We report the successful use of continuous wavelet transforms applied to atomic force microscope data sets for landmark recognition of biological features. The data sets were images of mixed red and white blood cells. Contrast enhancement followed by continuous wavelet transform of the data was used to successfully distinguish erythrocytes from neutrophil and monocyte leukocytes within the mixed cell images. All of the above are spherical objects between 6 and 8 microns in diameter, which demonstrates the ability to sort similar biological objects into distinct classes. The implications for development of on-line scanning probe recognition microscopy are discussed.
Scanning probe microscopy (SPM) provides highresolution imaging of specimens, including biological specimens. SPM-based nanomanipulation is a newly emerging area that offers an orders-of-magnitude improvement over current manipulation capabilities. Together, the two offer the possibility of site-specific direct investigations of biological events. Our group has developed a landmark recognition scheme for use within an adaptive nonlinear neural network controller, for high-end control of the X-Y motion of an SPM tip.’+ Such a specially equipped SPM can be used for direct site-specific investigations of particular nanobiological features and interactions.
In this paper, we present our recent research on landmark recognition of biological features. The data sets were atomic force microscope (AFM) images containing mixed erythrocytes (red blood cells) and leukocytes (white blood cells). Each image was a 5 12 x 512 pixel raster scan with three x-y-z points per pixel. Such large data sets are typical for AFM images. Contrast enhancement followed by continuous wavelet transform of the data set was used to successfully distinguish erythrocytes from neutrophil and monocyte leukocytes within the mixed cell images. All of the above are spherical objects between 6 and 8 p m in diameter.
2.1. Mixed Cell V P E And Afm Data Set Acquisition
Blood samples (about 3 ml), from male Wistar rats (Charles River Laboratories, Wilmington, MA), were centrifuged at 300 rpm at 4 “C for 15 min. Small volumes ( t l ml) containing mainly neutrophilic leukocytes and a small amount of erythrocytes on top of the centrifuged samples were extracted with a pipette and placed on a glass cover slide. AFM images of the mixed cell types were obtained with a Digital Instruments Nanoscope IIIa operated in tapping mode in ambient air. Other experimental included: use of a J scanner with a maximum 125 x 125 pm2 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 visible evidence of tip-induced damage to the samples.
A typical mixed cell image is shown in Figure 1 . By inspection, it contains seven erythrocytes (red blood cells) and four leukocytes (white blood cells). In addition to the neutrophil leukocytes, identifiable by their crescent-shaped nucleus, an anomalous leukocyte is also observed. This is possibly a monocyte, a white blood cell that responds to chronic inflammation, as opposed to a neutrophil, a white blood cell that responds to acute inflammation. Therefore, lowest to highest value. Within an image, many z values may cluster within a limited subset of the full range. To increase the contrast of the image, the data values z(x, y ) were remapped to utilize the full dynamic range, using a linear mapping,
1-0 Z(X9 Y ) = max(z(x, y ) ) -min(z(x, Y ) ) x (~( x , Y ) -min(z(x, Y ) ) )
An example is shown in Figure 2 . The enhanced data sets were used in all subsequent processing steps. Although contrast enhancement based on a statistical differencing filtef is an available feature in the SPM, this paper implements a linear mapping for enhancing contrast of the raw image from the SPM. This allows inversion of glgorithm as appropriate for a particular data set. Figure 2a . In Illuminate Plot type, which is the usual encoding of SPM data for the convenience of a human observer, the data are displayed as if a light source is shining on the sample surface from a selectable direction. This artificial lighting is unnecessary for the recognition algorithm. An image displayed in Height Plot type will look “murky” by comparison with an image displayed in Illuminate Plot type. Next contrast enhancement was performed as a preprocessing step. In SPM the value of the z coordinate as a function of (x, y ) is projected over a range from the Fig. 2. (a) The initial data values, with artificial lighting removed. the wavelet basis set derived from a mother wavelet8 *.
The scale parameter cr plays a crucial role. Wavelet transforms process data at different scales or resolutions. At each scale they compute the similarity of the image data with the wavelet kernel at the selected scale u. At large scales, the transform coefficients W(cr, 71, r 2 ) are dorninant for data from objects in the image that correspond to the larger scale wavelet kernel. Similarly, for small scales, small features are highlighted in the W(c, T , , r 2 ) transform domain. By choosing the appropriate scale, we can get the relevant details from the image that are necessary to perform a particular recognition task across multiple scales. The resolution of the multiscale recognition technique corresponds to the resolution of the features within the image. This is nanometer scale for AFM images and angstrom scale for STM images.
The multiscale analysis procePure begins by d5fining a mother wavelet function I). One candidate I) is expressed as where rp is a function used for systematic generation of images of slowly varying scale u. A Gaussian is a commonly used function whose scale is determined by the variance u. A multiscale edge detector can be derived from the spatial derivatives of 9.
Edges associated with abrupt transitions in the image were detected with a two dimensional multiscale Gaussian differential operator defined as The scaled decomposition of the image can be performed by convolving the image data Z(x, y) with the differential Gaussian wavelet parameterized by scale a. For a fixed value of scale, we can calculate the 2D CWT in fi-equency domain, where zI’ is the Fourier Transform of 4.
2.3. Analysis Of Afm Data Sets
Analysis of the AFM data sets from several mixed cell images was performed by contrast enhancement followed by continuous wavelet transformation, with the scale parameter a = 6. The horizontal and vertical cross sections of representative continuous wavelet transforms W ( a , T,, T2) are shown in Figure 3 (the examples shown correspond to the cell types in Fig. 1 W ( a , T , , 7,) shown for horizontal (y = 0) and vertical (x = 0) axes. The mean value m is displayed for each plot. Number of zero crossing n = number of times, the plot intersects the mean line. For all specimens studied, the number of zero crossings n < 4 corresponded to a red blood cell and n > 4 to a white blood cell.