Decision-based Vector Directional Filter

Generally speaking, GVDF has good performance on the multi-channel image processing. When it is applied on the purpose of removing hot spot noise in the image processing, however, the output performance is barely satisfied. Moreover, it possibly changes too much details to retrieve the corrupted image. That is to say GVDF fails to preserve the most pixels in the original input image and it violates the original intention of our filter design. Consequently, we develop a decision-based vector directional filter (DBVDF) to enhance the performance of the GVDF.

The algorithm of DBVDF involves 2 criterions and 5 stages. Two criterions for hot spot noise detection comes from the concept of using information of four neighborhood adjoin pixels, as shown in Fig. 3.1., to determine whether the processing pixel is to filter or not. Decisions made in these two criterions are

responsible for fast processing and high detection rate of proposed filter. The parameters in these two criterions are obtained from observing and summarizing.

Besides, three of five stages have thresholds as decision. The 3rd stage is applied GVDF only, though the trimming length in the directional processing of GVDF is also a selected decision too. The whole DBVDF procedure is simply represented in the flowchart, as shown in Fig. 3.2. Thereafter, we will interpret the contents stage by stage explicitly.

Two Criterions:

Our proposed algorithm exploits low computation characteristic of two criterion to achieve the fast filtering and high noise detection rate. The definitions of Matrix Cross, Matrix Cros12, Matrix Cross23 , Matrix Cross1234 and _ò0, all in the intensity sense, help to clearly describe the algorithm of adopted criterion in the first two components of DBVDF. It is noticed that the principal content in the criterion 1 is aiming at fast hot spot noise detection. The parameters in the description are experienced and experimental results. In addition, it is unnecessary to adjust these parameters for different processing images since the performances change slightly. In the criterion 2, there are four situations to comment. Different numbers of contaminated-likely neighborhood needs to be considered respectively. Indeed, the criterion 1 owns more severe restriction than criterion.

Definition:

b) x(i,j)>=1.2_âCross12 AND Cross(3)>=220 AND Cross(4)>=220 c) Cross(2)>=210 AND Cross(3)>=210 AND Cross(4)>=210 d) ò0>=1.35 AND Not{Cross(1)>=210 AND Cross(2)>=210 AND

Cross(3)>=210 AND Cross(4)>=210}

Stage 1:

In the region of our 3 â 3 moving processing mask, the intensity of every pixel is not supposed to vary too much because of the characteristic of nature light [1]. That is to say that intensities in limited-area local region seem to be somewhat continuous.

Thus, we use the sum of intensity difference as a criterion to restrict the filtering so that the processing area with little intensity variation will be bypassed. It’s not only decreasing our image processing time but preserving the most uncontaminated part of the original input. Consequently, the output resembles the image without noise much more and the rate of correction gains high.

The threshold picked in this stage arises from the contents in the previous listed reasons. Considering a 3 â 3 moving processing mask as in Fig. 3.3, decision

Over chromaticity

Fig. 3.2. Flow chart of decision-based vector directional filter.

Bypass

restrains as ò1 [21], if ò1 is greater than the threshold picked in this stag, then the proposed decision mechanism is meant to regard the processing pixel as an outlier one.

Stage 2:

As the assumption in the stage 1, the color difference in the neighborhood of

moving processing mask is supposed not to alter abruptly. In these two stages, we are expected to process comparatively normal contaminated-images with no abnormal intensity and color difference bounces. Once we filter a particular input that has a lot of edges in its detail, however, so long as the threshold selected in this stage be enlarged enough to prevent from modifying the complex color variation regions (usually refer to edges) as far as possible. Since contaminated pixels mostly are discontinuous in color with its neighbor clean pixels and usually have a great jump in every dimension of 3 color components with uncontaminated neighborhood, this stage employs the characteristic of the hot pixel noise to decide whether the moving mask is

x₁ x₂ x₃

x₄ x₅ x₆

x₇ x₈ x₉

Fig. 3.3. 3 â 3 moving window mask with every entry indexed in stage 1.

going to be processing or just neglect the filtering in this pixel. This step saves lots of processing time again and even preserves the originality of the most pixels of input image further.

Considering a 3 â3 moving processing mask as in Fig. 3.2, decision restrain is selected by ò2, if ò2 is greater than the threshold picked in this stage, then the proposed decision mechanism is meant to regard the processing pixel as an outlier one.

Both of the stage 1 and stage 2 are highly related to the performing time cost. It is because that they determine whether the processing pixel is to be filtering or not.

By these two stage’s criterions, we can save the a large quantity of processing time cause proceeds on filtering the uncontaminated-likely pixels with the GVDF in the next stage would takes a huge amount of time for its vast complexity of

computations.

Stage 3:

Every pixel in the image can be seen as a vector as in Fig. 3.4. On account of color characteristic, we introduce the GVDF as a main filter in whole. The GVDF utilizes its principal viewpoint based on the color space concept and this is more close to the fundamental property in color image processing than any other filters. Although

GVDF costs considerably long time, it still has an outstanding performance in the multi-channels signal process. That’s the reason why we use the GVDF as a main filter [11] in the entire process. What is more in our design, the filter is appended the restrictions previously in this stage like those in stage 1 and stage 2, thus we can decrease the processing time effectively by the way of adequately choosing the more possible contaminated-likely pixels to handle.

The strategy here is to adopt the 3 â3 moving mask too while signal length criterion should be take into consideration so that the output signal length of GVDF is not varying far from the adjoining pixels of input. In the algorithm of GVDF, we take half numbers of input signals (that is in general) to be the trimming target. Therefore, four input pixels that deviate from the other five inputs are passed over because they are seemed to be noise-like ones.

Stage 4:

In fact, the GVDF uses a cascade of directional processing and magnitude processing that is shown in Fig. 3.5. As we describe at the previous chapter, three

Fig. 3.4. Perspective representation of the color cube.

filters have been used for the step of magnitude processing: the ë-trimmed mean [16], [17] the morphological open-close [18], and the multistage max/median [19].

However we do not expect to replace the processing pixel directly with the output of vector directional filter (VDF) [11] or output of GVDF cascaded with one of these three different kinds of filters. Instead of those filters, the mean filter in the intensity sense is adopted in the step of magnitude processing. Nevertheless it is just only a reference so that we can make decision of what pixel is selected to replace the current processing contaminated-likely pixel. In other words, decision in this stage is that we substitute the contaminated-like pixel (judged via our algorithm) by the one whose intensity is more probably closed to the original uncontaminated pixel, of course, they are all in the moving mask. It really makes the retrieval pixel with intensity more continuous nearby the processing region.

The substitution is implemented in all the three color channels, thus, the output turns to be more excellent and more continuous with neighborhood in the color sense than that directly processed by GVDF and cascaded ordinary filter.

Stage 5:

In order to restore the most uncontaminated pixel of the input image, the last criterion is to let the output of our design much more resemble the original without too much artificial alteration. It is compensating for the condition once our decision goes wrong that results in filtering the clean pixel. We set a threshold ò to achieve

this goal in this stage. First we duplicate a copy of original input image. If the chromatic difference (absolute value) of the processing pixel in the original contaminated image and the output of stage 4 is smaller than ò3, then we do not modify the local processing pixel in the copy image. In case of the difference is greater than the threshold, we substitute the processing pixel in the duplicated image by the output of stage 4. In other words, we try to preserve the most original appearance in the input image again. The threshold should not be set too low so that the image contains too much artificial modification and most of that often are somehow dissimilar from the original. On the other hand, the duplicated copy may be remain unchanged for the most part as input image if the threshold is set too high so that we lose to filter out the hot spot like noise.

To summarize our design, we develop a decision-based GVDF applying on multi-channel image processing for removing the hot pixel like noise. The GVDF with a proper decision criterion is good because it would considerably reduce the required time for processing and attain a more excellent performance than that is implemented by GVDF only. Consequently we design a five-stage decision-based GVDF that considers both the chromaticity and the intensity content. In the simulation section, we will discuss its advantage by some assessment criterion.

Fig. 3.5. Multi-channel image processing using a cascade of directional processing and magnitude processing.