriate for analyzing typical properties of blood cells, we defi ned the shape feature using functions of the second central moment (Gonzalez and Woods 1992) . Wavelet analysis has been successfully used in both object segmentation (Unser 1995) and feature enhancement (Laine et al 1994) . One property of the blood cells investigated in this paper is that they have objects which involve different scales. Since wavelet transform provides a multi-resolution analysis of the image, it can be used to detect objects of different scales. Another key property of the wavelet transform is its ability to characterize the local regularity of a data set. Thus, by choosing the appropriate scale, we can get the relevant details from the images that are necessary to perform a particular recognition task across multiple scales. The resolution limit of the CWT multiscale recognition technique corresponds to the resolution within the image, which is nanometer scale for AFM (Wiesendanger 1994) .
The classifier which we have developed has a tree structure. At each node, only a single feature is used to get effi cient result. Each feature is normalized to be translation, scale, and rotation invariant, which makes the classifi er robust.
Step A. Preprocessing An atomic force microscope image of a cell is a map of the surface topography. The map is stored as pixelated data points (x, y, z). In a conventional AFM raster-scanned image, not all data points represent a cell. The overall measured image can be segmented into background (substrate) and cell (object) pixels which is superimposed with noise and artifacts due to operational parameters. Hence it is important to process the AFM image data to remove the background and the noise retain all cell features.
The fi rst step involves the use of a threshold (Gonzalez and Woods 1992) to identify and discriminate the cells from the background and any noise, as shown in Figure 3 . A high threshold value was used to remove the noise pixels and a second low threshold value was used to eliminate the background pixels. The thresholding fi lter can be expressed as
Step A. Preprocessing
Step B. Feature extraction
Step C. Classification (1)
where f (x,y) is the original image, t 1 is the low threshold, t 2 is the high threshold, and g(x, y) is the image after thresholding. The thresholds t 1 and t 2 were selected using a histogram based procedure (Tou and Gonzalez 1974) in which pixel intensities in the AFM is binned as shown in Figure 3 (b) . After creating the histogram of original image, t 1 was chosen automatically by using Ostu’s method (1978) , which maximizes the between-class variance. t 2 was chosen manually by observing the histogram. If an image has considerable amount of high intensity noise pixels, a third peak may appear in the histogram in addition to the two peaks corresponding to background and object pixels. t 2 was chosen as a value below any third peak to eliminate such noise points. Results of the fi rst thresholding operation illustrating the approach are given in Figure 3 (a-c) for typical cell and also tissue scaffolding examples. As seen in Figure 3 (c), thresholding alone may not be suffi cient to eliminate all of the background and the noise pixels. Therefore, after thresholding, the data was passed through a customized fi lter. In this fi lter, the area of each connected region was calculated, and those regions having small area were assumed to be noise regions and were removed. The results of thresholding combined with the second fi ltering operation were seen to be satisfactory for all data sets under investigation and are shown in Figure 3(d) .
Step B. Feature extraction Feature 1 (leukocyte versus erythrocyte)
Both leukocytes and erythrocytes have globular shapes. A distinguishing characteristic between them is that erythrocytes are anucleate. In previous work (Goolsby et al 2003) , we have used a CWT method to successfully distinguish erythrocytes from leukocytes.
A CWT is a scale based two-dimensional transformation:
W f x y dxdy x y ( , , ) ( , ) * ( , ) σ τ τ σ τ σ τ σ 1 2 1 2 1 = ∫∫ − − ψ (2)