eec-tively convolved with
2561
2
6
6
6
6
6
6
6
6
4
1 4 6 4 1 4 16 24 16 4 6 24 36 24 6 4 16 24 16 4 1 4 6 4 1
3
7
7
7
7
7
7
7
7
5
(5
:
7)and so on. The bandwidth of the smoothing lter is thus controlled by the number of cycles performed.
The primary dierence between Keast's design and the MSV network is in the functions performed by the circuits placed between the nodes. The multi-scale veto rule is imple-mented by the edge precharge circuits, shown in Figure 5-4 and indicated by the boxes labeled EPC in Figure 5-3. In each of these, a capacitor is initially charged with an `edge' signal. At each smoothing cycle, the absolute value of the dierence between the node volt-ages is compared to a threshold; and if the threshold is greater, the capacitor is discharged.
The complete execution of the multi-scale veto algorithm consists of the following steps:
The array is initialized by transferring signal charge proportional to image brightness under each node gate (pixel) and by charging the edge capacitors. The signal charge is formed either by direct acquisition using the CCD array, or by loading the pixel values from an o-chip sensor. Several smoothing cycles, 5{10, with the accompanying threshold tests, are then performed.
When these are completed, the edge charges from the four precharge circuits connected to each node are tested; and, if any of them is non-zero, i.e., if an edge was detected between the node and one of its four neighbors, a binary value is set at the node to indicate that it is an edge pixel.
Attenuation Factors
Smoothing Cycle: 1 2 3 4 5
Horizontal step edge 0.500 0.375 0.313 0.273 0.246 Diagonal step edge 0.375 0.273 0.226 0.196 0.176 Horizontal 1-pixel line 0.250 0.125 0.078 0.055 0.041 Diagonal 1-pixel line 0.125 0.055 0.032 0.022 0.016 Horizontal 2-pixel line 0.500 0.313 0.219 0.164 0.129 Diagonal 2-pixel line 0.313 0.164 0.105 0.074 0.056 1-pixel impulse noise 0.125 0.047 0.024 0.015 0.010 4-pixel square impulse 0.375 0.195 0.120 0.081 0.058 Horizontal 3-pixel ramp 0.750 0.688 0.641 0.602 0.568
Table 5.1: Attenuation factors for dierent types of features as a function of smoothing threshold test at all smoothing cycles. Following the same notation used in the example given earlier, let
k
denote the number of smoothing cycles performed, and letk denote the threshold for thek
th cycle. Given the convolution kernel (5.6) which is implemented by the smoothing network, at each cycle, the attenuation factors,G
k for the dierence signals corresponding to several idealized features are computed as a function of smoothing and given in Table 5.1.The ideal step edge refers to a two-dimensional feature which is innite in one dimension but has an abrupt change from one pixel to the next in the other dimension. The ideal line corresponds to back-to-back step edges facing in opposite directions so that its 1-D cross-section resembles that of the impulse in Figure 5-1. The labels `1-pixel line' and `2-pixel line' in Table 5.1 refer to the width of the 1-D impulse. Impulse noise is a local abrupt change in brightness which is nite in both dimensions. Here, the labels `1-pixel impulse' and `4-pixel square impulse' refer to the area of the local discontinuity. Finally, the ideal ramp is an feature similar to a step edge, but for which the change in brightness occurs over several pixels (in this case 3) rather than abruptly. Some graphic examples of these features are shown in Figure 5-5.
We also distinguish between horizontal features, which are those that are aligned with the rectangular pixel grid, while diagonal ones are oriented at 45o with respect to the grid.
It can be seen from the values in the table that diagonal features are attenuated somewhat more than horizontal ones due to the nature of the smoothing operator, and consequently, edges aligned with the grid are favored over skewed edges. An isotropic operator could
0 10
20 30
40
0 10 20 30 400 0.2 0.4 0.6 0.8 1
0 10
20 30
40
0 10 20 30 400 0.2 0.4 0.6 0.8 1
a.) Horizontal step edge b.) Horizontal 3-pixel ramp
0 10
20 30
40
0 10 20 30 40
0 0.2 0.4 0.6 0.8 1
0 10
20 30
40
0 10 20 30 40
0 0.2 0.4 0.6 0.8 1
c.) Horizontal 1-pixel line d.) 4-pixel square impulse
Figure 5-5: Ideal 2-D image features.
be implemented with a hexagonally connected network. However, based on the numerous simulations performed to produce edges for the matching algorithm, the added complexity in the design does not seem to be warranted by the slight improvement in the results that an isotropic operator would provide.
The values in Table 5.1 can be used as a guide for setting the parameters for more general types of features. As a specic example, suppose we want to retain only the boundaries from large objects in the image and remove all small scale features. The threshold
0 can be set as a function of the contrast in the image. We can perform 5 smoothing cycles and set5 =:
2460. Features resembling step changes in brightness which passed the threshold atk
= 0 will have little trouble passing the test atk
= 5, while features resembling 4-pixel square impulses will need to have an original dierence greater than 4:
20 in order to pass.A simpler method to generate all the thresholds is to choose one idealized feature as a model and to compute
k =G
k;f0 (5:
8)where