Research Article  Open Access
HighPerformance TimingDriven Rank Filter
Abstract
This paper presents an FPGA implementation of a highperformance rank filter for video and image processing. The architecture exploits the features of current FPGAs and offers tradeoffs between complexity and performance. By maximizing the operating frequency, the complexity of the filter structure can be considerably reduced compared to previous 2D architectures.
1. Introduction
Rankorder filtering is a nonlinear filtering technique, which selects an element from an ordered list of TAP number of samples. In the twodimensional (2D) case, filtering takes place on the contents of a rectangular window (or more generally, an arbitrary shape), which slides across the image. Every time the window is moved by one pixel column, a set of obsolete elements is discarded and a set of new elements is inserted. The samples within the window are sorted and the element with the specified rank replaces the output element of the window. Most typical ranks are median, minimum, and maximum, but the selection can be easily tailored to the needs of any application. Compared to other filters, such as FIR, Laplacian, or blur filters, rank filters can effectively remove impulses like noises while preserving the edges of the original image. This can be very useful for various applications, for instance, removing certain types of transmission noises or preprocessing for edge detection. This paper presents a hardware architecture that is tailored for highperformance color video processing, but it can be used in various applications such as IP block by taking advantage of design time parameterization. The paper concentrates on the timingdriven architecture selection which exploits the high operating frequency of recent FPGA and ASIC technologies, thus reducing hardware resource requirements.
2. Previous Work
The successful adaptation of rank filters in different applications catalyzed research activities for new algorithms and implementations.
Bitserial approaches [1, 2] provide the lowest complexity, but they do not lend themselves well to high sample rate implementations as filtering performance is proportional to the precision of the input data. However, the processing rate typically does not depend on the number of samples which changes between processing cycles.
Insert/delete or sorting networkbased architectures [3, 4] explicitly order incoming samples. In every cycle, the least recent sample is discarded and the most recent input is inserted into the magnitude sorting structure at the appropriate location. While these solutions require relatively few comparators, the feedback nature of the algorithm hinders pipelining.
Another set of applications stores the samples in the order of arrival and selects the appropriate output sample by calculating the location of the output sample dynamically. These architectures are easier to pipeline and they still require few comparators.
3. Proposed Architecture
On filtering images or videos, the filter window is sliding horizontally across the input image, as illustrated in Figure 1. In case of a simple rectangular window, to generate a valid output, WV (vertical size of the filter window) new input samples should be processed. Wordserial architectures can process one input sample per clock cycle. When comparing different solutions, an important classification criterion is the level of input parallelization. In the 2D filtering case, the filter should operate at WV times of the input pixel frequency and generate a valid input sample every WVth clock cycle.
Fully parallel filters can generate a valid output sample every clock cycle, irrespective of the number of input samples required to achieve this process. Consequently, such filters process WV new samples in a single clock cycle, and the required operating frequency is equal to the input pixel frequency. At the same time, hardware resource requirements are greatly increased. Previous papers typically considered fully parallel architectures such as 2D filters; however, as this paper proves, using recent FPGA technologies, this solution is suboptimal due to the inefficient resource utilization.
Multiword architectures are hybrid solutions; in one cycle, they can handle more than one input sample, but less than the fully parallel implementation. This solution allows finding an optimal balance between operating frequency and hardware complexity. Using given filter window and input pixel frequency, with NI defining the number of new input samples in a single cycle, the required operating frequency can be computed as
On processing color images, using the full perpixel information (e.g., full RGB or YCbCr values) is not an efficient solution. Filtering these components independently not only increases computational requirements but may also introduce blur effects, as it may generate new color values which did not exist on the input image. A better solution is to use a magnitudelike value, such as luminosity. If the input format does not contain such a component, it can be generated within the filter.
3.1. Global Filter Architecture
The proposed architecture consists of five main components (as illustrated in Figure 2): the line buffer (LB), the optional filter value generator (FVG), the delay line (DL), the filter core (FC), and the control unit (CNTRL).
The LB stores WV1 lines of the original input frame in the internal memory. The FVG is only required if the input format does not contain a magnitudelike component. For YCbCr or YUV input representations, this module can be omitted as the Y component lends itself well to magnitude ordering. For RGB input (luminance), a typical magnitude value can be calculated. The DL is an addressable FIFO which stores the full perpixel information of the pixels residing inside the FC. The FC itself uses the values computed by the FVG and generates the appropriate address for the DL. CNTRL generates properly delayed synchronization signals and output valid signals. As the rest of the architecture is independent of the FC solution, further discussion will focus on the FC and its extensions.
3.2. WordSerial Filter Core
The operation of the FC is based on observations introduced in [5]. As a first assumption, the filter contains TAP number of different samples. For each sample, an index value is generated, which is equal to the number of samples which are smaller than the given sample.
This results in TAP distinct values for the TAP samples which range from 0 (the smallest sample) to TAP1 (the largest sample). The ranked sample is the one which has the index value equal to the required rank. The block diagram in Figure 3 illustrates the hardware implementation of the algorithm for TAP = 5. The D[3:0] data registers store older filter values, while the new data value is saved into the ND register. In every cycle, these registers shift their data to the left. Older values are compared with the new value (the result is “1” if the new value is smaller than the older ones, and “0” otherwise), and the comparison result is saved into the LSB position of TAP1, TAP wide registers (CR[3:0]). The MSB positions of these CR registers are updated with the value of the previous CR register. So, the full content of the CR registers is where (:) denotes bit selection, denotes concatenation, and C[k] denotes the kth comparison result. The comparison result of a given value is shifted to the left together with the filter value. Therefore, at any given time, CR[k] stores the comparison results of D[k] with all the other values within the filter. The TAP wide register for the new value (CN) is computed differently; it is generated using the negated result of the comparators; namely, the kth bit is updated with the (k+1)th comparison result. The 0th bit (selfcomparison) is set to “0.” Counting the “1”s in the CR and CN registers gives a number of values which are smaller than the given value. These bit summing operations are carried out by the 1CNT modules. The straightforward way is to use an adder tree with TAP onebit inputs. For the CN register, this is the only solution, as its content can change arbitrarily from clock to clock. Generation of CR[k] can be optimized taking into consideration the fact that only two bits change from CR[k−1]: the MSB (comparison result with the discarded sample) and the LSB (comparison result with the new value). Therefore, bit summing can be implemented using an incrementer/decrementer. The results of the bit summing blocks are compared with the required rank, generating a TAP bit wide vector of results containing exactly one “1” at the position of the cell which contains the required output. An encoder passes this position to the DL as an address. Table 1 shows an example with the data registers (D, ND), CR, CN and the output of the 1CNT blocks.

3.3. Multiword Filter Core
The architecture presented in the previous section can be easily extended to process more than one new filter value per clock cycle. Instead of one, the data registers (D) and the comparator result shift registers (CR) should shift by NI data positions. The yet single CN and CR registers become register arrays with NI elements. The number of comparators is increased, as all old samples should be compared with all new samples and new samples should be compared with each other. The required number of comparators for a TAP sized filter with NI new samples is
If WV is not an integer multiply of NI, the bandwidth of the filter core input supersedes that of the input stream. So in some clock cycles, the number of valid new data is going to be less than NI. The simplest solution to make the filter capable of processing different number of new samples is to insert multiplexers into the appropriate data paths, in front of D, ND, CR, and CN registers. Twotoone multiplexers always suffice as the number of valid new inputs is either NI or WV mod NI (see Figure 4). Still, for large apertures, numerous multiplexers may be required.
Another solution is to insert padding samples as necessary such that in every clock cycle NI new samples can be entered, thus creating a virtual filter kernel (VK). Figure 4 illustrates such kernel for WV = 3 and NI = 2 case. Valid samples in the window are marked with light grey; padding samples are marked with dark grey (the actual value of the padding samples are irrelevant). Obviously, this method makes the size of the VK larger than that of the real filter window, hence requiring more hardware resources as parts of the FC scale with the size of the VK.
Figure 5 presents the contents of the data registers clock by clock, using the example in Figure 4, as new inputs are inserted and the filter window is moved horizontally. Background shading of valid and invalid (padding) samples corresponds to Figure 4. Samples on the right are the input samples. As any given register may contain valid or invalid samples during operation, comparisons are done using all data registers, irrespective of the validity. Therefore, the number of comparators required scales with the size of the VK.
Padding samples are masked after the comparator result registers (CR, CN), but before the 1CNT blocks. For each older sample, masking is done for 2^{*}NI bits. NI bits mask the comparison results with the NI new samples, and other NI bits mask the comparison results of the oldest NI samples. The output ranking part is the same as in the singleword case. The number of required equality comparators is proportional to the size of the real filter window as it is sufficient to select the appropriate output when all samples in a new column have been inserted into the filter. In these cycles, the locations of the valid samples are well defined.
3.4. Multiword Filter with Multiple Outputs
In case valid samples are used for padding, the virtual filter kernel can be viewed as NP + 1 filter windows processed together, where NP is the number of padding lines added to the filter window to form the VK. For example, the 3×4 virtual kernel in Figure 4 can be viewed as two 3×3 partially overlapping filter windows. The FC presented in the previous section already computes all the required comparison results to generate valid outputs for both of the 3×3 filter windows. However, to come up with 2 separate outputs, the mask generator, the onecounters, and the output address generator should be replicated. The advantage is that the relation between the operating frequency and the number of new inputs processed in a single cycle becomes even better, significantly improving efficiency:
The drawback is that the LB should store WV lines of the input image instead of WV−1. In case of realtime video filtering, an output buffer may also be required.
3.5. Nonrectangular Filter Window
The maskbased filtering architecture allows for the easy implementation of nonrectangular (convex and nonconvex) filter windows. The most significant difference compared to the multiworld implementation described above is that the valid or invalid status of a given filter value may change as the filter window slides across the input image. For example, in Figure 6, pixel 10 is invalid in the first computation cycle it is used, but as the window slides one pixel to the right, it becomes valid.
Consequently, bit summing becomes more complex as the number of possible transitions between the masked CR and CN registers is increased. Nonrectangular windows typically increase the number of invalid samples within the VK. Therefore, using the bit summing block for the valid samples only may reduce resource requirements. Practically, in the latter implementation, only the number of ND and D registers scales with the virtual filter window; all other processing units are implemented only for the valid data.
3.6. Weighted Rank Filtering
Some applications require the use of weighted filter windows, rendering some input samples more significant than others when determining the output of the filter. The proposed method allows for the application of integer weights. The comparison result bits (CR and CN registers’ outputs) are replicated as many times as determined by the corresponding weight factor. However, the bit summing blocks become increasingly complex as their inputs become wider due to bit replication. Also, the TAP bit summing operation results in TAP different values, which are in the range of 0…W−1, where W is the summation of all the weights. As TAP is smaller than W, not all integer values will be presented at the outputs of the bit summing units. Therefore, a simple equality comparator is no longer adequate to determine the ranked sample. Instead, the filter has to find the sample which has the closest bit summing value to the required rank (which is in the range of 0…W−1).
To facilitate the correct selection, the proposed architecture (see Figure 7 employs several difference computing units and a selection tree. The difference computing units process the required rank and the outputs of the bit summing units. The two input minimum calculators select the smaller of their inputs together with a binary flag which shows whether the left or the right input was selected. At the root of the tree, the concatenated tag bits determine the location of the sample which has the closest bit summing value to the required rank. This value can be used to address the DL.
4. Implementation Results
The following implementation results were obtained using 24bit RGB input, with an FVG that sums the three color components and outputs a 10bit result. Table 2 summarizes the operating frequencies obtained for the wordserial architecture for different Xilinx FPGA families and different TAP numbers. These values can be used as a reference to help determine the required parallelization level of the FC, depending on the input pixel frequency and the filter window size.

Table 2 offers different solutions even for one of the most demanding commercial video format, HDTV1080p, which has a pixel frequency of 75 MHz. For example, a Virtex4 device can perform realtime filtering on HDTV source using a 49tap filter by employing a multiword FC configuration with 2 input samples per clock cycle. Figure 8 summarizes the resource requirements of a 49tap rank filter using different FC configurations (configuration WVxWH/NI). LUT and FF denote the number of lookup tables and flip flops in Virtex4 and Virtex5 devices, respectively. Figure 6 demonstrates that some multiword configurations (such as 7×7/5, 7×7/6) may require more resources than the full parallel architecture (7×7/7). The reason for this is that the VK becomes much larger than the valid filter window due to the enormous number of padding samples.
These configurations are inferior to the full parallel architecture in terms of throughput and silicon real estate. The presented architecture can take advantage of the 6input LUTs of the Virtex5 FPGA family, resulting in 20–30% reduction in the design size.
Tables 3, 4, 5, and 6 summarize the achievable operating frequencies and resource requirements of several filter configurations using Spartan3, Virtex4, and Virtex5 devices, respectively. For every filter size and FPGA family, the configurations marked with light grey background can be used to filter HDTV (1920×1080 30 p—75 MHz pixel clock) input. The lowerperformance configurations are still adequate for lowerresolution video inputs, like SDTV.




Although the longest registertoregister path does not depend on the filter configuration, as the complexity of the filter increases, the achievable operating frequency still decreases. This is common when using FPGAs and should be taken into consideration when selecting the filter configuration for given input format and filter size.
5. Conclusion
An efficient architecture for highperformance twodimensional rank filters was presented. Rankorder filters, especially median filters, are used extensively for removing nonGaussian (salt and pepper) noise from images and video streams. Targeting FPGA implementations for video applications, a parameterizable structure was proposed which delivers an efficient solution custom tailored to different pixel clock rates, available resources, and operating speeds. Compared to previous 2D architectures, the size and complexity of the filter structure were considerably reduced by balancing the number of new input samples entered into the core and the available operating frequency of the filter. The proposed solution is independent of input data type, as it offers great flexibility to generate magnitude information corresponding to RGB data, or it can take advantage of preexisting magnitude information if such data are already available. The solution presented can handle nonrectangular filter windows or weighted samples as well, which widens the domain of possible applications even further.
References
 R. Roncella, R. Saletti, and P. Terreni, “70MHz 2$\mu $m CMOS bitlevel systolic array median filter,” IEEE Journal of Solid State Circuits, vol. 28, no. 5, pp. 530–536, 1993. View at: Publisher Site  Google Scholar
 B. K. Kar and D. K. Pradhan, “New algorithm for order statistic and sorting,” IEEE Transactions on Signal Processing, vol. 41, no. 8, pp. 2688–2694, 1993. View at: Publisher Site  Google Scholar
 C. Chakrabarti and L.Y. Wang, “Novel sorting networkbased architectures for rank order filters,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 2, no. 4, pp. 502–507, 1994. View at: Publisher Site  Google Scholar
 P. Szántó, G. Szedő, and B. Fehér, “Implementing 2D median filter in FPGAs,” in Proceedings of the 7th International Carpathian Control Conference (ICCC '06), Roznov, Czech Republic, May 2006. View at: Publisher Site  Google Scholar
 C. Chakrabarti, “High sample rate array architectures for median filters,” IEEE Transactions on Signal Processing, vol. 42, no. 3, pp. 707–712, 1994. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2008 Péter Szántó et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.