DCE AutoEnhance and Hot Pixels Eliminator

DCE AutoEnhance and Hot Pixels Eliminator [22], [23] which are famous web sites concerning hot pixel reduction in the world wide web. The algorithms of these two methods are not available but executable programs are provided in the web. It has been proved that the decision-based VMF outperforms both of these two methods. Fig.

4.2 shows the filtered Airplane, Lena, Peppers, and Sailboat images from DCE AutoEnhance and Hot Pixels Eliminator, respectively. Again, we show the zoomed images for the purpose of clearly observing the texture and color contents in the filtered images. If we compare the images filtered by these two methods with the input processing images, we can find that the color and luster alter too much in the filtered images that we might think they possibly are not the results of the processing image. The filtered images looks like being shot under different light sources or in which the contents are appeared to be in different hues and saturations. Despite the two methods filtering out nearly all the hot spot noise, they are barely satisfied for the severe drawback of losing nature color of original input processing images.

Although DBVMF, DCE AutoEnhance, and Hot Pixels Eliminator have their defect respectively, they all possess the characteristic of low processing time which is the ultimate drawback of the VDF and DBVDF.

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Fig. 4.2. (a) Zoomed “Airplane＂ filtered by the DCE AutoEnhance filter. (b) Zoomed “Airplane＂ filtered by the HotPixels Eliminator filter. (c) Zoomed“Lena＂ filtered by the DCE AutoEnhance filter. (d) Zoomed “Lena＂

filtered by the HotPixels Eliminator filter.

4.1.3 Generalized Vector Directional Filter and Decision-Based Vector Directional Filter

Fig. 4.3 and Fig. 4.4 show the experimental results via GVDF and DBVDF respectively. We may see that images filtered by DBVDF has effectively reduced the hot spot noise, and better preserve the texture of the original image than GVDF. The output images of DBVDF are more realistic because of the fundamental characteristic of the DBVDF algorithm. And it might be easily perceived since images filtered by DBVDF are more natural in coloring comparing to those filtered by GVDF. Although the proposed filter outperforms GVDF, the slightly excessive pixels filtered by DBVDF seem to be observable than the other type of filters, because of over detection mentioned previously. However, our proposed filter bypasses the most uncontami- nated pixels to preserving the details and sharpness of the input processing images.

The quantitative tables will be listed in the following section and we will show the excellence of DBVDF comparing to the other filters introduced in this thesis, especially comparing to GVDF which is the basic model adopted in our filter＇s framework.kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkframework

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Fig. 4.3. (a) Zoomed “Airplane＂ filtered by the generalized vector directional filter. (b) Zoomed “Lena＂ filtered by the generalized vector directional filter. (c) Zoomed “Peppers＂ filtered by the generalized vector directional filter. (d) Zoomed

“Sailboat＂ filtered by the generalized vector directional filter.

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Fig. 4.4. (a) Zoomed “Airplane＂ filtered by the decision-based vector directional filter. (b) Zoomed “Lena＂ filtered by the decision-based vector directional filter. (c) Zoomed “Peppers＂ filtered by the decision-based vector directional filter. (d) Zoomed “Sailboat＂ filtered by the decision-based vector directional filter.

4.1.4 Experiment of Real World Image Corrupted with Hot Pixel Noise

Here, two images corrupted with the real hot pixel noise will be tested. Figs. 4.5 and 4.6 show the tested image and filtered image, respectively.

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Fig. 4.5. (a) A real world image corrupted with hot pixel noise. (b) The noisy resulting image filtered by the decision based vectorized median filter at ^{ò= 1.40}. (c) The noisy resulting image filtered by the DCE AutoEnhance filter. (d) The noisy resulting image filtered by the Hotpixels Eliminator filter. (e) The noisy resulting image filtered by the vector directional filter. (f) The noisy resulting image filtered by the decision-based vector directional filter.

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Fig. 4.6. (a) A real world image corrupted with hot pixel noise. (b) The noisy resulting image filtered by the decision based vectorized median filter with CMF at

ò= 1.40. (c) The noisy resulting image filtered by the DCE AutoEnhance filter. (d) The noisy resulting image filtered by the Hotpixels Eliminator filter. (e) The noisy resulting image filtered by the vector directional filter. (f) The noisy resulting image filtered by the decision-based vector directional filter.

4.2 Performance Comparison

4.2.1 Normalized Mean Square Error and Mean Chromaticity Error

From the experimental results above, the resulting images by the introduced filter:

BDVMF, DCE AutoEnhance, VDF, and DBVDF methods are difficult to assess visually. We find that the proposed DBVDF method provides high efficiency in eliminating the hot spot noise by the human vision perception. Two quantitative measures are employed to compare the performance of these filters [11]. The first is the normalized mean squared error NMSE( ), which is a standard measure as given by the original and the estimated image vector at pixel (i, j), respectively. The second measure is the mean chromaticity error MCRE( ). Since the GVDF and DBVDF operate as chromaticity filters, consequently their performance in terms of chromaticity error should be evaluated. MCRE is defined as

MCRE = _N1N2 chromaticity error between vectors f(i, j), and fê(i, j). It is defined as the distance

P Pê between the two points P and Pê, which are the intersection points of f(i, j), and fê(i, j) with the Maxwell triangle, respectively. This is shown graphically in Fig. 4.7 and we summarize the results in Tables I and II which respectively show the NMSE and MCRE of the various filters we introduced. However, we cannot, in practice, calculate the NMSE or MCRE to compare the efficiency about the real world corrupted images with our proposed DBVDF and the other filters owing to the lack of the images uncorrupted with the hot pixel noise.

4.2.2 Noise Detection and Weighted Peak Signal to Noise Ratio

The noise detection and filtering rate of hot spot noise for the images

“Airplane,” “Lena,” “Peppers,” and “Sailboat” are shown in Tables VI-X. It is to be noticed that the true positive values of our proposed filter are almost 100% for these four images and false negative values are higher than the other filters. That is, our proposed filter detects all the hot spot noise in the contaminated images and keeps most uncorrupted pixels unchanged. In addition to the quantitative evaluation presented above, a qualitative evaluation is necessary since the visual assessment of the processed image is, the must subjective measure of the efficiency of any method.

Therefore we introduce weighted peak signal to noise ratio WPSNR( ) to stress on reducing the hot spot noise or not of the filters. The weight vector W~ = W( ₁, W2, W3) is adopted to reflect the hot pixels by weights to account the removing capability of the filters. In the above, W1 indicates the weight to emphasize the hot spot noisy pixel that is detected to be contaminated and then the processing filter filtered indeed. W

indicates the weight to the hot spot noisy pixel not detected to be contaminated. W3 indicates the weight to the clean pixel is detected contaminated and filtered. The processing results of the introduced filters are shown in Tables III–XI.

It is obviously seen that our proposed filter is better than the other filters in the three of four processing images on the access measure of NMSE and MCRE, even in WPSNR. We might find that when the threshold ò3 increases in the experiment, the false detection of hot spot noise of our proposed filter decreases meanwhile leaves more uncontaminated pixels bypass. However, there are more hot spot noise not detected in the mean time, that represents the capability of filtering out hot spot noise decreases. The adjustability is the crucial reason that makes our filter more competitive and selective than DBVMF.

Fig. 4.7. Definition of the chromaticity error for two vectors fˆ .

TABLE I

NMSE (×₁₀à6) FOR THE IMAGES

filters or ò3 Airplane Lena Peppers Sailboat

DBVMF 104.4 142.4 279.2 500.8

filters or ò3 Airplane Lena Peppers Sailboat

DBVMF 17.3 22.0 26.0 18.4*

Thresholds in stage 1 and 2: both defined as 500

TABLE III

NOISE DETECTION AND FILTERINGOFTHEIMAGE “AIRPLANE” (PIXELS)

filters or ò3 True Positive True Negative False Positive False Negative

DBVMF 49 100 204943 57052

Total numbers of pixel: 512â512 GVDF: cascaded with median filter

Thresholds in stage 1 and 2: both defined as 500

TABLE IV

D^ETECTION R^{ATEOF THEIMAGE “}AIRPLANE” (%)

True False

filters or ò3 Positive Negative Positive

DBVMF 33 67 78 22

Thresholds in stage 1 and 2: both defined as 500

TABLE V

NOISE DETECTION AND FILTERINGOFTHEIMAGE “LENA” (PIXELS)

filters or ò3 True Positive True Negative False Positive False Negative

DBVMF 120 34 121908 140082

Thresholds in stage 1 and 2: both defined as 500

TABLE VI

D^ETECTION R^{ATEOF THEIMAGE “}L^{ENA” (%)}

True False

filters or ò3 Positive Negative Positive

DBVMF 78 22 47 53

Thresholds in stage 1 and 2: both defined as 500

TABLE VII

NOISE DETECTION AND FILTERINGOFTHEIMAGE “PEPPERS” (PIXELS)

filters or ò3 True Positive True Negative False Positive False Negative

DBVMF 118 36 171891 90099

Thresholds in stage 1 and 2: both defined as 500

TABLE VIII

D^ETECTION R^{ATEOF THEIMAGE “}PEPPERS” (%)

True False

filters or ò3 Positive Negative Positive

DBVMF 77 23 66 34

TABLE IX

N^OISE DETECTION AND F^{ILTERINGOFTHEIMAGE “}SAILBOAT” (PIXELS)

filters or ò3 True Positive True Negative False Positive False Negative

DBVMF 101 52 172971 89020

filters or ò3 Positive Negative Positive

DBVMF 66 34 66 34

TABLE XI

WPSNR comparisons of “Airplane,＂ “Lena,＂ “Peppers,＂ and “Sailboat＂

by five different filters with different ò³ (a)

filters or ò3 Airplane Lena Peppers Sailboat

GVDF: cascaded with median filter

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Table XII shows our proposed DBVDF saves lot of processing time via GVDF.

In fact, the elapsed time is correlated to the threshold we defined in DBVDF and the complexity of the input image. Obviously, huge computational complexity significantly limits GVDF practical usability. It is proved that DBVDF considerably reduces the computational complexity of the GVDF because of its decision-based algorithm. The speed improvement achieved nearly 100 times of simply applying GVDF only.

TABLE XII

P^ROCESSING T^IME (sec) ^FOR E^ACH F^ILTER

Image Airplane Lena Peppers Sailboat

VDF 2859.45 2803.00 2796.64 2807.89

DBVDF 40.62 25.28 28.39 32.34

GVDF: cascaded with median filter

Thresholds in stage 1 and 2: both defined as 500 _ò3: defined as 100

Chapter 5 Conclusion

In this thesis, a decision-based vector directional filter is proposed to reduce the hot spot noise in the images. In this scheme, we construct a two criterion and five-stage filter that saves lot of the processing time and preserves the image details better than the GVDF, as demonstrated in the experimental results. Indeed, we enhance the functionality of GVDF and exploit its original chrominance characteristic, which is very important in visual perception of color image, when applying on reducing the hot spot noise. Moreover, it can be implemented easily. Comparing to the conventional filter, DBVMF, and the famous filters on the web site: DCE AutoEnhance, DBVDF outperforms each of these filters. In the image processing, DBVDF demonstrates its effectiveness in less time consumption comparing to GVDF and in fidelity to the original uncontaminated image than the other filters. These features are reflected on the measures of NMSE and the detection rate. In the era of color image, DBVDF is supposed to be the most attractive filter for its internal color conception. Of course, DBVDF is on using in recovering the contaminated images corrupted by the hot spot noise.

Though DBVDF improves GVDF in both time consumption and details preservation, it is difficult to implement DBVDF in the real time designing mainly because it is still intrinsically computative. Future work about this field should be concentrated on the promotion of time efficiency, and that is expected to be a great challenge, a giant milestone in the meantime, in the progress of vector directional filter.

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