![]() Spatial Filtering The filtering techniques are image transformations "pixel" by "pixel", which are not dependent only in the "pixel" gray level, but also the gray level value of the neighborhood "pixels", in the original image. The filtering process is executed using matrices named mask which are applied on the image. Example: the original image is a 512 by 512 matrix with numerical values, a 3 by 3 mask is applied; each value of the 3 by 3 mask corresponds to a weight. Example: Mask with a center positioned at (2,2). The mask application centered at position (i,j), being i the number of a certain row and j the number of a given column over the image, consists in the "pixel" value substitution at position (i,j) by a new value, which depends on the neighbor "pixel" values and the mask weights. The resulting image after applying a filter is a new image where the elimination of initial and final lines and columns in the original image. The spatial filters can be classified in low-passing, high-passing, or band-passing. The first two are the most common in image processing. The band-passing filter is used only in specific processing, mainly to remove periodic noise. In SPRING filtering module, three operation classes are available: linear filtering, non-linear filtering and filters for Radar, described next:
How to get other conceptual information. Other Image Processing techniques. Linear FiltersThe filters are used to smooth or enhance image details, or even to minimize noise effects. The system provides some pre defined masks to each kind of filter. In the linear filtering case masks are available for the low-passing and high-passing filters, described next. Low-PassingThe low-passing filter has a smoothing visual effect of the image and the reduction of the gray level numbers in the scene. The high frequency, corresponding to abrupt transitions are attenuated. The smoothing minimizes noise and presents the blurring effect in the image. Some windows that make a low-passing filtering, in a 3x3, 5x5 or 7x7 neighborhood dimension are indicated below. These filters are known by average filters, because they get the average of the neighbor points.
Other low-passing filter types, known as weighted average filters, are used when the weights are defined as a function of its distance to the central weight. These type of filters with 3 x 3 dimensions are:
The figures below show two scenes of the Landsat 5 satellite (band 5), where the left is the linearly highlighted original image and the right one corresponds to the same image, but after applying a low-pass, 7 by 7, filter.
High-PassingThe high-passing filtering highlights details, producing a "sharpening" effect in the image, that is, the transitions between different regions become stronger. Examples: boundaries in a cultivated field, geological lineament etc. These filters can be used to highlight some characteristics present in the image, such as boundaries, curved lines or spots. The undesired effect is that noise, sometimes, maybe enhanced. In the high-passing filtering case, some examples can be observed below: The boundaries enhancing filters give gray level values for the "pixels" in the original scene, influenced by their neighbor "pixels". This greater or smaller influence will be a function of values (positives, negatives, or zeros) given by the user and set to the mask elements, considered using the user filter configuration. It is through the combination of these input values or weights, which will be obtained a greater or smaller highlight of the scene, according to a preferential interest directions. The windows below are used to highlight boundaries in several directions. The name given to the masks indicates the orthogonal preferential direction in which the boundary limit will be highlighted. In this way, for instance, the north mask highlights horizontal limits.
Enhancing non-directional boundaries: it is used when the user wants to enhance boundaries, independently of the direction. The SPRING suggests three masks, when the intensity high values of gray levels present in the resulting image differ. In this case, the boundaries can be enhanced with the following intensities: The high mask allow to pass less the low gray level, that is, the image becomes lighter. The low mask produce a darker image than the previous one. The medium mask presents intermediate results. Enhancing images: this option corresponds the mask utilization appropriate to enhancing image characteristics obtained by specific sensors. Actually, it is available only for TM/Landsat images. In this case the mask used is: This enhancing was defined to compensate sensor radiometric distortions TM. The "pixel" which has its digital value substituted by the mask application, corresponds to the shadowed position. The figures below show two satellite scenes Landsat 5 (band 5), where the left is the original image enhanced linearly and the right image corresponds to the same image, after applying an enhancing filter in the TM Image mentioned above.
Mask EditorBesides these options for linear filtering with pre defined masks, there is also a mask Editor for linear filters. In this way the user can create, update, remove and apply its own masks and visualize pre defined masks for the system, which can not be modified. The masks created have to have m x n dimensions, where m = 1, 3, 5, or 7 and n = 1, 3, 5 or 7; may or may not be normalized and applied k times, where k = 1, 2, ... , 10. Mask NormalizationNormalizing a mask means that the resulting value of the mask application will be divided by the weight summation. For example, in a 3x3 mask, with value 1, each obtained value of the mask application over an image will be divided by 9. The normalization guarantees that the image statistical characteristics (such as average), will be kept in the filtered image. The user can decide if the mask will be normalized or not. NON-LINEAR FiltersNon-linear filters are used to change the image, without reducing its resolution. They serve to minimize/enhance noise and smooth/enhance edges. In the non-linear filtering category, the available filters are: edge detection operators and morphological filters. Follow the description. Edge Detection OperatorsDetecting the characteristics, such as boundaries, lines, curves and spots, can also be performed using non-linear filters. In the system the available operators are: Roberts and Sobel. Roberts Operator: the Roberts gradient operator is the simplest non-linear method used for boundary detection. It presents a disadvantage, depending on the direction - some boundaries can be more enhanced than others, even if they have the same magnitude. As a result of its application, an image with high gray level values is obtained, in regions with well defined limits and small values in regions with smooth limits, where "0" (zero) is used for regions with a constant gray level. The operator consists in the following function: (a') = (a - d)2 + (c - b)2
where: a' - is the gray level corresponding to the location "a", which will be substituted; a, b, c, d - are the locations where values will be computed for the operation. The next figure shows the result when applying the Roberts operator. Sobel Operator: the Sobel gradient operator has the property to enhance vertical and horizontal lines darker than the background, without enhancing isolated points. It consists in the application of two masks, described next, which gives a unique result: The (a) mask detects the variations in the horizontal direction and the (b) mask, in the vertical direction. The result of this application, in each "pixel", is given by: where a' is the gray level value corresponding to the location of the mask central element. The following figure shows the effect of its application. The figures below show two scenes from the Landsat 5 satellite (band 5), where the left is the original image linearly enhanced and the right image corresponds to the same image, but applying a Sobel enhancing filter.
Morphological FiltersMorphological filters explore the geometrical properties of the signals (gray level of the image). For morphological filters, the masks are denominated, structuring elements. These elements have to present values "0" or "1", so the "pixel" corresponding to the matrix position will be considered or not. The SPRING gives the following morphological filters: the median, erosion and dilation filters. The median morphological filter: it is used for smoothing and noise elimination. The image size is kept. Example: The shadowed position will be changed to the value 6, because it is the median value in the [2,3,6,6,8] vector. The erosion morphological filter: it effects the image in its lighter parts (high gray levels) causing an erosion, generating darker images. Considering the previous example, the value to be substituted in the shadowed position corresponds to the smallest value in the ordered vector, in this case, 2. The dilation morphological filter: it effects the image in its darker parts (low gray levels) causing a dilation, generating lighter images. Considering the previous example, the resulting value of the application of this filter is the highest value in the ordering, in this case, 8. For the application of these filters, the system provides the following structuring elements pre-defined:
Opening and closing an image, generally erosion and dilation filters with the same structuring elements are chained to get the opening and closing effects. The opening is obtained by chaining the erosion filter, followed by the dilation filter, as shown in Figure (a), next. In the example, there is isthmus breaks and cables and islands elimination.
Fig. (a) - Erosion Example. The original figure shows the representation of a binary image (values of gray levels 0 and 1). The closing effect is obtained by chaining the dilation filter, followed by the erosion filter. In the example (Fig. (b)), there is a gulf elimination and a bay closing.
Fig. (b) - Dilation Example. Structured Elements EditorThere is also a structuring elements Editor to morphological filters. In this case, the structuring elements have the fixed 3 x 3 dimension, and its elements can be only 0's or 1's. In the editor, the structuring elements can be applied k times, where k = 1, ..., 10.
Filter for RADAR ImageMany spatial filters have been designed for the Speckle noise reduction and for increasing the signal-noise ratio, giving a better separability between the surface target with a minimum information lost. Frost Filter [Frost-1982]: is a linear convolution filter, derived from the squared mean error minimization over the noise multiplicative model. In this filter the original signal statistical dependencies is incorporated, once an exponential spatial correlation function is assumed among the pixels. It is an adaptive filter that preserves the boundary structure. Lee Filter [Lee-1981]: it adopts a multiplicative model for the noise and obeys the "local linear minimum mean square error" criteria. Local, because it uses pixel local statistics to be filtered, assuming that the average and signal variance are stationary. It is a linear filter because it makes a linearization by expanding a Taylor series of the signal multiplication and the noise around the average, using just the linear terms. The linearization result transforms the noise multiplicative model in addition, that is, the noise and the signal become independent; and, finally, "minimum mean square error", because it minimizes the squared mean error through a Wiener filter (filter based on the minimum squared mean error criteria). The Lee filter is an adaptive filter in general. Kuan/Nathan Filter [Kuan et al.-1982]: it adopts a multiplicative model. The procedure is similar to the Lee procedure, where the point by point estimation is performed using the Wiener filter. The difference between them consists in the fact that in the Kuan/Nathan filter no approximation is performed. It is also a general and adaptive filter. The following figures show an original (ERS-1, 8 "looks") image and the corresponding filtered images, using the following filters: 5x5 average Filter, adaptive Frost Filter, median Filter, fixed Lee Filter, and fixed Kuan Filter (window = 3).
Quantitative measures in the tested filters, shows that the Lee, Kuan, Frost and the Average filters preserves the image average value. The non-specific noise filters Speckle, Average, and Median, present a considerable reduction in the standard deviation, which implies a large information lost (resolution lost). The Frost filter presents the maximum texture preservation and a smaller information lost. Using a determined filter is dependent of the desired application. For a certain application, if the most important factor is:
About RADAR images ![]() |