Patent Publication Number: US-2022215506-A1

Title: Circuit for combined down sampling and correction of image data

Description:
BACKGROUND 
     1. Field of the Disclosure 
     The present disclosure relates to a circuit for processing image data, and more specifically to a circuit for combined down sampling and correction of image data to correct chromatic aberrations in captured images. 
     2. Description of the Related Arts 
     Image data captured by an image sensor or received from other data sources is often processed in an image processing pipeline before further processing or consumption. For example, raw image data may be corrected, filtered, or otherwise modified before being provided to subsequent components such as a video encoder. To perform corrections or enhancements for captured image data, various components, unit stages or modules may be employed. 
     Such an image processing pipeline may be structured so that corrections or enhancements to the captured image data can be performed in an expedient way without consuming other system resources. Although many image processing algorithms may be performed by executing software programs on central processing unit (CPU), execution of such programs on the CPU would consume significant bandwidth of the CPU and other peripheral resources as well as increase power consumption. Hence, image processing pipelines are often implemented as a hardware component separate from the CPU and dedicated to performing one or more image processing algorithms. 
     However, image processing pipelines do not account for the use of a wide-angle lens (e.g., a fisheye lens) to generate the image data. When a wide-angle lens is used to generate the image data, the refraction angle of light with different wavelength varies thereby manifesting itself on the image sensor as shifted focal points that are not aligned among red, green, and blue color channels. Thus, color fringing is present at sharp and high contrast edges of full-color images generated from the image data. 
     SUMMARY 
     Embodiments relate to an image processor that includes a foveated down sampling and correction circuit for correcting chromatic aberrations in images captured by one or more image sensors coupled to the image processor. The foveated down sampling and correction circuit includes a first correction circuit (e.g., a vertical foveated down sampling and correction circuit) and a second correction circuit (e.g., a horizontal correction circuit) coupled to the first correction circuit. The first correction circuit performs down sampling and interpolation of pixel values of a first subset of pixels of a same color in a raw image using first down sampling scale factors and first interpolation coefficients to generate first corrected pixel values for pixels of the same color in a first corrected version of the raw image. The pixels in the first subset are arranged in a first direction (e.g., vertical direction), the first down sampling scale factors gradually vary along the first direction, and the first interpolation coefficients correspond to first offset values. The first offset values represent first distances from each down sampling pixel location along the first direction to corresponding first virtual pixels in the first direction. 
     The second correction circuit receives the first corrected pixel values of the first corrected version and performs interpolation of pixel values of a second subset of the pixels in the first corrected version using second interpolation coefficients to generate second corrected pixel values for pixels of the same color in a second corrected version of the raw image. The pixels in the second subset are arranged in a second direction (e.g., horizontal direction) perpendicular to the first direction, and the second interpolation coefficients correspond to second offset values. The second offset values represent second distances from the second subset of pixels to corresponding second virtual pixels in the second direction. 
     In some embodiments, the image processor further includes a down sampling circuit coupled to the second correction circuit. The down sampling circuit receives the second corrected pixel values for pixels of the same color in the second corrected version. The down sampling circuit performs down sampling of a subset of the pixels of the same color of the second corrected version using second down sampling scale factors to generate corrected pixel values for pixels of the same color in a corrected version of the raw image. The pixels in the subset are arranged in the second direction, and the second down sampling scale factors gradually vary along the second direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Figure ( FIG. 1  is a high-level diagram of an electronic device, according to one embodiment. 
         FIG. 2  is a block diagram illustrating components in the electronic device, according to one embodiment. 
         FIG. 3  is a block diagram illustrating image processing pipelines implemented using an image signal processor, according to one embodiment. 
         FIG. 4A  is a conceptual diagram illustrating longitudinal/axial chromatic aberration, according to one embodiment. 
         FIG. 4B  is a conceptual diagram illustrating lateral/transverse chromatic aberration, according to one embodiment. 
         FIG. 5  is a conceptual diagram illustrating raw image data generated by an image sensor using a wide-angle lens, according to one embodiment. 
         FIG. 6  is a block diagram illustrating a detailed view of a foveated down sampling and correction circuit, according to one embodiment. 
         FIG. 7A  is a conceptual diagram illustrating a combined vertical foveated down sampling and interpolation of the raw image data, according to one embodiment. 
         FIG. 7B  is a conceptual diagram illustrating a horizontal interpolation of the raw image data, according to one embodiment, according to one embodiment. 
         FIG. 8  is a diagram illustrating pixel neighbors of a given pixel, according to one embodiment. 
         FIG. 9  is a flowchart illustrating a method of performing foveated down sampling and correction to reduce color fringing of the raw image data, according to one embodiment. 
     
    
    
     The figures depict, and the detail description describes, various non-limiting embodiments for purposes of illustration only. 
     DETAILED DESCRIPTION 
     Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the various described embodiments. However, the described embodiments may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments. 
     Embodiments of the present disclosure relate to a foveated down sampling and correction circuit in an image processor for correcting chromatic aberrations in captured images generated by one or more image sensors coupled to the image processor. The foveated down sampling and correction circuit includes a vertical foveated down sampling and correction circuit as well as a horizontal correction circuit coupled to an output of the vertical foveated down sampling and correction circuit. The vertical foveated down sampling and correction circuit performs the combined foveated down sampling and chromatic aberration recovery in the vertical direction of a raw image generated by the one or more image sensors. The vertical foveated down sampling and correction circuit generate first corrected pixel values for pixels of a same color in a first corrected version of the raw image. The horizontal correction circuit receives the first corrected pixel values from the vertical foveated down sampling and correction circuit, and performs chromatic aberration recovery in the horizontal direction of the first corrected version of the raw image. The horizontal correction circuit generates second corrected pixel values for pixels of the same color in a second corrected version of the raw image with chromatic aberrations reduced in comparison with the raw image. 
     Exemplary Electronic Device 
     Embodiments of electronic devices, user interfaces for such devices, and associated processes for using such devices are described. In some embodiments, the device is a portable communications device, such as a mobile telephone, that also contains other functions, such as personal digital assistant (PDA) and/or music player functions. Exemplary embodiments of portable multifunction devices include, without limitation, the iPhone®, iPod Touch®, Apple Watch®, and iPad® devices from Apple Inc. of Cupertino, Calif. Other portable electronic devices, such as wearables, laptops or tablet computers, are optionally used. In some embodiments, the device is not a portable communication device, but is a desktop computer or other computing device that is not designed for portable use. In some embodiments, the disclosed electronic device may include a touch-sensitive surface (e.g., a touch screen display and/or a touchpad). An example electronic device described below in conjunction with Figure ( FIG. 1  (e.g., device  100 ) may include a touch-sensitive surface for receiving user input. The electronic device may also include one or more other physical user-interface devices, such as a physical keyboard, a mouse and/or a joystick. 
     Figure ( FIG. 1  is a high-level diagram of an electronic device  100 , according to one embodiment. Device  100  may include one or more physical buttons, such as a “home” or menu button  104 . Menu button  104  is, for example, used to navigate to any application in a set of applications that are executed on device  100 . In some embodiments, menu button  104  includes a fingerprint sensor that identifies a fingerprint on menu button  104 . The fingerprint sensor may be used to determine whether a finger on menu button  104  has a fingerprint that matches a fingerprint stored for unlocking device  100 . Alternatively, in some embodiments, menu button  104  is implemented as a soft key in a graphical user interface (GUI) displayed on a touch screen. 
     In some embodiments, device  100  includes touch screen  150 , menu button  104 , push button  106  for powering the device on/off and locking the device, volume adjustment buttons  108 , Subscriber Identity Module (SIM) card slot  110 , head set jack  112 , and docking/charging external port  124 . Push button  106  may be used to turn the power on/off on the device by depressing the button and holding the button in the depressed state for a predefined time interval; to lock the device by depressing the button and releasing the button before the predefined time interval has elapsed; and/or to unlock the device or initiate an unlock process. In an alternative embodiment, device  100  also accepts verbal input for activation or deactivation of some functions through microphone  113 . Device  100  includes various components including, but not limited to, a memory (which may include one or more computer readable storage mediums), a memory controller, one or more central processing units (CPUs), a peripherals interface, an RF circuitry, an audio circuitry, speaker  111 , microphone  113 , input/output (I/O) subsystem, and other input or control devices. Device  100  may include one or more image sensors  164 , one or more proximity sensors  166 , and one or more accelerometers  168 . Device  100  may include more than one type of image sensors  164 . Each type may include more than one image sensor  164 . For example, one type of image sensors  164  may be cameras and another type of image sensors  164  may be infrared sensors that may be used for face recognition. Additionally or alternatively, image sensors  164  may be associated with different lens configuration. For example, device  100  may include rear image sensors, one with a wide-angle lens and another with as a telephoto lens. Device  100  may include components not shown in  FIG. 1  such as an ambient light sensor, a dot projector and a flood illuminator. 
     Device  100  is only one example of an electronic device, and device  100  may have more or fewer components than listed above, some of which may be combined into a component or have a different configuration or arrangement. The various components of device  100  listed above are embodied in hardware, software, firmware or a combination thereof, including one or more signal processing and/or application specific integrated circuits (ASICs). While the components in  FIG. 1  are shown as generally located on the same side as the touch screen  150 , one or more components may also be located on an opposite side of device  100 . For example, the front side of device  100  may include an infrared image sensor  164  for face recognition and another image sensor  164  as the front camera of device  100 . The back side of device  100  may also include additional two image sensors  164  as the rear cameras of device  100 . 
       FIG. 2  is a block diagram illustrating components in device  100 , according to one embodiment. Device  100  may perform various operations including image processing. For this and other purposes, the device  100  may include, among other components, image sensors  202 , system-on-a chip (SOC) component  204 , system memory  230 , persistent storage (e.g., flash memory)  228 , orientation sensor  234 , and display  216 . The components as illustrated in  FIG. 2  are merely illustrative. For example, device  100  may include other components (such as speaker or microphone) that are not illustrated in  FIG. 2 . Further, some components (such as orientation sensor  234 ) may be omitted from device  100 . 
     Image sensors  202  are components for capturing image data. Each of image sensors  202  may be embodied, for example, as a complementary metal-oxide-semiconductor (CMOS) active-pixel sensor, a camera, video camera, or other devices. Image sensors  202  generate raw image data that is sent to SOC component  204  for further processing. In some embodiments, the image data processed by SOC component  204  is displayed on display  216 , stored in system memory  230 , persistent storage  228  or sent to a remote computing device via network connection. The raw image data generated by image sensors  202  may be in a Bayer color filter array (CFA) pattern (hereinafter also referred to as “Bayer pattern”). Image sensor  202  may also include optical and mechanical components that assist image sensing components (e.g., pixels) to capture images. The optical and mechanical components may include an aperture, a lens system, and an actuator that controls the focal length of image sensor  202 . 
     Motion sensor  234  is a component or a set of components for sensing motion of device  100 . Motion sensor  234  may generate sensor signals indicative of orientation and/or acceleration of device  100 . The sensor signals are sent to SOC component  204  for various operations such as turning on device  100  or rotating images displayed on display  216 . 
     Display  216  is a component for displaying images as generated by SOC component  204 . Display  216  may include, for example, a liquid crystal display (LCD) device or an organic light emitting diode (OLED) device. Based on data received from SOC component  204 , display  116  may display various images, such as menus, selected operating parameters, images captured by image sensors  202  and processed by SOC component  204 , and/or other information received from a user interface of device  100  (not shown). 
     System memory  230  is a component for storing instructions for execution by SOC component  204  and for storing data processed by SOC component  204 . System memory  230  may be embodied as any type of memory including, for example, dynamic random access memory (DRAM), synchronous DRAM (SDRAM), double data rate (DDR, DDR2, DDR3, etc.) RAMBUS DRAM (RDRAM), static RAM (SRAM) or a combination thereof. In some embodiments, system memory  230  may store pixel data or other image data or statistics in various formats. 
     Persistent storage  228  is a component for storing data in a non-volatile manner. Persistent storage  228  retains data even when power is not available. Persistent storage  228  may be embodied as read-only memory (ROM), flash memory or other non-volatile random access memory devices. 
     SOC component  204  is embodied as one or more integrated circuit (IC) chip and performs various data processing processes. SOC component  204  may include, among other subcomponents, image signal processor (ISP)  206 , a central processor unit (CPU)  208 , a network interface  210 , motion sensor interface  212 , display controller  214 , graphics processor (GPU)  220 , memory controller  222 , video encoder  224 , storage controller  226 , and various other input/output (I/O) interfaces  218 , and bus  232  connecting these subcomponents. SOC component  204  may include more or fewer subcomponents than those shown in  FIG. 2 . 
     ISP  206  is hardware that performs various stages of an image processing pipeline. In some embodiments, ISP  206  may receive raw image data from image sensors  202 , and process the raw image data into a form that is usable by other subcomponents of SOC component  204  or components of device  100 . ISP  206  may perform various image-manipulation operations such as image translation operations, horizontal and vertical scaling, color space conversion and/or image stabilization transformations, as described below in detail with reference to  FIG. 3 . 
     CPU  208  may be embodied using any suitable instruction set architecture, and may be configured to execute instructions defined in that instruction set architecture. CPU  208  may be general-purpose or embedded processors using any of a variety of instruction set architectures (ISAs), such as the x86, PowerPC, SPARC, RISC, ARM or MIPS ISAs, or any other suitable ISA. Although a single CPU is illustrated in  FIG. 2 , SOC component  204  may include multiple CPUs. In multiprocessor systems, each of the CPUs may commonly, but not necessarily, implement the same ISA. 
     Graphics processing unit (GPU)  220  is graphics processing circuitry for performing operations on graphical data. For example, GPU  220  may render objects to be displayed into a frame buffer (e.g., one that includes pixel data for an entire frame). GPU  220  may include one or more graphics processors that may execute graphics software to perform a part or all of the graphics operation, or hardware acceleration of certain graphics operations. 
     I/O interfaces  218  are hardware, software, firmware or combinations thereof for interfacing with various input/output components in device  100 . I/O components may include devices such as keypads, buttons, audio devices, and sensors such as a global positioning system. I/O interfaces  218  process data for sending data to such I/O components or process data received from such I/O components. 
     Network interface  210  is a subcomponent that enables data to be exchanged between devices  100  and other devices via one or more networks (e.g., carrier or agent devices). For example, video or other image data may be received from other devices via network interface  210  and be stored in system memory  230  for subsequent processing (e.g., via a back-end interface to image signal processor  206 , such as discussed below in  FIG. 3 ) and display. The networks may include, but are not limited to, Local Area Networks (LANs) (e.g., an Ethernet or corporate network) and Wide Area Networks (WANs). The image data received via network interface  210  may undergo image processing processes by ISP  206 . 
     Motion sensor interface  212  is circuitry for interfacing with motion sensor  234 . Motion sensor interface  212  receives sensor information from motion sensor  234  and processes the sensor information to determine the orientation or movement of the device  100 . 
     Display controller  214  is circuitry for sending image data to be displayed on display  216 . Display controller  214  receives the image data from ISP  206 , CPU  208 , graphic processor or system memory  230  and processes the image data into a format suitable for display on display  216 . 
     Memory controller  222  is circuitry for communicating with system memory  230 . Memory controller  222  may read data from system memory  230  for processing by ISP  206 , CPU  208 , GPU  220  or other subcomponents of SOC component  204 . Memory controller  222  may also write data to system memory  230  received from various subcomponents of SOC component  204 . 
     Video encoder  224  is hardware, software, firmware or a combination thereof for encoding video data into a format suitable for storing in persistent storage  228  or for passing the data to network interface  210  for transmission over a network to another device. 
     In some embodiments, one or more subcomponents of SOC component  204  or some functionality of these subcomponents may be performed by software components executed on ISP  206 , CPU  208  or GPU  220 . Such software components may be stored in system memory  230 , persistent storage  228  or another device communicating with device  100  via network interface  210 . 
     Image data or video data may flow through various data paths within SOC component  204 . In one example, raw image data may be generated from image sensors  202  and processed by ISP  206 , and then sent to system memory  230  via bus  232  and memory controller  222 . After the image data is stored in system memory  230 , it may be accessed by video encoder  224  for encoding or by display  116  for displaying via bus  232 . 
     In another example, image data is received from sources other than image sensors  202 . For example, video data may be streamed, downloaded, or otherwise communicated to the SOC component  204  via wired or wireless network. The image data may be received via network interface  210  and written to system memory  230  via memory controller  222 . The image data may then be obtained by ISP  206  from system memory  230  and processed through one or more image processing pipeline stages, as described below in detail with reference to  FIG. 3 . The image data may then be returned to system memory  230  or be sent to video encoder  224 , display controller  214  (for display on display  216 ), or storage controller  226  for storage at persistent storage  228 . 
     Example Image Signal Processing Pipelines 
       FIG. 3  is a block diagram illustrating image processing pipelines implemented using ISP  206 , according to one embodiment. In the embodiment of  FIG. 3 , ISP  206  is coupled to an image sensor system  201  that includes one or more image sensors  202 A through  202 N (hereinafter collectively referred to as “image sensors  202 ” or also referred individually as “image sensor  202 ”) to receive raw image data. Image sensor system  201  may include one or more sub-systems that control image sensors  202  individually. In some cases, each image sensor  202  may operate independently while, in other cases, image sensors  202  may share some components. For example, in one embodiment, two or more image sensors  202  may share the same circuit board that controls the mechanical components of the image sensors (e.g., actuators that change the focal lengths of each image sensor). The image sensing components of image sensor  202  may include different types of image sensing components that may provide raw image data in different forms to ISP  206 . For example, in one embodiment, the image sensing components may include multiple focus pixels that are used for auto-focusing and multiple image pixels that are used for capturing images. In another embodiment, the image sensing pixels may be used for both auto-focusing and image capturing purposes. 
     ISP  206  implements an image processing pipeline which may include a set of stages that process image information from creation, capture or receipt to output. ISP  206  may include, among other components, sensor interface  302 , central control  320 , front-end pipeline stages  330 , back-end pipeline stages  340 , image statistics module  304 , vision module  322 , back-end interface  342 , output interface  316 , and auto-focus circuits  350 A through  350 N (hereinafter collectively referred to as “auto-focus circuits  350 ” or referred individually as “auto-focus circuits  350 ”). ISP  206  may include other components not illustrated in  FIG. 3  or may omit one or more components illustrated in  FIG. 3 . 
     In one or more embodiments, different components of ISP  206  process image data at different rates. In the embodiment of  FIG. 3 , front-end pipeline stages  330  (e.g., raw processing stage  306  and resample processing stage  308 ) may process image data at an initial rate. Thus, the various different techniques, adjustments, modifications, or other processing operations performed by these front-end pipeline stages  330  at the initial rate. For example, if front-end pipeline stages  330  process two pixels per clock cycle, then raw processing stage  306  operations (e.g., black level compensation, highlight recovery and defective pixel correction) may process two pixels of image data at a time. In contrast, one or more back-end pipeline stages  340  may process image data at a different rate less than the initial data rate. For example, in the embodiment of  FIG. 3 , back-end pipeline stages  340  (e.g., noise processing stage  310 , color processing stage  312 , and output rescale  314 ) may be processed at a reduced rate (e.g., one pixel per clock cycle). 
     Raw image data captured by image sensors  202  may be transmitted to different components of ISP  206  in different manners. In one embodiment, raw image data corresponding to the focus pixels may be sent to auto-focus circuits  350  while raw image data corresponding to the image pixels may be sent to sensor interface  302 . In another embodiment, raw image data corresponding to both types of pixels may simultaneously be sent to both auto-focus circuits  350  and sensor interface  302 . 
     Auto-focus circuits  350  may include hardware circuit that analyzes raw image data to determine an appropriate focal length of each image sensor  202 . In one embodiment, the raw image data may include data that is transmitted from image sensing pixels that specializes in image focusing. In another embodiment, raw image data from image capture pixels may also be used for auto-focusing purpose. Auto-focus circuit  350  may perform various image processing operations to generate data that determines the appropriate focal length. The image processing operations may include cropping, binning, image compensation, scaling to generate data that is used for auto-focusing purpose. The auto-focusing data generated by auto-focus circuits  350  may be fed back to image sensor system  201  to control the focal lengths of image sensors  202 . For example, image sensor  202  may include a control circuit that analyzes the auto-focusing data to determine a command signal that is sent to an actuator associated with the lens system of image sensor  202  to change the focal length of image sensor  202 . The data generated by auto-focus circuits  350  may also be sent to other components of ISP  206  for other image processing purposes. For example, some of the data may be sent to image statistics module  304  to determine information regarding auto-exposure. 
     Auto-focus circuits  350  may be individual circuits that are separate from other components such as image statistics module  304 , sensor interface  302 , front-end  330  and back-end  340 . This allows ISP  206  to perform auto-focusing analysis independent of other image processing pipelines. For example, ISP  206  may analyze raw image data from image sensor  202 A to adjust the focal length of image sensor  202 A using auto-focus circuit  350 A while performing downstream image processing of the image data from image sensor  202 B simultaneously. In one embodiment, the number of auto-focus circuits  350  may correspond to the number of image sensors  202 . In other words, each image sensor  202  may have a corresponding auto-focus circuit that is dedicated to the auto-focusing of image sensor  202 . Device  100  may perform auto focusing for different image sensors  202  even if one or more image sensors  202  are not in active use. This allows a seamless transition between two image sensors  202  when device  100  switches from one image sensor  202  to another. For example, in one embodiment, device  100  may include a wide-angle camera and a telephoto camera as a dual back camera system for photo and image processing. Device  100  may display images captured by one of the dual cameras and may switch between the two cameras from time to time. The displayed images may seamless transition from image data captured by one image sensor  202  to image data captured by another image sensor  202  without waiting for second image sensor  202  to adjust its focal length because two or more auto-focus circuits  350  may continuously provide auto-focus data to image sensor system  201 . 
     Raw image data captured by different image sensors  202  may also be transmitted to sensor interface  302 . Sensor interface  302  receives raw image data from image sensors  202  and processes the raw image data into an image data processable by other stages in the pipeline. Sensor interface  302  may perform various preprocessing operations, such as image cropping, binning or scaling to reduce image data size. In some embodiments, pixels are sent from image sensors  202  to sensor interface  302  in raster order (e.g., horizontally, line by line). The subsequent processes in the pipeline may also be performed in raster order and the result may also be output in raster order. Although only a single image sensor system  201  and a single sensor interface  302  are illustrated in  FIG. 3 , when more than one image sensor system is provided in device  100 , a corresponding number of sensor interfaces may be provided in ISP  206  to process raw image data from each image sensor system. 
     Front-end pipeline stages  330  process image data in raw or full-color domains. Front-end pipeline stages  330  may include, but are not limited to, raw processing stage  306  and resample processing stage  308 . A raw image data may be in a Bayer raw image format, for example. In the Bayer raw image format, pixel data with values specific to a particular color (instead of all colors) is provided in each pixel. In an image capturing sensor, image data is typically provided in the Bayer pattern. Raw processing stage  306  may process image data in the Bayer raw image format. 
     The operations performed by raw processing stage  306  include, but are not limited, sensor linearization, black level compensation, fixed pattern noise reduction, defective pixel correction, raw noise filtering, lens shading correction, white balance gain, highlight recovery, and chromatic aberration recovery (or correction). Sensor linearization refers to mapping non-linear image data to linear space for other processing. Black level compensation refers to providing digital gain, offset and clip independently for each color component (e.g., Gr, R, B, Gb) of the image data. Fixed pattern noise reduction refers to removing offset fixed pattern noise and gain fixed pattern noise by subtracting a dark frame from an input image and multiplying different gains to pixels. Defective pixel correction refers to detecting defective pixels, and then replacing defective pixel values. Raw noise filtering refers to reducing noise of image data by averaging neighbor pixels that are similar in brightness. Highlight recovery refers to estimating pixel values for those pixels that are clipped (or nearly clipped) from other channels. Lens shading correction refers to applying a gain per pixel to compensate for a dropoff in intensity roughly proportional to a distance from a lens optical center. White balance gain refers to providing digital gains for white balance, offset and clip independently for all color components (e.g., Gr, R, B, Gb in the Bayer pattern). 
     A foveated down sampling and correction (FDS-C) circuit  307  in raw processing stage  306  performs the chromatic aberration recovery by performing foveated down sampling and aberration correction. The chromatic aberration recovery performed by FDS-C circuit  307  refers to correcting chromatic aberrations in raw image data resulting from the use of wide-angle lenses in image sensors  202  to generate raw images. Details about a structure and operation of FDS-C circuit  307  are provided in relation to  FIG. 6 ,  FIGS. 7A-7B , and  FIG. 9 . Components of ISP  206  may convert raw image data into image data in full-color domain, and thus, raw processing stage  306  may process image data in the full-color domain in addition to or instead of raw image data. 
     Resample processing stage  308  performs various operations to convert, resample, or scale image data received from raw processing stage  306 . Operations performed by resample processing stage  308  may include, but not limited to, demosaic operation, per-pixel color correction operation, Gamma mapping operation, color space conversion and downscaling or sub-band splitting. Demosaic operation refers to converting or interpolating missing color samples from raw image data (for example, in the Bayer pattern) to output image data into a full-color domain. Demosaic operation may include low pass directional filtering on the interpolated samples to obtain full-color pixels. Per-pixel color correction operation refers to a process of performing color correction on a per-pixel basis using information about relative noise standard deviations of each color channel to correct color without amplifying noise in the image data. Gamma mapping refers to converting image data from input image data values to output data values to perform gamma correction. For the purpose of Gamma mapping, lookup tables (or other structures that index pixel values to another value) for different color components or channels of each pixel (e.g., a separate lookup table for R, G, and B color components) may be used. Color space conversion refers to converting color space of an input image data into a different format. In one embodiment, resample processing stage  308  converts RGG format into YCbCr format for further processing. In another embodiment, resample processing state  308  concerts RBD format into RGB format for further processing. 
     Central control module  320  may control and coordinate overall operation of other components in ISP  206 . Central control module  320  performs operations including, but not limited to, monitoring various operating parameters (e.g., logging clock cycles, memory latency, quality of service, and state information), updating or managing control parameters for other components of ISP  206 , and interfacing with sensor interface  302  to control the starting and stopping of other components of ISP  206 . For example, central control module  320  may update programmable parameters for other components in ISP  206  while the other components are in an idle state. After updating the programmable parameters, central control module  320  may place these components of ISP  206  into a run state to perform one or more operations or tasks. Central control module  320  may also instruct other components of ISP  206  to store image data (e.g., by writing to system memory  230  in  FIG. 2 ) before, during, or after resample processing stage  308 . In this way full-resolution image data in raw or full-color domain format may be stored in addition to or instead of processing the image data output from resample processing stage  308  through backend pipeline stages  340 . 
     Image statistics module  304  performs various operations to collect statistic information associated with the image data. The operations for collecting statistics information may include, but not limited to, sensor linearization, replace patterned defective pixels, sub-sample raw image data, detect and replace non-patterned defective pixels, black level compensation, lens shading correction, and inverse black level compensation. After performing one or more of such operations, statistics information such as 3A statistics (auto white balance (AWB), auto exposure (AE), histograms (e.g., 2D color or component) and any other image data information may be collected or tracked. In some embodiments, certain pixels&#39; values, or areas of pixel values may be excluded from collections of certain statistics data when preceding operations identify clipped pixels. Although only a single statistics module  304  is illustrated in  FIG. 3 , multiple image statistics modules may be included in ISP  206 . For example, each image sensor  202  may correspond to an individual image statistics module  304 . In such embodiments, each statistic module may be programmed by central control module  320  to collect different information for the same or different image data. 
     Vision module  322  performs various operations to facilitate computer vision operations at CPU  208  such as facial detection in image data. Vision module  322  may perform various operations including pre-processing, global tone-mapping and Gamma correction, vision noise filtering, resizing, keypoint detection, generation of histogram-of-orientation gradients (HOG) and normalized cross correlation (NCC). The pre-processing may include subsampling or binning operation and computation of luminance if the input image data is not in YCrCb format. Global mapping and Gamma correction can be performed on the pre-processed data on luminance image. Vision noise filtering is performed to remove pixel defects and reduce noise present in the image data, and thereby, improve the quality and performance of subsequent computer vision algorithms. Such vision noise filtering may include detecting and fixing dots or defective pixels, and performing bilateral filtering to reduce noise by averaging neighbor pixels of similar brightness. Various vision algorithms use images of different sizes and scales. Resizing of an image is performed, for example, by binning or linear interpolation operation. Keypoints are locations within an image that are surrounded by image patches well suited to matching in other images of the same scene or object. Such keypoints are useful in image alignment, computing camera pose and object tracking. Keypoint detection refers to the process of identifying such keypoints in an image. HOG provides descriptions of image patches for tasks in mage analysis and computer vision. HOG can be generated, for example, by (i) computing horizontal and vertical gradients using a simple difference filter, (ii) computing gradient orientations and magnitudes from the horizontal and vertical gradients, and (iii) binning the gradient orientations. NCC is the process of computing spatial cross-correlation between a patch of image and a kernel. 
     Back-end interface  342  receives image data from other image sources than image sensor  102  and forwards it to other components of ISP  206  for processing. For example, image data may be received over a network connection and be stored in system memory  230 . Back-end interface  342  retrieves the image data stored in system memory  230  and provides it to back-end pipeline stages  340  for processing. One of many operations that are performed by back-end interface  342  is converting the retrieved image data to a format that can be utilized by back-end processing stages  340 . For instance, back-end interface  342  may convert RGB, YCbCr 4:2:0, or YCbCr 4:2:2 formatted image data into YCbCr 4:4:4 color format. 
     Back-end pipeline stages  340  processes image data according to a particular full-color format (e.g., YCbCr 4:4:4 or RGB). In some embodiments, components of the back-end pipeline stages  340  may convert image data to a particular full-color format before further processing. Back-end pipeline stages  340  may include, among other stages, noise processing stage  310  and color processing stage  312 . Back-end pipeline stages  340  may include other stages not illustrated in  FIG. 3 . 
     Noise processing stage  310  performs various operations to reduce noise in the image data. The operations performed by noise processing stage  310  include, but are not limited to, color space conversion, gamma/de-gamma mapping, temporal filtering, noise filtering, luma sharpening, and chroma noise reduction. The color space conversion may convert an image data from one color space format to another color space format (e.g., RGB format converted to YCbCr format). Gamma/de-gamma operation converts image data from input image data values to output data values to perform gamma correction or reverse gamma correction. Temporal filtering filters noise using a previously filtered image frame to reduce noise. For example, pixel values of a prior image frame are combined with pixel values of a current image frame. Noise filtering may include, for example, spatial noise filtering. Luma sharpening may sharpen luma values of pixel data while chroma suppression may attenuate chroma to gray (e.g., no color). In some embodiment, the luma sharpening and chroma suppression may be performed simultaneously with spatial nose filtering. The aggressiveness of noise filtering may be determined differently for different regions of an image. Spatial noise filtering may be included as part of a temporal loop implementing temporal filtering. For example, a previous image frame may be processed by a temporal filter and a spatial noise filter before being stored as a reference frame for a next image frame to be processed. In other embodiments, spatial noise filtering may not be included as part of the temporal loop for temporal filtering (e.g., the spatial noise filter may be applied to an image frame after it is stored as a reference image frame and thus the reference frame is not spatially filtered. 
     Color processing stage  312  may perform various operations associated with adjusting color information in the image data. The operations performed in color processing stage  312  include, but are not limited to, local tone mapping, gain/offset/clip, color correction, three-dimensional color lookup, gamma conversion, and color space conversion. Local tone mapping refers to spatially varying local tone curves in order to provide more control when rendering an image. For instance, a two-dimensional grid of tone curves (which may be programmed by central control module  320 ) may be bilinearly interpolated such that smoothly varying tone curves are created across an image. In some embodiments, local tone mapping may also apply spatially varying and intensity varying color correction matrices, which may, for example, be used to make skies bluer while turning down blue in the shadows in an image. Digital gain/offset/clip may be provided for each color channel or component of image data. Color correction may apply a color correction transform matrix to image data. 3D color lookup may utilize a three-dimensional array of color component output values (e.g., R, G, B) to perform advanced tone mapping, color space conversions, and other color transforms. Gamma conversion may be performed, for example, by mapping input image data values to output data values in order to perform gamma correction, tone mapping, or histogram matching. Color space conversion may be implemented to convert image data from one color space to another (e.g., RGB to YCbCr). Other processing techniques may also be performed as part of color processing stage  312  to perform other special image effects, including black and white conversion, sepia tone conversion, negative conversion, or solarize conversion. 
     Output rescale module  314  may resample, transform and correct distortion on the fly as ISP  206  processes image data. Output rescale module  314  may compute a fractional input coordinate for each pixel and uses this fractional coordinate to interpolate an output pixel via a polyphase resampling filter. A fractional input coordinate may be produced from a variety of possible transforms of an output coordinate, such as resizing or cropping an image (e.g., via a simple horizontal and vertical scaling transform), rotating and shearing an image (e.g., via non-separable matrix transforms), perspective warping (e.g., via an additional depth transform) and per-pixel perspective divides applied in piecewise in strips to account for changes in image sensor during image data capture (e.g., due to a rolling shutter), and geometric distortion correction (e.g., via computing a radial distance from the optical center in order to index an interpolated radial gain table, and applying a radial perturbance to a coordinate to account for a radial lens distortion). 
     Output rescale module  314  may apply transforms to image data as it is processed at output rescale module  314 . Output rescale module  314  may include horizontal and vertical scaling components. The vertical portion of the design may implement series of image data line buffers to hold the “support” needed by the vertical filter. As ISP  206  may be a streaming device, it may be that only the lines of image data in a finite-length sliding window of lines are available for the filter to use. Once a line has been discarded to make room for a new incoming line, the line may be unavailable. Output rescale module  314  may statistically monitor computed input Y coordinates over previous lines and use it to compute an optimal set of lines to hold in the vertical support window. For each subsequent line, output rescale module may automatically generate a guess as to the center of the vertical support window. In some embodiments, the output rescale module  314  may implement a table of piecewise perspective transforms encoded as digital difference analyzer (DDA) steppers to perform a per-pixel perspective transformation between an input image data and output image data in order to correct artifacts and motion caused by sensor motion during the capture of the image frame. Output rescale may provide image data via output interface  316  to various other components of device  100 , as discussed above with regard to  FIGS. 1 and 2 . 
     In various embodiments, the functionally of components  302  through  350  may be performed in a different order than the order implied by the order of these functional units in the image processing pipeline illustrated in  FIG. 3 , or may be performed by different functional components than those illustrated in  FIG. 3 . Moreover, the various components as described in  FIG. 3  may be embodied in various combinations of hardware, firmware or software. 
     Chromatic Aberration Recovery 
     In general, chromatic aberration is caused by the inability of a lens to focus different wavelengths of light (e.g., different colors of light) to the same focal point.  FIG. 4A  illustrates an example of longitudinal (e.g., axial) chromatic aberration. As shown in  FIG. 4A , a wide-angle lens  402  refracts light  404  such that different wavelengths of light (e.g., red light, green light, and blue light) are focused at different distances from wide-angle lens  402  (e.g., at different distances from a focal plane  406 ) along an optical axis  408 .  FIG. 4B  illustrates lateral (e.g., transverse) chromatic aberration, according to one embodiment. As shown in  FIG. 4B , a wide-angle lens  410  refracts light  412  such that different wavelengths of light (e.g., red light, green light, and blue light) are focused at different positions on a focal plane  414  (e.g., at different distances from an optical axis  416 ). Chromatic aberration due to the usage of wide-angle lenses  402 ,  410  as described with respect to  FIGS. 4A and 4B  manifests itself as color fringing at edges in full color images. 
       FIG. 5  illustrates raw image data generated using light  404  captured by image sensor  202  using wide-angle lens  402 , according to one embodiment. As shown in  FIG. 5 , the raw image data is in a Bayer pattern  502 . Bayer pattern  502  includes alternating rows of red-green pixels and green-blue pixels. Generally, Bayer pattern  502  includes more green pixels than red or blue pixels due to the human eye being more sensitive to green light than both red light and blue light. 
     Example Foveated Down Sampling and Correction Circuit 
       FIG. 6  is a block diagram illustrating a detailed view of a foveated down sampling and correction (FDS-C) circuit  307 , according to one embodiment. FDS-C circuit  307  corrects chromatic aberrations in raw image  602  generated by one or more image sensors  202 . Specifically, FDS-C circuit  307  performs combined foveated down sampling and chromatic aberration recovery in a first direction (e.g., vertical direction) of raw image  602  to generate first corrected pixel values  632  of a first corrected version of raw image. FDS-C circuit  307  further performs chromatic aberration recovery in a second direction (e.g., horizontal direction) of the first corrected version of raw image to generate second corrected pixel values  636  of a second corrected version of raw image with reduced chromatic aberrations. In one or more embodiments, raw image  602  is in the Bayer pattern and is generated by at least one image sensor  202  using at least one wide-angle lens as described with respect to  FIG. 5 . A full-color image directly generated from raw image  602  would include chromatic aberrations due to utilizing the at least one wide-angle lens to generate raw image  602 . By using second corrected pixel values  636  of the second corrected version to generate a full-color image rather than raw image  602 , chromatic aberrations in the full-color image are reduced. 
     In one embodiment, FDS-C circuit  307  includes a pixel locator circuit  603 , down sampling scaling factor look-up table (LUT)  604 , a foveated down sampling locator circuit  608 , an offset LUT  612 , an offset interpolator circuit  616 , a vertical phase LUT  622 , a horizontal phase LUT  624 , a vertical foveated down sampling and correction circuit  630 , and a horizontal correction circuit  634 . Additionally, FDS-C circuit  307  is coupled to a horizontal foveated down sampling and scaler circuit  648 . In other embodiments, FDS-C circuit  307  may have additional or fewer circuits and LUTs than those shown in  FIG. 6 . For example, horizontal foveated down sampling and scaler circuit  648  may be part of FDS-C circuit  307 . 
     Down sampling scaling factor LUT  604  stores down sampling scale factors indexed by locations in a first direction (e.g., vertical direction) of an image (e.g., raw image  602 ). Down sampling scaling factor LUT  604  receives indexing information  605  related to a location of a corresponding pixel along the first direction in raw image  602 . Indexing information  605  for the corresponding pixel along the first direction in raw image  602  is extracted by pixel locator circuit  603 . Upon receiving indexing information  605 , down sampling scaling factor LUT  604  outputs a corresponding down sampling scaling factor  606  that is passed onto foveated down sampling pixel locator circuit  608 . 
     Foveated down sampling locator circuit  608  receives down sampling scaling factor  606  from down sampling scaling factor LUT  604 , and calculates a down sampling pixel location  610  (e.g., a down sampling landing) along the first direction of raw image  602 . Information about down sampling pixel location  610  calculated by foveated down sampling locator circuit  608  is provided to offset LUT  612 . 
     Offset LUT  612  stores a grid of pre-calculated horizontal and vertical offset values. A horizontal offset value and a vertical offset value for a certain pixel represent, respectively, a horizontal distance and a vertical distance to a virtual pixel with a pixel value that corresponds to a pixel value of the certain pixel had there not been any chromatic aberrations. The grid includes multiple grid points having multiple pixel offset values. The pre-calculated offset values in the grid may be associated with optical configurations of a corresponding image sensor  202  (e.g., use of a specific wide-angle lens). Thus, offset LUT  612  may store different sets of offset values that are each associated with different image sensors  202 . In one or more embodiments, the grid is coarser than the arrangement of pixels of Bayer pattern  502 . A particular pixel location may be associated with one or more grid points and includes four pixel offset values: a horizontal pixel offset value for the red pixels, a vertical pixel offset value for the red pixels, a horizontal offset value for the blue pixels, and a vertical offset value for the blue pixels. Horizontal offset values for the green pixels and vertical offset values for the green pixels may be set to zeroes. 
     Upon receiving information about down sampling pixel locations  610  in the first direction of raw image  602 , offset LUT  612  may provide corresponding vertical offset values  614  to offset interpolator circuit  616 . Furthermore, offset LUT  612  may provide corresponding horizontal offset values  614  to offset interpolator circuit  616  based on information about locations of a subset of pixels of raw image  602  arranged in a second direction (e.g., horizontal direction) perpendicular to the first direction. 
     Offset interpolator circuit  616  is coupled to offset LUT  612  and receives pre-calculated horizontal and vertical offset values  614  from offset LUT  612 . In one embodiment, offset interpolator circuit  616  calculates horizontal and vertical offset values for subsets of pixels (e.g., blue and red pixels) included in raw image  602 . Specifically, offset interpolator circuit  616  calculates first offset values  618  (e.g., vertical offset values) of a blue or red pixel by performing interpolation on pre-calculated vertical offset values  614 . Furthermore, offset interpolator circuit  616  calculates second offset values  620  (e.g., horizontal offset values) of a blue or red pixel by performing interpolation on pre-calculated vertical offset values of grid points surrounding the blue or red pixel as described below with reference to  FIG. 8 . That is, for each red or blue pixel in raw image  602 , offset interpolator circuit  616  calculates a horizontal pixel offset for the red color channel of the pixel, a vertical pixel offset value for the red color channel of the pixel, a horizontal pixel offset for the blue color channel of the pixel, and a vertical pixel offset value for the blue color channel of the pixel. In one or more embodiments, offset interpolator circuit  616  does not calculate vertical and horizontal pixel offsets for the green color channel of the pixel (e.g., vertical and horizontal pixel offsets for the green color channel are zero). However, in one or more other embodiments, offset interpolator circuit  616  may also calculate a horizontal pixel offset for the green color channel of the pixel and a vertical pixel offset value for the green color channel of the pixel. Generally, when the horizontal and vertical pixel offsets for two color channels are calculated, the horizontal and vertical pixel offsets for the remaining color channel (RGB) are not calculated. 
       FIG. 7A  illustrates vertical foveated down sampling and interpolation based on vertical offset pixel correction for a red color channel of a subset of pixels included in raw image  602 , according to one embodiment. Due to chromatic aberration in the vertical direction, the pixel value of red pixel P 2  captured by image sensor  202  (as part of Bayer pattern  502 ) is inaccurate. A corrected pixel value (e.g., first corrected pixel value  632 ) at a down sampling pixel location  702  is obtained using a pixel value of a virtual pixel  706  at location obtained by offsetting down sampling pixel location  702  (if there is no horizontal shifting of a focal point due to chromatic aberrations) vertically by a distance  704  (e.g., a negative vertical pixel offset). Thus, the corrected pixel value is generated at down sampling pixel location  702  and output from vertical foveated down sampling and correction circuit  630  as first corrected pixel value  632 . Similarly, for a positive vertical pixel offset, a corrected pixel value (e.g., first corrected pixel value  632 ) at a down sampling pixel location  712  is obtained using a pixel value of a virtual pixel  716  at location obtained by offsetting down sampling pixel location  712  vertically by a distance  714  (e.g., the positive vertical pixel offset). Thus, the corrected pixel value is generated at down sampling pixel location  712  and output from vertical foveated down sampling and correction circuit  630  as first corrected pixel value  632 . 
     As will be further described below, first offset value  704  (or first offset value  714 ) is used as a parameter to obtain a phase value for a bilinear or bicubic interpolation (e.g., equal to a distance from location of virtual pixel  706  to red pixel P 2 , and similarly equal to a distance from location of virtual pixel  716  to red pixel P 2 ). The phase value is used to obtain interpolation coefficients for the bilinear or bicubic interpolation of pixel values of neighboring red pixels P 0 , P 1 , P 2 , and P 3  in the vertical direction to compute the pixel value of virtual pixel  706  (or virtual pixel  716 ). The computed pixel value of virtual pixel  706  (or the computed pixel value of virtual pixel  716 ) then becomes first corrected pixel value  632  output from vertical foveated down sampling and correction circuit  630  at down sampling pixel location  702  (or at down sampling pixel location  712 ). Such corrections of pixel values and pixel locations are performed for all red pixels to account for the vertical chromatic aberration and/or the vertical foveated down sampling. The blue color channel of pixels also have their vertical offset corrected in a similar manner as the red color channel of pixels shown in  FIG. 7A . 
       FIG. 7B  illustrates horizontal interpolation based on horizontal offset pixel correction for a red color channel of a subset of pixels, according to one embodiment. The red pixels in  FIG. 7B  have pixel values corrected using vertical offsets as explained above with reference to  FIG. 7A . The pixel value of red pixel P 6  corrected for the vertical chromatic aberration does not take into account the horizontal chromatic aberration. In order to account for the horizontal chromatic aberration, the pixel value of pixel P 6  is replaced with a pixel value of a virtual pixel  726  (or a virtual pixel  736 ) that is horizontally offset from a location  722  of pixel P 6  by a distance  724  (or a second offset value) for a negative horizontal pixel offset or by a distance  734  (or a second offset value) for a positive horizontal pixel offset. As will be further described below, second offset value  724  (or second offset value  734 ) is used as a parameter to interpolate pixel values of neighboring pixels P 4 , P 5 , P 6 , and P 7  in the horizontal direction. Such replacement is performed across all red pixels to correct the horizontal chromatic aberration. The blue color channel of pixels also have their horizontal offset corrected in a similar manner as the red color channel of pixels shown in  FIG. 7B . 
       FIG. 8  illustrates grid points GP 0  through GP 3  that surrounds a given pixel  802 , according to one embodiment. As described above, each of grid points GP 0  through GP 3  has an associated vertical and horizontal offset values for red and blue pixels stored in offset LUT  612 . If pixel  802  is a red pixel, offset interpolator circuit  616  performs a bilinear interpolation or bicubic interpolation on four vertical offset values of the four grid points GP 0  through GP 3  for red pixels and generates an interpolated vertical offset value  618  for the red pixel. Offset interpolator circuit  616  also performs a bilinear interpolation or bicubic interpolation on four horizontal offset values of the four grid points GP 0  through GP 3  for red pixels and generates an interpolated horizontal offset value  620  for the red pixel. If pixel  802  is a blue pixel, offset interpolator circuit  616  performs a bilinear interpolation or bicubic interpolation on four vertical offset values of the four grid points GP 0  through GP 3  for blue pixels and generates an interpolated vertical offset value (or first offset value)  618  for blue red pixel, and performs a bilinear interpolation or bicubic interpolation on four horizontal offset values of the four grid points GP 0  through GP 3  for blue pixels and generates an interpolated horizontal offset value (or second offset value)  620  for the blue pixel. 
     Referring back to  FIG. 6 , offset interpolator circuit  616  provides, based on down sampling pixel locations  610  and pre-calculated vertical offset values  614 , first offset values  618  (e.g., vertical pixel offset values) for the red and blue color channels of each pixel in raw image  602  to vertical phase LUT  622 . Offset interpolator circuit  616  further provides, based on pre-calculated horizontal offset values  614 , second offset values  620  (e.g., horizontal pixel offset values) for the red and blue color channels to horizontal phase LUT  624 . In one embodiment, vertical phase LUT  622  stores a table of interpolation coefficients (e.g., bicubic or bilinear interpolation coefficients) for multiple phases in the first (e.g., vertical) direction where each phase has a set of coefficients (e.g., interpolation coefficients C 0 , C 1 , C 2 , and C 3 ). Similarly, horizontal phase LUT  624  stores a table of interpolation coefficients (e.g., bicubic or bilinear interpolation coefficients) for multiple phases in the second (e.g., horizontal) direction where each phase has a set of coefficients (e.g., interpolation coefficients C 4 , C 5 , C 6 , and C 7 ). Each table of interpolation coefficients is pre-computed and is associated with the same wide-angle lens that is associated with offset LUT  612 . 
     Vertical phase LUT  622  uses first offset values  618  (e.g., vertical pixel offsets) calculated for the red and blue color channels for each pixel to define the phase of bilinear or bicubic interpolation in the first (e.g., vertical) direction. Similarly, horizontal phase LUT  624  uses second offset values  620  (e.g., horizontal pixel offsets) calculated for the red and blue color channels for each pixel to define the phase of bilinear or bicubic interpolation in the second (e.g., horizontal) direction. The phase in each of the first (e.g., vertical) and second (e.g., horizontal) directions functions as an index to its respective set of coefficients in the respective vertical and horizontal phase LUT  622 ,  624 . 
     Vertical phase LUT  622  identifies first interpolation coefficients  626  that are associated with first offset values  618  for a specific color channel and provides first interpolation coefficients  626  to vertical foveated down sampling and correction circuit  630 . Similarly, horizontal phase LUT  624  identifies second interpolation coefficients  628  that are associated with second offset values  620  for the specific color channel and provides second interpolation coefficients  628  to horizontal correction circuit  634 . 
     Vertical foveated down sampling and correction circuit  630  performs combined foveated down sampling and chromatic aberration recovery in the first (e.g., vertical) direction of raw image  602 . Vertical foveated down sampling and correction circuit  630  calculates corrected pixel values  632  with chromatic aberrations corrected in the first direction relative to raw image  602 . In one embodiment, vertical foveated down sampling and correction circuit  630  calculates vertically down sampled and corrected versions of the pixel values (P v ) of a specific color using interpolation, i.e., 
         P   v   =C   0   P   0   +C   1   P   1   +C   2   P   2   +C   3   P   3 ,  (1)
 
     where P 0  through P 3  represent pixel values of four pixels in a same column of raw image  602  and closest to a virtual pixel corresponding to the pixel whose value is being corrected to account for vertical chromatic aberration and/or vertical foveated down sampling, and C 0  through C 3  are first interpolation coefficients  626 . 
     To calculate vertically corrected pixel value  632  for a pixel of a specific color, vertical foveated down sampling and correction circuit  630  obtains first interpolation coefficients  626  from vertical phase LUT  622  that retrieves first interpolation coefficients  626  (e.g., the set of interpolation coefficients C 0 , C 1 , C 2 , and C 3 ) corresponding to first offset value  618  from vertical phase LUT  622 . First offset value  618  represents a first distance (e.g., distance  704 ) from each down sampling pixel location  610  (or down sampling pixel location  702 ) to a corresponding virtual pixel (e.g., virtual pixel  706 ) in the first direction. Using first offset values  618  and first interpolation coefficients  626 , vertical foveated down sampling and correction circuit  630  calculates corrected pixel value  632  of the specific color channel for the pixel closest to the virtual pixel using equation (1). Corrected pixel value  632  replaces the original pixel value for the specific color channel at down sampling pixel location  610  in the first direction. 
     Horizontal correction circuit  634  calculates pixel values  636  of a specific color channel with chromatic aberration corrected in the second (e.g., horizontal) direction relative to raw image  602 . In one embodiment, horizontal correction circuit  634  calculates horizontally correction versions of pixel values  636  (P h ) using interpolation, i.e., 
         P   h   =C   4   P   4   +C   5   P   5   C   6   P   6   +C   7   P   7 ,  (2)
 
     where P 4  through P 7  represent pixel values of four pixels in a same row and closest to a virtual pixel corresponding to the pixel whose value is being corrected to account for horizontal chromatic aberration, and C 4  through C 7  are second interpolation coefficients  628 . 
     To calculate horizontally corrected pixel value  636  for a pixel of a specific color, horizontal correction circuit  634  obtains second interpolation coefficients  628  from horizontal phase LUT  624  that retrieves second interpolation coefficients  628  (e.g., the set of coefficients C 4 , C 5 , C 6 , and C 7 ) corresponding to second offset value  620  from horizontal phase LUT  624 . Second offset value  620  represents a second distance (e.g., distance  724 ) from a pixel location (e.g., location of pixel P 6 ) to a corresponding virtual pixel (e.g., virtual pixel  726 ) in the second direction. Using second offset values  620  and second interpolation coefficients  628 , horizontal correction circuit  634  calculates corrected pixel value  636  of the specific color channel for the pixel closest to the virtual pixel using equation (2). Corrected pixel value  636  replaces corresponding vertically corrected pixel value  632  at a same pixel location of vertically corrected pixel value  632  as no down sampling is performed by horizontal correction circuit  634 . 
     Corrected pixel values  636  for pixels from raw image  602  represent a second corrected raw image  636  vertically down sampled with mitigated chromatic aberrations in vertical and horizontal directions. Second corrected raw image  636  can be used by image signal processor  206  to generate a full-color image with reduced chromatic aberrations. 
     Horizontal foveated down sampling and scaler circuit  648  is coupled to an output of FDS-C circuit  307 . Horizontal foveated down sampling and scaler circuit  648  receives pixel values of second corrected raw image  636  and performs horizontal foveated down sampling and scaling to the pixel values of second corrected raw image  636 . 
     Down sampling scaling factor LUT  640  stores second down sampling scale factors indexed by locations in the second direction (e.g., horizontal direction) of an image (e.g., corrected raw image  636 ). Down sampling scaling factor LUT  640  receives indexing information  638  related to a location of a corresponding pixel along the second direction in second corrected raw image  636 . Indexing information  638  for the corresponding pixel along the second direction in second corrected raw image  636  is extracted by pixel locator circuit  637 . Upon receiving indexing information  638 , down sampling scaling factor LUT  640  outputs a corresponding second down sampling scaling factor  642  that is passed onto foveated down sampling locator circuit  644 . 
     Foveated down sampling locator circuit  644  receives down sampling scaling factor  642  from down sampling scaling factor LUT  640 , and calculates a down sampling pixel location  646  (e.g., down sampling landing) along the second direction of second corrected raw image  636 . Information about down sampling pixel location  646  calculated by foveated down sampling locator circuit  644  is provided to horizontal foveated down sampling and scaler circuit  648 . 
     Horizontal foveated down sampling and scaler circuit  648  performs down sampling of a subset of pixels of a same color of second corrected raw image  636  arranged in the second direction using second down sampling scale factors  642  gradually varying along the second direction to generate corrected pixel values for pixels of the same color in corrected raw image  650 . The corrected pixel values of corrected raw image  650  replace pixel values  636  of the specific color channel at down sampling pixel locations  646 . 
     Example Process of Foveated Down Sampling and Correction Circuit 
       FIG. 9  is a flowchart illustrating a method of performing foveated down sampling and correction by an image processor (e.g., image signal processor  206 ) to reduce color fringing of raw image data, according to one embodiment. The image processor performs  902  (e.g., by vertical foveated down sampling and correction circuit  630 ) combined vertical foveated down sampling and interpolation of pixel values of a first subset of pixels of a same color in a raw image (e.g., pixels of raw image  602 ) using down sampling scale factors (e.g., first down sampling scale factors  606 ) and first interpolation coefficients (e.g., first interpolation coefficients  626 ) to generate first corrected pixel values (e.g., corrected pixel values  632 ) for pixels of the same color in a first corrected version of the raw image. The pixels in the first subset are arranged in a first direction (e.g., vertical direction), the down sampling scale factors gradually vary along the first direction, and the first interpolation coefficients correspond to first offset values (e.g., first offset values  618 ). 
     The first offset values represent first distances (e.g., distances  704 ,  714 ) from each down sampling pixel location (e.g., each down sampling pixel location  610 ,  702 ,  712 ) along the first direction to corresponding first virtual pixels (e.g., virtual pixels  706 ,  716 ) in the first direction. The image processor generates (e.g., by vertical foveated down sampling and correction circuit  630 ) one of the first corrected pixel values for a pixel in the first corrected version by down sampling and interpolating a number of pixels in the same column of the raw image using a corresponding one of the down sampling scale factors and a corresponding subset of the first interpolation coefficients. 
     The image processor receives  904  (e.g., by horizontal correction circuit  634 ) the first corrected pixel values (e.g., corrected pixel values  632 ) of the first corrected version. The image processor performs  906  (e.g., by horizontal correction circuit  634 ) interpolation of pixel values of a second subset of the pixels in the first corrected version using second interpolation coefficients (e.g., second interpolation coefficients  628 ) to generate second corrected pixel values (e.g., corrected pixel values  636 ) for pixels of the same color in a second corrected version of the raw image. The pixels in the second subset are arranged in a second direction (e.g., horizontal direction) perpendicular to the first direction, and the second interpolation coefficients correspond to second offset values (e.g., second offset values  620 ). 
     The second offset values represent second distances (e.g., distances  724 ,  734 ) from the second subset of pixels to corresponding second virtual pixels (e.g., virtual pixels  726 ,  736 ) in the second direction. The image processor generates (e.g., by horizontal correction circuit  634 ) one of the second corrected pixel values for a pixel in the second corrected version by interpolating a number of pixels in the same row of the first corrected version using a corresponding subset of the second interpolation coefficients. 
     The first subset of pixels are in a same column of the raw image having the Bayer pattern, and the second subset of pixels are in a same row of the first corrected version of the raw image having the Bayer pattern. A value of each down sampling scale factor depends on locations of a number of pixels in the same column of the raw image along the first direction, the number of pixels used for down sampling and interpolation to generate a corresponding corrected pixel value for a pixel in the first corrected version. In some embodiments, the down sampling scale factors are gradually varying along the first direction based on piecewise fixed scaling (e.g., the down sampling scale factors can be divided into up to five different regions), curvature continuous scaling, linear continuous scaling, some other scaling, or combination thereof. In one or more embodiments, one or more portions of the down sampling scale factors are gradually scaled down at each defined down sampling pixel location in the first direction, and one or more other portions of the down sampling scale factors are gradually scaled up at each defined down sampling pixel location in the first direction. 
     The image processor may further perform (e.g., by horizontal foveated down sampling and scaler circuit  648 ) horizontal foveated down sampling and scaling of the second corrected pixel values (e.g., corrected pixel values  636 ) for pixels of the same color in the second corrected version. The image processor may perform down sampling of a subset of the pixels of the same color of the second corrected version using second down sampling scale factors (e.g., second down sampling scaling factors  642 ) to generate corrected pixel values for pixels of the same color in a corrected version of the raw image (e.g., corrected raw image  650 ). The pixels in the subset are arranged in the second (e.g., horizontal) direction, and the second down sampling scale factors gradually vary along the second direction. 
     Embodiments of the process as described above with reference to  FIG. 9  are merely illustrative. Moreover, sequence of the process may be modified or omitted. 
     While particular embodiments and applications have been illustrated and described, it is to be understood that the invention is not limited to the precise construction and components disclosed herein and that various modifications, changes and variations which will be apparent to those skilled in the art may be made in the arrangement, operation and details of the method and apparatus disclosed herein without departing from the spirit and scope of the present disclosure.