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Showing papers on "Bilateral filter published in 2004"


Journal ArticleDOI
TL;DR: This paper proposes an alternate approach using L/sub 1/ norm minimization and robust regularization based on a bilateral prior to deal with different data and noise models and demonstrates its superiority to other super-resolution methods.
Abstract: Super-resolution reconstruction produces one or a set of high-resolution images from a set of low-resolution images. In the last two decades, a variety of super-resolution methods have been proposed. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses their shortcomings. We propose an alternate approach using L/sub 1/ norm minimization and robust regularization based on a bilateral prior to deal with different data and noise models. This computationally inexpensive method is robust to errors in motion and blur estimation and results in images with sharp edges. Simulation results confirm the effectiveness of our method and demonstrate its superiority to other super-resolution methods.

2,175 citations


Journal ArticleDOI
TL;DR: It is shown that kernel density estimation applied in the joint spatial–range domain yields a powerful processing paradigm—the mean shift procedure, related to bilateral filtering but having additional flexibility, which establishes an attractive relationship between the theory of statistics and that of diffusion and energy minimization.

246 citations


Proceedings ArticleDOI
15 Apr 2004
TL;DR: A novel filtering technique namely trilateral filter is proposed, which can achieve edge-preserving smoothing with a narrow spatial window in only a few iterations and provides greater noise reduction than bilateral filtering and smooths biomedical images without over-smoothing ridges and shifting the edge locations.
Abstract: Filtering is a core operation in low level computer vision. It is a preliminary process in many biomedical image processing applications. Bilateral filtering has been applied to smooth biomedical images while preserving the edges. However, to avoid oversmoothing structures of sizes comparable to the image resolutions, a narrow spatial window has to be used. This leads to the necessity of performing more iterations in the filtering process. In this paper, we propose a novel filtering technique namely trilateral filter, which can achieve edge-preserving smoothing with a narrow spatial window in only a few iterations. The experimental results have shown that our novel method provides greater noise reduction than bilateral filtering and smooths biomedical images without over-smoothing ridges and shifting the edge locations, as compared to other noise reduction methods.

94 citations


Patent
Sachin G. Deshpande1, Hao Pan
07 Jun 2004
TL;DR: In this paper, an image de-ringing filter that includes a determination unit, an adaptive filter and a nonlinear low-pass filter is used to remove ringing artifacts from a quantized image.
Abstract: Ringing artifacts are removed from a quantized image by an image de-ringing filter that includes a determination unit, an adaptive filter and a nonlinear low-pass filter. The determination unit determines whether each selected pixel of a first set of selected pixels of an image contains a ringing artifact based on, for example, gray-level values of selected pixels within a determination kernel of pixels relating to the selected pixel. The adaptive filter generates a filtered gray-level value for each pixel determined by the determination unit to contain a ringing artifact based on, for example, gray-level values of selected pixels within a filtering kernel of pixels relating to the pixel. The nonlinear low-pass filter generates a low-pass-filtered gray-level value for each selected pixel of a second set of selected pixels of the image.

89 citations


Journal ArticleDOI
TL;DR: It is argued that for point rendering, removing noise from normals is more important than removes noise from geometry, because normals have a greater impact on the model's perceived quality.
Abstract: Models created from 3D scanners are becoming more prevalent as the demand for realistic geometry grows and scanners become more common. Unfortunately, scanned models are invariably noisy. This noise corrupts both samples' positions and normals. Our proposed method for improving normals is derived from a feature-preserving geometry filter. Many such filters are available, most operating on models represented as triangle meshes. We argue that for point rendering, removing noise from normals is more important than removing noise from geometry, because normals have a greater impact on the model's perceived quality. Two approaches for smoothing point models have been proposed. Point set surfaces estimate smoothed normals and geometry by least-squares fitting to locally weighted neighborhoods. The spectral processing method creates a local height field, which is then filtered and resampled. The former method is not feature preserving, while the latter requires resampling to a regular grid, which can degrade features. Our method is novel in that it preserves features and doesn't require resampling.

76 citations


Proceedings ArticleDOI
06 Sep 2004
TL;DR: This paper presents a modification of the standard band-pass filtering technique used by many SSD- and SAD-based correlation algorithms, and shows that in conjunction with SAD correlation, this new method improves stereo quality at range discontinuities while maintaining real-time performance.
Abstract: In recent years, there have been significant strides in increasing quality of range from stereo using global techniques such as energy minimization. These methods cannot yet achieve real-time performance. However, the need to improve range quality for real-time applications persists. All real-time stereo implementations rely on a simple correlation step which employs some local similarity metric between the left and right image. Typically, the correlation takes place on an image pair modified in some way to compensate for photometric variations between the left and right cameras. Improvements and modifications to such algorithms tend to fall into one of two broad categories: those which address the correlation step itself (e.g., shiftable windows, adaptive windows) and those which address the preprocessing of input imagery (e.g. band-pass filtering, Rank, Census). Our efforts lie in the latter area. We present in this paper a modification of the standard band-pass filtering technique used by many SSD- and SAD-based correlation algorithms. By using the bilateral filter of Tomasi and Manduchi [(1998)], we minimize blurring at the filtering stage. We show that in conjunction with SAD correlation, our new method improves stereo quality at range discontinuities while maintaining real-time performance.

51 citations


Patent
23 Nov 2004
TL;DR: In this article, the filter weights are based on edge contents of at least a portion of the at least one image, and the method includes filtering the image information using the identified filter weights.
Abstract: A method includes receiving image information representing at least one image. The image information defines multiple pixels in the at least one image. The method also includes identifying filter weights associated with the pixels. The filter weights are based on edge contents of at least a portion of the at least one image. In addition, the method includes filtering the image information using the identified filter weights.

48 citations


Patent
14 Oct 2004
TL;DR: In this article, a method for classifying pixels in an image by first partitioning the image into blocks and then, the blocks are classified into classes according to the maximum variance.
Abstract: A method classifies pixels in an image by first partitioning the image into blocks. A variance of an intensity is determined for each pixel, and for each block the pixel with the maximum variance is identified. Then, the blocks are classified into classes according to the maximum variance.

39 citations


Patent
14 Oct 2004
TL;DR: In this paper, a method for filtering pixels in an image, by first partitioning the image into blocks, is presented, and each pixel in each edge block is filtered with a filter that is dependant on the variance of the pixel.
Abstract: A method filters pixels in an image, by first partitioning the image into blocks. Edge block are identified. A variance of an intensity for each pixel in each edge block is determined. Then, each pixel in each edge block is filtered with a filter that is dependant on the variance of the pixel.

38 citations


Patent
10 Mar 2004
TL;DR: In this article, the authors proposed a method to identify pixels having values that do not fall in the range defined by the immediately neighboring pixels and the deviate from the neighboring pixels by more than a threshold amount.
Abstract: Defective pixels in a CMOS array give rise to spot noise that diminishes the integrity of the resulting image. Because CMOS arrays and digital logic can be fabricated on the same integrated circuit using the same processing technology and relatively inexpensive and fast circuit can be employed to digitally filter the pixel data stream and to identify pixels having values that do not fall in the range defined by the immediately neighboring pixels and the deviate from the neighboring pixels by more than a threshold amount. Such conditions would indicate that the deviation is caused by a defective pixel rather than by desired image data. The threshold amount can be preprogrammed or can be provided by a user or can be dynamically set using feedback indicating image quality. The filter would also provide a solution for other sensors such as CCD, although a single chip solution would likely not be possible.

33 citations


Proceedings ArticleDOI
09 Jun 2004
TL;DR: Anisotropic 3D scan point filtering is introduced, which is defined as 3D Geometric Bilateral Filtering (GBF) and is robust, simple and fast.
Abstract: In recent years, reverse engineering (RE) techniques have been developed for surface reconstruction from 3D scanned data. Typical sampling data, however, usually is large scale and contains unorganized points, thus leading to some anomalies in the reconstructed object. To improve performance and reduce processing time, Hierarchical Space Decomposition (HSD) methods can be applied. These methods are based on reducing the sampled data by replacing a set of original points in each voxel by a representative point, which is later connected in a mesh structure. This operation is analogous to smoothing with a simple low- pass filter (LPF). Unfortunately, this principle also smoothes sharp geometrical features, an effect that is not desired. The high performance results of bilateral filtering for removing noise from 2D images while preserving details motivated us to extend this filtering and apply it to 3D scan points. This paper introduces anisotropic 3D scan point filtering, which we have defined as 3D Geometric Bilateral Filtering (GBF). The proposed GBF method smoothes low curvature regions while preserving sharp geometric features, and it is robust, simple and fast.

Patent
Haan Gerard De1
31 Mar 2004
TL;DR: In this article, the authors proposed an image conversion unit (200) for converting an input image with a first resolution into an output image having a second resolution being different from the first resolution.
Abstract: The invention relates to an image conversion unit (200) for converting an input image with a first resolution into an output image with a second resolution being different from the first resolution. The image conversion unit (200) comprises: a coefficient-determining means (106) for determining a first filter coefficient on basis of pixel values of a group of pixels of the first image; combining means (204-210) for combining the first filter coefficient with a predetermined filter coefficient into a final filter coefficient; and an adaptive filtering means (104) for computing a second pixel value of the second image on basis of a first one of the pixel values of the first image and the final filter coefficient.

Patent
27 Apr 2004
TL;DR: In this paper, a system and method for enhancing images of barcodes and other similar objects taken by the digital camera connected to or embedded in a mobile device is presented, which works by converting the image into its equivalent gray scale and then computes the mean pixel intensity value of a row of pixels in the image.
Abstract: This present invention discloses a system and method for enhancing images of barcodes and other similar objects taken by the digital camera connected to or embedded in a mobile device. This filter works by converting the image into its equivalent gray scale. The algorithm then computes the mean pixel intensity value of a row of pixels in the image. The row is divided into sections and the mean pixel intensity of each section is also calculated. The pixels in each section are processed according to the relation of the relative mean intensities of the row and the section. Once each pixel has been processed, the image is reassembled from its divided sections.

Patent
27 Feb 2004
TL;DR: In this paper, a filter kernel is received to determine one or more filtered values for each pixel in a sequence of pixels, where adjacent pixels are separated by a characteristic distance in the image.
Abstract: Methods and apparatus, including computer program products, for filtering an image. A filter kernel is received to determine one or more filtered values for each pixel in a sequence of pixels, where adjacent pixels are separated by a characteristic distance in the image. A difference kernel is defined based on local differences between a first kernel and a second kernel that are defined by the filter kernel centered at a first location and a second location, respectively. The second location is separated from the first location by the characteristic distance separating adjacent pixels in the sequence. The difference kernel is used to determine a difference between filtered values of adjacent pixels in the sequence. For depth of field filtering, the filter kernel can include a blur filter kernel that is based upon depth values of pixels in the sequence.

Patent
20 Aug 2004
TL;DR: In this article, a system and method for filtering pixels in an image using only fixed-point and summation operations is presented, where pixel intensities, fuzzy filter weights and the normalization factor are used to obtain an output pixel corresponding to the input pixel.
Abstract: An invention provides a system and method for filtering pixels in an image using only fixed-point and summation operations. First, a filtering window is centered on an input pixel. Based on a difference between the intensity of the input pixel and its neighboring pixels, fuzzy filter weights are obtained. A sum of the fuzzy filter weights is used to determine a normalization factor. Then, the pixel intensities, fuzzy filter weights and the normalization factor are used to obtain an output pixel corresponding to the input pixel.

Patent
22 Dec 2004
TL;DR: In this article, the authors propose a bilateral filter that includes a coefficient arithmetic section 51 for calculating coefficients of a filter and a filter section 52 for applying filtering processing to a filter object region of the visible light image Visible.
Abstract: PROBLEM TO BE SOLVED: To provide an image processing apparatus, an image processing method, a program, and a recording medium for reducing noise while storing an edge even if the edge exists in one of a plurality of images. SOLUTION: A bilateral filter 5 includes a coefficient arithmetic section 51 for calculating coefficients of a filter and a filter section 52. The coefficient arithmetic section 51 calculates the coefficients W of the filter on the basis of two images comprising a visible light image Visible imaged by a visible light imaging section 2 and an infrared ray image Infr imaged by an infrared ray imaging section 3. The filter section 52 uses the coefficients W to apply filtering processing to a filter object region of the visible light image Visible. COPYRIGHT: (C)2006,JPO&NCIPI

01 Jan 2004
TL;DR: Bilateral filtering is applied in spatio-temporal domain and provides control over the level of details in reconstructed lighting and proves to be efficient in preserving sharp features in lighting which is in particular important for high-quality caustic reconstruction.
Abstract: Photon tracing and density estimation are well established techniques in global illumination computation and rendering of high-quality animation sequences. Using traditional density estimation techniques it is difficult to remove stochastic noise inherent for photon-based methods while avoiding overblurring lighting details. In this paper we investigate the use of bilateral filtering for lighting reconstruction based on the local density of photon hit points. Bilateral filtering is applied in spatio-temporal domain and provides control over the level-of-details in reconstructed lighting. All changes of lighting below this level are treated as stochastic noise and are suppressed. Bilateral filtering proves to be efficient in preserving sharp features in lighting which is in particular important for high-quality caustic reconstruction. Also, flickering between subsequent animation frames is substantially reduced due to extending bilateral filtering into temporal domain

Patent
13 Aug 2004
TL;DR: In this article, a difference filter is used to detect whether an edge is or is not located between two pixels in an image, which pixels are adjacent to each other, and a judgment is made as to whether an absolute value of the thus obtained difference is or not equal to at least a predetermined threshold value.
Abstract: Filtering processing is performed with a difference filter and on two pixels in an image, which pixels are adjacent to each other, and a difference between pixel values of the two pixels, which are adjacent to each other, is thus obtained. A judgment is made as to whether an absolute value of the thus obtained difference is or is not equal to at least a predetermined threshold value. In cases where the absolute value of the difference has been judged to be equal to at least the predetermined threshold value, it is judged that an edge is located between the two pixels, which are adjacent to each other. Detection as to whether an edge is or is not located between the pixels in the image is thus capable of being made quickly with simple operation processing.

01 Jan 2004
TL;DR: Channel smoothing is found to be superior in four respects: it has a lower computational complexity, it is easy to implement, it chooses the global minimum error instead of the nearest local minimum, and it can also be used on nonlinear spaces, such as orientation space.
Abstract: In this paper we present a new and efficient method to implement robust smoothing of low-level signal features: B-spline channel smoothing. This method consists of three steps: encoding of the signal features into channels, averaging of the channels, and decoding of the channels. We show that linear smoothing of channels is equivalent to robust smoothing of the signal features, where we make use of quadratic B-splines to generate the channels. The linear decoding from B-spline channels allows to derive a robust error norm which is very similar to Tukey's biweight error norm. Channel smoothing is superior to iterative robust smoothing implementations like non-linear diffusion, bilateral filtering, and mean-shift approaches for four reasons: it has lower computational complexity, it is easy to implement, it chooses the global minimum error instead of the nearest local minimum, and it can also be used on non-linear spaces, such as orientation space. In the experimental part of the paper we compare channel smoothing and the previously mentioned three other approaches for 2D orientation data.

01 Jan 2004
TL;DR: A novel Monte Carlo noise reduction operator that can suppress the outliers, as well as the inter-pixel incoherence in a non-iterative way, and be easily integrated into existing rendering systems is proposed in this paper.
Abstract: A novel Monte Carlo noise reduction operator is proposed in this paper. We apply and extend the standard bilateral filtering method and build a new local adaptive noise reduction kernel. It first computes the initial estimate of each pixel, and then applies bilateral filtering using this initial estimate in its range filtering kernel. It is simple both in formulation and implementation. The new operator is robust and fast in the sense that it can suppress the outliers, as well as the inter-pixel incoherence in a non-iterative way. It can be easily integrated into existing rendering systems, and such a framework is shown in this paper. The results of our approach are compared with those of other methods. A GPU implementation of our algorithm runs in 500ms for a 512×512 image.

Patent
David Drezner1, Gideon Kojokaro1
02 Nov 2004
TL;DR: In this paper, a method for reducing random noise in a sequence of digital video frames comprising the following steps: 1. for each pixel (center pixel) in a frame a set of adjacent pixels is defined; for each of the adjacent pixels the difference of their values in the current frame and the previous frame is calculated, whereby the value of the center pixel is omitted; each difference value is shifted right for a predefined number of bits.
Abstract: The invention refers to an apparatus and a method for reducing random noise in a sequence of digital video frames comprising the following steps: 1. for each of the pixels (center pixel) in a frame a set of adjacent pixels is defined; 2. for each of the adjacent pixels the difference of their values in the current frame and the previous frame is calculated, whereby the value of the center pixel is omitted; 3. each difference value is shifted right for a predefined number of bits; 4. the square of the difference value is added to an activity value of that center pixel; 5. if the activity value remains below a predefined threshold value, then a weighting factor depending from activity value is calculated and 6. the value of the center pixel is set to a weighted value.

01 Jan 2004
TL;DR: This paper presents a novel filtering method, integrating geometric, photometric and local structural similarities, to achieve edge-preserving smoothing in medical images, and finds that this new approach provides greater noise reduction than that of BF with a 3-pixel-width spatial window.
Abstract: INTRODUCTION Filtering is a preliminary process in many medical image processing applications, which is aimed at restoring a noise-corrupted image to its noiseless counterpart. Post-processing tasks, e.g., visualization, segmentation and quantification, may benefit from the reduction of noise. Diffusion equations with scalar-valued and tensor-valued diffusivities [1] and non-linear filters [2] have been used to perform smoothing in medical images. In this paper, we present a novel filtering method, integrating geometric, photometric and local structural similarities, to achieve edge-preserving smoothing in medical images. It is simple to implement and is applicable to multi-dimensional signals. The experimental results have shown that this new technique provides greater noise reduction than other denoising techniques. Our method uses a narrow spatial window (3 pixels in each dimension) and takes only a few iterations (3 iterations in the experiments in this work) in the smoothing process. METHODS Bilateral filtering (BF) [3] is a simple, non-iterative and local approach to edge-preserving smoothing. A filtered image is obtained by replacing the intensity value of each pixel with an average value weighted by the geometric and photometric similarities between neighboring pixels within a spatial window. The novel filtering method proposed in this paper, namely trilateral filtering (TF), works along the same lines as BF; it takes the geometric, photometric and local structural similarities to smooth the images with a narrow spatial window while preserving the edges. Local structural information is used to determine inhomogeneity in the images and influence the smoothing process with orientation information. On one hand, low-pass filtering is performed in the homogeneous regions. On the other hand, smoothing along edges is achieved by considering the three similarities between neighborhoods in the inhomogeneous regions. We found that this new approach provides greater noise reduction than that of BF with a 3-pixel-width spatial window. TF is expressed as follows:

Patent
Sachin G. Deshpande1
29 Dec 2004
TL;DR: In this paper, an image de-ringing filter system and method is presented, which consists of accepting image pixels (504), collecting data from a first group of pixels neighboring a test pixel (506); in response to the first group data, deciding if the test pixel includes image ringing artifacts (508); collecting data of a second group of pixel neighboring the test pixels (510); and, generating a filtered value (FV) (512b/512f).
Abstract: An image de-ringing filter system and method are provided. The method comprises: accepting image pixels (504); collecting data from a first group of pixels neighboring a test pixel (506); in response to the first group data, deciding if the test pixel includes image ringing artifacts (508); collecting data from a second group of pixels neighboring the test pixel (510); in response to the second group data, generating a filtered value (FV) (512b/512f); and, replacing the test pixel actual value with FV (514). Typically, collecting data from the first and second group of pixels includes the performance of a mathematical operation. For example, a matrix may be defined for the multiplication of the first group of pixels. Values of pixels on a first side of the coordinate axis may be subtracted from pixels on a second side of the coordinate axis, opposite of the first side. Then, the difference is compared to a threshold.

01 Jun 2004
TL;DR: In this article, the edge detection algorithm with the application of a bilateral filter in Gaussian form in Spiral Architecture is presented, where edge maps of the original image and its successively smoothed versions are used to produce the final edge map.
Abstract: Real images are often corrupted by noise from various sources. Bilateral filtering is a nonlinear filter that considers intensity variations as well as spatial closeness in the noise smoothing process. It has been demonstrated to have a better edge-preserving quality than linear filters in certain applications. This paper presents the new edge detection algorithm with the application of a bilateral filter in Gaussian form in Spiral Architecture. Spiral Architecture is a relatively new concept in the area of image representation and offers distinctive advantages. The approach to edge detection is multi-scale. Edge maps of the original image and its successively smoothed versions are used to produce the final edge map.

Patent
Nathan Moroney1
14 Sep 2004
TL;DR: A method and apparatus for edge-preserving processing of digital images includes selecting an input pixel from a digital image, choosing a set of neighboring pixels from an area around the input pixel according to a sparse matrix constructed according to the distribution as mentioned in this paper.
Abstract: A method and apparatus for edge-preserving processing of digital images includes selecting an input pixel from a digital image, choosing a set of neighboring pixels from an area around the input pixel according to a sparse matrix constructed according to a distribution, determining the similarity in value of each neighboring pixel to that of the input pixel according to a metric, and calculating a weighted average of the values of the neighboring pixels by weighting by a first smaller weight those pixels which are less similar to the input pixel and weighting by a second greater weight those pixels which are more similar to the input pixel.

01 Apr 2004
TL;DR: This work presents a robust filter which operates directly on points using higher order surface approximations, computed iteratively, and extends the bilateral filter by using and filtering surface curvature, and introducing a quality parameter based on the authors' local surface approximation.
Abstract: Processing noisy point data is a tedious task. It often requires smoothing and meshing, followed by mesh processing algorithms. In this work we present a robust filter which operates directly on points using higher order surface approximations, computed iteratively. We extend the bilateral filter by using and filtering surface curvature, and introducing a quality parameter based on our local surface approximation. Using this process input point data is denoised and smoothed, while preserving features. We also extend our filter to allow feature enhancement, by controlling shock formation resulting in sharp edges in regions of high curvature. We show results of our algorithms on several scanned point sets.

Proceedings ArticleDOI
16 Jun 2004
TL;DR: Bilateral filtering is applied in spatio-temporal domain and provides control over the level of details in reconstructed lighting and proves to be efficient in preserving sharp features in lighting which is in particular important for high-quality caustic reconstruction.
Abstract: Photon tracing and density estimation are well established techniques in global illumination computation and rendering of high-quality animation sequences. Using traditional density estimation techniques it is difficult to remove stochastic noise inherent for photon-based methods while avoiding overblurring lighting details. In this paper we investigate the use of bilateral filtering for lighting reconstruction based on the local density of photon hit points. Bilateral filtering is applied in spatio-temporal domain and provides control over the level-of-details in reconstructed lighting. All changes of lighting below this level are treated as stochastic noise and are suppressed. Bilateral filtering proves to be efficient in preserving sharp features in lighting which is in particular important for high-quality caustic reconstruction. Also, flickering between subsequent animation frames is substantially reduced due to extending bilateral filtering into temporal domain

Patent
04 May 2004
TL;DR: In this paper, a method and system for smoothing a frame to remove jagged edges is presented. But the method is based on a normalized linear combination of a first edge end pixel, a second edge end pixels, and center entry of the smoothing filter.
Abstract: A method and system for smoothing a frame to remove jagged edges are presented. The method and system generates a smoothing filter with consolidated pixels. Edges within the smoothing filter are analyzed to select an edge direction used for smoothing. A smoothed pixel is generated based on a normalized linear combination of a first edge end pixel, a second edge end pixel and center entry of the smoothing filter. Subtle structure checking can be used to determine whether to use the smoothed pixel in place of the current pixel.

Journal ArticleDOI
TL;DR: A robust mesh smoothing operator called mean value coordinates flow is introduced to modify mean curvature flow and make it more stable and compared with previous algorithms, the result shows it is simple, efficient and robust.
Abstract: This paper proposes a vertex-estimation-based, feature-preserving smoothing technique for meshes. A robust mesh smoothing operator called mean value coordinates flow is introduced to modify mean curvature flow and make it more stable. Also the paper proposes a three-pass vertex estimation based on bilateral filtering of local neighbors which is transferred from image processing settings and a Quasi-Laplacian operation, derived from the standard Laplacian operator, is performed to increase the smoothness order of the mesh rapidly whilst denoising meshes efficiently, preventing volume shrinkage as well as preserving sharp features of the mesh. Compared with previous algorithms, the result shows it is simple, efficient and robust.

Patent
Sakamoto Shohei1
02 Jun 2004
TL;DR: In this paper, a low pass filter processing is carried out by a noise reduction circuit, which restricts a difference between a value of each of the peripheral pixels and a value value of a center pixel to a value having a predetermined noise constant defined as an upper limit with respect to each of peripheral pixels, e.g., a pixel space of 5×5.
Abstract: Noise included in image data output from an analog processing unit, is eliminated by a noise reduction circuit. The noise reduction circuit restricts a difference between a value of each of peripheral pixels and a value of a center pixel to a value a value having a predetermined noise constant defined as an upper limit with respect to each of the peripheral pixels, e.g., a pixel space of 5×5. The values of the peripheral pixels whose upper limits are restricted are defined as new values of the peripheral pixels. The value of the center pixel is converted into a value obtained by averaging the new values of the peripheral pixels and the value of the center pixel. In this manner, low pass filter processing is carried out.