Image Operations

Image Operations Overview

Vulkan Image Operations are operations performed by those SPIR-V Image Instructions which take an OpTypeImage (representing a VkImageView) or OpTypeSampledImage (representing a (VkImageView, VkSampler) pair). Read, write, and atomic operations also take texel coordinates as operands, and return a value based on a neighborhood of texture elements (texels) within the image. Query operations return properties of the bound image or of the lookup itself. The Depth operand of OpTypeImage is ignored.

Image Operations include the functionality of the following SPIR-V Image Instructions:

• OpImageSample* and OpImageSparseSample* read one or more neighboring texels of the image, and filter the texel values based on the state of the sampler.
  • Instructions with ImplicitLod in the name determine the LOD used in the sampling operation based on the coordinates used in neighboring fragments.
  • Instructions with ExplicitLod in the name determine the LOD used in the sampling operation based on additional coordinates.
  • Instructions with Proj in the name apply homogeneous projection to the coordinates.
• OpImageFetch and OpImageSparseFetch return a single texel of the image. No sampler is used.
• OpImage*Gather and OpImageSparse*Gather read neighboring texels and return a single component of each.
• OpImageRead (and OpImageSparseRead) and OpImageWrite read and write, respectively, a texel in the image. No sampler is used.
• OpImageSampleFootprintNV identifies and returns information about the set of texels in the image that would be accessed by an equivalent OpImageSample* instruction.
• OpImage*Dref* instructions apply depth comparison on the texel values.
• OpImageSparse* instructions additionally return a sparse residency code.
• OpImageQuerySize, OpImageQuerySizeLod, OpImageQueryLevels, and OpImageQuerySamples return properties of the image descriptor that would be accessed. The image itself is not accessed.
• OpImageQueryLod returns the LOD parameters that would be used in a sample operation. The actual operation is not performed.
• OpImageWeightedSampleQCOM reads a 2D neighborhood of texels and computes a weighted average using weight values from a separate weight texture.
• opImageBlockMatchSADQCOM and opTextureBlockMatchSSD compare 2D neighborhoods of texels from two textures.
• OpImageBoxFilterQCOM reads a 2D neighborhood of texels and computes a weighted average of the texels.
• opImageBlockMatchWindowSADQCOM and opImageBlockMatchWindowSSDQCOM compare 2D neighborhoods of texels from two textures with the comparison repeated across a window region in the target texture.
• opImageBlockMatchGatherSADQCOM and opImageBlockMatchWindowSSDQCOM compares four 2D neighborhoods of texels from a target texture with a single 2D neighborhood in the reference texture. The R component of each comparison is gathered and returned in the output.

Texel Coordinate Systems

Images are addressed by texel coordinates. There are three texel coordinate systems:

• normalized texel coordinates [0.0, 1.0]
• unnormalized texel coordinates [0.0, width / height / depth)
• integer texel coordinates [0, width / height / depth)

SPIR-V OpImageFetch, OpImageSparseFetch, OpImageRead, OpImageSparseRead, opImageBlockMatchSADQCOM, opImageBlockMatchSSDQCOM, opImageBlockMatchWindowSADQCOM, opImageBlockMatchWindowSSDQCOM, and OpImageWrite instructions use integer texel coordinates.

Other image instructions can use either normalized or unnormalized texel coordinates (selected by the unnormalizedCoordinates state of the sampler used in the instruction), but there are limitations on what operations, image state, and sampler state is supported. Normalized coordinates are logically converted to unnormalized as part of image operations, and certain steps are only performed on normalized coordinates. The array layer coordinate is always treated as unnormalized even when other coordinates are normalized.

Normalized texel coordinates are referred to as (s,t,r,q,a), with the coordinates having the following meanings:

• s: Coordinate in the first dimension of an image.
• t: Coordinate in the second dimension of an image.
• r: Coordinate in the third dimension of an image.
  • (s,t,r) are interpreted as a direction vector for Cube images.
• q: Fourth coordinate, for homogeneous (projective) coordinates.
• a: Coordinate for array layer.

The coordinates are extracted from the SPIR-V operand based on the dimensionality of the image variable and type of instruction. For Proj instructions, the components are in order (s, [t,] [r,] q), with t and r being conditionally present based on the Dim of the image. For non-Proj instructions, the coordinates are (s [,t] [,r] [,a]), with t and r being conditionally present based on the Dim of the image and a being conditionally present based on the Arrayed property of the image. Projective image instructions are not supported on Arrayed images.

Unnormalized texel coordinates are referred to as (u,v,w,a), with the coordinates having the following meanings:

• u: Coordinate in the first dimension of an image.
• v: Coordinate in the second dimension of an image.
• w: Coordinate in the third dimension of an image.
• a: Coordinate for array layer.

Only the u and v coordinates are directly extracted from the SPIR-V operand, because only 1D and 2D (non-Arrayed) dimensionalities support unnormalized coordinates. The components are in order (u [,v]), with v being conditionally present when the dimensionality is 2D. When normalized coordinates are converted to unnormalized coordinates, all four coordinates are used.

Integer texel coordinates are referred to as (i,j,k,l,n), with the coordinates having the following meanings:

• i: Coordinate in the first dimension of an image.
• j: Coordinate in the second dimension of an image.
• k: Coordinate in the third dimension of an image.
• l: Coordinate for array layer.
• n: Index of the sample within the texel.

They are extracted from the SPIR-V operand in order (i [,j] [,k] [,l] [,n]), with j and k conditionally present based on the Dim of the image, and l conditionally present based on the Arrayed property of the image. n is conditionally present and is taken from the Sample image operand.

If an accessed image was created from a view using VkImageViewSlicedCreateInfoEXT and accessed through a VK_DESCRIPTOR_TYPE_STORAGE_IMAGE descriptor, then the value of k is incremented by VkImageViewSlicedCreateInfoEXT::sliceOffset, giving k ← sliceOffset + k. The image’s accessible range in the third dimension is k < sliceOffset + sliceCount. If VkImageViewSlicedCreateInfoEXT::sliceCount is VK_REMAINING_3D_SLICES_EXT, the range is inherited from the image’s depth extent as specified by Image Mip Level Sizing.

For all coordinate types, unused coordinates are assigned a value of zero.

The Texel Coordinate Systems - For the example shown of an 8×4 texel two dimensional image.

• Normalized texel coordinates:
  • The s coordinate goes from 0.0 to 1.0.
  • The t coordinate goes from 0.0 to 1.0.
• Unnormalized texel coordinates:
  • The u coordinate within the range 0.0 to 8.0 is within the image, otherwise it is outside the image.
  • The v coordinate within the range 0.0 to 4.0 is within the image, otherwise it is outside the image.
• Integer texel coordinates:
  • The i coordinate within the range 0 to 7 addresses texels within the image, otherwise it is outside the image.
  • The j coordinate within the range 0 to 3 addresses texels within the image, otherwise it is outside the image.
• Also shown for linear filtering:
  • Given the unnormalized coordinates (u,v), the four texels selected are i₀j₀, i₁j₀, i₀j₁, and i₁j₁.
  • The fractions α and β.
  • Given the offset Δ_i and Δ_j, the four texels selected by the offset are i₀j'₀, i₁j'₀, i₀j'₁, and i₁j'₁.

The Texel Coordinate Systems - For the example shown of an 8×4 texel two dimensional image.

• Texel coordinates as above. Also shown for nearest filtering:
  • Given the unnormalized coordinates (u,v), the texel selected is ij.
  • Given the offset Δ_i and Δ_j, the texel selected by the offset is ij'.

For corner-sampled images, the texel samples are located at the grid intersections instead of the texel centers.

Conversion Formulas

RGB to Shared Exponent Conversion

An RGB color (red, green, blue) is transformed to a shared exponent color (red_shared, green_shared, blue_shared, exp_shared) as follows:

First, the components (red, green, blue) are clamped to (red_clamped, green_clamped, blue_clamped) as:

• red_clamped = max(0, min(sharedexp_max, red))
• green_clamped = max(0, min(sharedexp_max, green))
• blue_clamped = max(0, min(sharedexp_max, blue))

where:

The largest clamped component, max_clamped is determined:

• max_clamped = max(red_clamped, green_clamped, blue_clamped)

A preliminary shared exponent exp' is computed:

The shared exponent exp_shared is computed:

Finally, three integer values in the range 0 to 2^N are computed:

Shared Exponent to RGB

A shared exponent color (red_shared, green_shared, blue_shared, exp_shared) is transformed to an RGB color (red, green, blue) as follows:

• $red = red\_{shared} \times {2^{(exp\_{shared}-B-N)}}$
• $green = green\_{shared} \times {2^{(exp\_{shared}-B-N)}}$
• $blue = blue\_{shared} \times {2^{(exp\_{shared}-B-N)}}$

where:

• N = 9 (number of mantissa bits per component)
• B = 15 (exponent bias)

Texel Input Operations

Texel input instructions are SPIR-V image instructions that read from an image. Texel input operations are a set of steps that are performed on state, coordinates, and texel values while processing a texel input instruction, and which are common to some or all texel input instructions. They include the following steps, which are performed in the listed order:

• Validation operations
  • Instruction/Sampler/Image validation
  • Coordinate validation
  • Sparse validation
  • Layout validation
• Format conversion
• Texel replacement
• Depth comparison
• Conversion to RGBA
• Component swizzle
• Chroma reconstruction
• Y′C_BC_R conversion

For texel input instructions involving multiple texels (for sampling or gathering), these steps are applied for each texel that is used in the instruction. Depending on the type of image instruction, other steps are conditionally performed between these steps or involving multiple coordinate or texel values.

If Chroma Reconstruction is implicit, Texel Filtering instead takes place during chroma reconstruction, before sampler Y′C_BC_R conversion occurs.

The operations described in block matching and weight image sampling are performed before Conversion to RGBA and Component swizzle.

Texel Input Validation Operations

Texel input validation operations inspect instruction/image/sampler state or coordinates, and in certain circumstances cause the texel value to be replaced or become undefined:. There are a series of validations that the texel undergoes.

Instruction/Sampler/Image View Validation

There are a number of cases where a SPIR-V instruction can mismatch with the sampler, the image view, or both, and a number of further cases where the sampler can mismatch with the image view. In such cases the value of the texel returned is undefined:.

These cases include:

• The sampler borderColor is an integer type and the image view format is not one of the VkFormat integer types or a stencil component of a depth/stencil format.
• The sampler borderColor is a float type and the image view format is not one of the VkFormat float types or a depth component of a depth/stencil format.
• The sampler borderColor is one of the opaque black colors (VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK or VK_BORDER_COLOR_INT_OPAQUE_BLACK) and the image view VkComponentSwizzle for any of the VkComponentMapping components is not the identity swizzle, and VkPhysicalDeviceBorderColorSwizzleFeaturesEXT::borderColorSwizzleFromImage feature is not enabled, and VkSamplerBorderColorComponentMappingCreateInfoEXT is not specified.
• VkSamplerBorderColorComponentMappingCreateInfoEXT::components, if specified, has a component swizzle that does not match the component swizzle of the image view, and either component swizzle is not a form of identity swizzle.
• VkSamplerBorderColorComponentMappingCreateInfoEXT::srgb, if specified, does not match the sRGB encoding of the image view.
• The sampler borderColor is a custom color (VK_BORDER_COLOR_FLOAT_CUSTOM_EXT or VK_BORDER_COLOR_INT_CUSTOM_EXT) and the supplied VkSamplerCustomBorderColorCreateInfoEXT::customBorderColor is outside the bounds of the values representable in the image view’s format.
• The sampler borderColor is a custom color (VK_BORDER_COLOR_FLOAT_CUSTOM_EXT or VK_BORDER_COLOR_INT_CUSTOM_EXT) and the image view VkComponentSwizzle for any of the VkComponentMapping components is not the identity swizzle, and VkPhysicalDeviceBorderColorSwizzleFeaturesEXT::borderColorSwizzleFromImage feature is not enabled, and VkSamplerBorderColorComponentMappingCreateInfoEXT is not specified.
• The VkImageLayout of any subresource in the image view does not match the VkDescriptorImageInfo::imageLayout used to write the image descriptor.
• The SPIR-V Image Format is not compatible with the image view’s format.
• The sampler unnormalizedCoordinates is VK_TRUE and any of the limitations of unnormalized coordinates are violated.
• The sampler was created with flags containing VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and the image was not created with flags containing VK_IMAGE_CREATE_SUBSAMPLED_BIT_EXT.
• The sampler was not created with flags containing VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and the image was created with flags containing VK_IMAGE_CREATE_SUBSAMPLED_BIT_EXT.
• The sampler was created with flags containing VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and is used with a function that is not OpImageSampleImplicitLod or OpImageSampleExplicitLod, or is used with operands Offset or ConstOffsets.
• The SPIR-V instruction is one of the OpImage*Dref* instructions and the sampler compareEnable is VK_FALSE
• The SPIR-V instruction is not one of the OpImage*Dref* instructions and the sampler compareEnable is VK_TRUE
• The SPIR-V instruction is one of the OpImage*Dref* instructions, the image view format is one of the depth/stencil formats, and the image view aspect is not VK_IMAGE_ASPECT_DEPTH_BIT.
• The SPIR-V instruction’s image variable’s properties are not compatible with the image view:
  • If the image view’s viewType is one of VK_IMAGE_VIEW_TYPE_1D_ARRAY, VK_IMAGE_VIEW_TYPE_2D_ARRAY, or VK_IMAGE_VIEW_TYPE_CUBE_ARRAY then the instruction must have Arrayed = 1. Otherwise the instruction must have Arrayed = 0.
  • If the image was created with VkImageCreateInfo::samples equal to VK_SAMPLE_COUNT_1_BIT, the instruction must have MS = 0.
  • If the image was created with VkImageCreateInfo::samples not equal to VK_SAMPLE_COUNT_1_BIT, the instruction must have MS = 1.
  • If the Sampled Type of the OpTypeImage does not match the SPIR-V Type.
  • If the signedness of any read or sample operation does not match the signedness of the image’s format.
• If the image was created with VkImageCreateInfo::flags containing VK_IMAGE_CREATE_CORNER_SAMPLED_BIT_NV, the sampler addressing modes must only use a VkSamplerAddressMode of VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE.
• The SPIR-V instruction is OpImageSampleFootprintNV with Dim = 2D and addressModeU or addressModeV in the sampler is not VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE.
• The SPIR-V instruction is OpImageSampleFootprintNV with Dim = 3D and addressModeU, addressModeV, or addressModeW in the sampler is not VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE.
• The sampler was created with a specified VkSamplerCustomBorderColorCreateInfoEXT::format which does not match the VkFormat of the image view(s) it is sampling.
• The sampler is sampling an image view of VK_FORMAT_B4G4R4A4_UNORM_PACK16, VK_FORMAT_B5G6R5_UNORM_PACK16, or VK_FORMAT_B5G5R5A1_UNORM_PACK16 format without a specified VkSamplerCustomBorderColorCreateInfoEXT::format.

Only OpImageSample* and OpImageSparseSample* can be used with a sampler or image view that enables sampler Y′C_BC_R conversion.

OpImageFetch, OpImageSparseFetch, OpImage*Gather, and OpImageSparse*Gather must not be used with a sampler or image view that enables sampler Y′C_BC_R conversion.

The ConstOffset and Offset operands must not be used with a sampler or image view that enables sampler Y′C_BC_R conversion.

If the underlying VkImage format has an X component in its format description, undefined: values are read from those bits.

Integer Texel Coordinate Validation

Integer texel coordinates are validated against the size of the image level, and the number of layers and number of samples in the image. For SPIR-V instructions that use integer texel coordinates, this is performed directly on the integer coordinates. For instructions that use normalized or unnormalized texel coordinates, this is performed on the coordinates that result after conversion to integer texel coordinates.

If the integer texel coordinates do not satisfy all of the conditions

• 0 ≤ i < w_s
• 0 ≤ j < h_s
• 0 ≤ k < d_s
• 0 ≤ l < layers
• 0 ≤ n < samples

where:

• w_s = width of the image level
• h_s = height of the image level
• d_s = depth of the image level
• layers = number of layers in the image
• samples = number of samples per texel in the image

then the texel fails integer texel coordinate validation.

There are four cases to consider:

1. Valid Texel Coordinates
   • If the texel coordinates pass validation (that is, the coordinates lie within the image),
   
   then the texel value comes from the value in image memory.
2. Border Texel
   • If the texel coordinates fail validation, and
   • If the read is the result of an image sample instruction or image gather instruction, and
   • If the image is not a cube image, or if a sampler created with VK_SAMPLER_CREATE_NON_SEAMLESS_CUBE_MAP_BIT_EXT is used,
   
   then the texel is a border texel and texel replacement is performed.
3. Invalid Texel
   • If the texel coordinates fail validation, and
   • If the read is the result of an image fetch instruction, image read instruction, or atomic instruction,
   
   then the texel is an invalid texel and texel replacement is performed.
4. Cube Map Edge or Corner
   Otherwise the texel coordinates lie beyond the edges or corners of the selected cube map face, and Cube map edge handling is performed.

Cube Map Edge Handling

If the texel coordinates lie beyond the edges or corners of the selected cube map face (as described in the prior section), the following steps are performed. Note that this does not occur when using VK_FILTER_NEAREST filtering within a mip level, since VK_FILTER_NEAREST is treated as using VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE.

• Cube Map Edge Texel
  • If the texel lies beyond the selected cube map face in either only i or only j, then the coordinates (i,j) and the array layer l are transformed to select the adjacent texel from the appropriate neighboring face.
• Cube Map Corner Texel
  • If the texel lies beyond the selected cube map face in both i and j, then there is no unique neighboring face from which to read that texel. The texel should be replaced by the average of the three values of the adjacent texels in each incident face. However, implementations may replace the cube map corner texel by other methods. The methods are subject to the constraint that for linear filtering if the three available texels have the same value, the resulting filtered texel must have that value, and for cubic filtering if the twelve available samples have the same value, the resulting filtered texel must have that value.

Sparse Validation

If the texel reads from an unbound region of a sparse image, the texel is a sparse unbound texel, and processing continues with texel replacement.

Layout Validation

If all planes of a disjoint multi-planar image are not in the same image layout, the image must not be sampled with sampler Y′C_BC_R conversion enabled.

Format Conversion

Texels undergo a format conversion from the VkFormat of the image view to a vector of either floating-point or signed or unsigned integer components, with the number of components based on the number of components present in the format.

• Color formats have one, two, three, or four components, according to the format.
• Depth/stencil formats are one component. The depth or stencil component is selected by the aspectMask of the image view.

Each component is converted based on its type and size (as defined in the Format Definition section for each VkFormat), using the appropriate equations in 16-Bit Floating-Point Numbers, Unsigned 11-Bit Floating-Point Numbers, Unsigned 10-Bit Floating-Point Numbers, Fixed-Point Data Conversion, and Shared Exponent to RGB. Signed integer components smaller than 32 bits are sign-extended.

If the image view format is sRGB, the color components are first converted as if they are UNORM, and then sRGB to linear conversion is applied to the R, G, and B components as described in the sRGB EOTF section of the Khronos Data Format Specification. The A component, if present, is unchanged.

If VkSamplerYcbcrConversionYcbcrDegammaCreateInfoQCOM::enableYDegamma is equal to VK_TRUE, then sRGB to linear conversion is applied to the G component as described in the sRGB EOTF section of the Khronos Data Format Specification. If VkSamplerYcbcrConversionYcbcrDegammaCreateInfoQCOM::enableCbCrDegamma is equal to VK_TRUE, then sRGB to linear conversion is applied to the R and B components as described in the sRGB EOTF section of the Khronos Data Format Specification. The A component, if present, is unchanged.

If the image view format is block-compressed, then the texel value is first decoded, then converted based on the type and number of components defined by the compressed format.

Texel Replacement

A texel is replaced if it is one (and only one) of:

• a border texel,
• an invalid texel, or
• a sparse unbound texel.

Border texels are replaced with a value based on the image format and the borderColor of the sampler. The border color is:

The custom border color (U) may be rounded by implementations prior to texel replacement, but the error introduced by such a rounding must not exceed one ULP of the image’s format.

This is substituted for the texel value by replacing the number of components in the image format

† S = B_g may be substituted as the replacement method by the implementation when VkSamplerCreateInfo::borderColor is VK_BORDER_COLOR_INT_CUSTOM_EXT and VkSamplerCustomBorderColorCreateInfoEXT::format is VK_FORMAT_UNDEFINED. Implementations should use S = B_r as the replacement method.

The value returned by a read of an invalid texel is undefined:, unless that read operation is from a buffer resource and the robustBufferAccess feature is enabled. In that case, an invalid texel is replaced as described by the robustBufferAccess feature. If the access is to an image resource and the x, y, z, or layer coordinate validation fails and the robustImageAccess feature is enabled, then zero must be returned for the R, G, and B components, if present. Either zero or one must be returned for the A component, if present. If If the robustImageAccess2 feature is enabled, zero values must be returned. If only the sample index was invalid, the values returned are undefined:.

Additionally, if the robustImageAccess feature is enabled, but the robustImageAccess2 feature is not, any invalid texels may be expanded to four components prior to texel replacement. This means that components not present in the image format may be replaced with 0 or may undergo conversion to RGBA as normal.

Loads from a null descriptor return a four component color value of all zeros. However, for storage images and storage texel buffers using an explicit SPIR-V Image Format, loads from a null descriptor may return an alpha value of 1 (float or integer, depending on format) if the format does not include alpha.

If the VkPhysicalDeviceSparseProperties::residencyNonResidentStrict property is VK_TRUE, a sparse unbound texel is replaced with 0 or 0.0 values for integer and floating-point components of the image format, respectively.

If residencyNonResidentStrict is VK_FALSE, the value of the sparse unbound texel is undefined:.

Depth Compare Operation

If the image view has a depth/stencil format, the depth component is selected by the aspectMask, and the operation is an OpImage*Dref* instruction, a depth comparison is performed. The result is 1.0 if the comparison evaluates to true, and 0.0 otherwise. This value replaces the depth component D.

The compare operation is selected by the VkCompareOp value set by VkSamplerCreateInfo::compareOp. The reference value from the SPIR-V operand D_ref and the texel depth value D_tex are used as the reference and test values, respectively, in that operation.

If the image being sampled has an unsigned normalized fixed-point format, then D_ref is clamped to [0,1] before the compare operation.

Conversion to RGBA

The texel is expanded from one, two, or three components to four components based on the image base color:

where one = 1.0f for floating-point formats and depth aspects, and one = 1 for integer formats and stencil aspects.

Component Swizzle

All texel input instructions apply a swizzle based on:

• the VkComponentSwizzle enums in the components member of the VkImageViewCreateInfo structure for the image being read if sampler Y′C_BC_R conversion is not enabled, and
• the VkComponentSwizzle enums in the components member of the VkSamplerYcbcrConversionCreateInfo structure for the sampler Y′C_BC_R conversion if sampler Y′C_BC_R conversion is enabled.

The swizzle can rearrange the components of the texel, or substitute zero or one for any components. It is defined as follows for each color component:

where:

If the border color is one of the VK_BORDER_COLOR_*_OPAQUE_BLACK enums and the VkComponentSwizzle is not the identity swizzle for all components, the value of the texel after swizzle is undefined:.

If the image view has a depth/stencil format and the VkComponentSwizzle is VK_COMPONENT_SWIZZLE_ONE, and VkPhysicalDeviceMaintenance5PropertiesKHR::depthStencilSwizzleOneSupport is not VK_TRUE, the value of the texel after swizzle is undefined:.

Sparse Residency

OpImageSparse* instructions return a structure which includes a residency code indicating whether any texels accessed by the instruction are sparse unbound texels. This code can be interpreted by the OpImageSparseTexelsResident instruction which converts the residency code to a boolean value.

Chroma Reconstruction

In some color models, the color representation is defined in terms of monochromatic light intensity (often called luma) and color differences relative to this intensity, often called chroma. It is common for color models other than RGB to represent the chroma components at lower spatial resolution than the luma component. This approach is used to take advantage of the eye’s lower spatial sensitivity to color compared with its sensitivity to brightness. Less commonly, the same approach is used with additive color, since the green component dominates the eye’s sensitivity to light intensity and the spatial sensitivity to color introduced by red and blue is lower.

Lower-resolution components are downsampled by resizing them to a lower spatial resolution than the component representing luminance. This process is also commonly known as chroma subsampling. There is one luminance sample in each texture texel, but each chrominance sample may be shared among several texels in one or both texture dimensions.

• _444 formats do not spatially downsample chroma values compared with luma: there are unique chroma samples for each texel.
• _422 formats have downsampling in the x dimension (corresponding to u or s coordinates): they are sampled at half the resolution of luma in that dimension.
• _420 formats have downsampling in the x dimension (corresponding to u or s coordinates) and the y dimension (corresponding to v or t coordinates): they are sampled at half the resolution of luma in both dimensions.

The process of reconstructing a full color value for texture access involves accessing both chroma and luma values at the same location. To generate the color accurately, the values of the lower-resolution components at the location of the luma samples are reconstructed from the lower-resolution sample locations, an operation known here as chroma reconstruction irrespective of the actual color model.

The location of the chroma samples relative to the luma coordinates is determined by the xChromaOffset and yChromaOffset members of the VkSamplerYcbcrConversionCreateInfo structure used to create the sampler Y′C_BC_R conversion.

The following diagrams show the relationship between unnormalized (u,v) coordinates and (i,j) integer texel positions in the luma component (shown in black, with circles showing integer sample positions) and the texel coordinates of reduced-resolution chroma components, shown as crosses in red.

Reconstruction is implemented in one of two ways:

If the format of the image that is to be sampled sets VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT, or the VkSamplerYcbcrConversionCreateInfo’s forceExplicitReconstruction is VK_TRUE, reconstruction is performed as an explicit step independent of filtering, described in the Explicit Reconstruction section.

If the format of the image that is to be sampled does not set VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT and if the VkSamplerYcbcrConversionCreateInfo’s forceExplicitReconstruction is VK_FALSE, reconstruction is performed as an implicit part of filtering prior to color model conversion, with no separate post-conversion texel filtering step, as described in the Implicit Reconstruction section.

Explicit Reconstruction

• If the chromaFilter member of the VkSamplerYcbcrConversionCreateInfo structure is VK_FILTER_NEAREST:
  • If the format’s R and B components are reduced in resolution in just width by a factor of two relative to the G component (i.e. this is a _422 format), the $\tau\_{ijk}\[level]$ values accessed by texel filtering are reconstructed as follows:$$\begin{aligned} \tau\_R'(i, j) & = \tau\_R(\left\lfloor{i\times 0.5}\right\rfloor, j)\[level] \\\ \tau\_B'(i, j) & = \tau\_B(\left\lfloor{i\times 0.5}\right\rfloor, j)\[level] \end{aligned}$$
  • If the format’s R and B components are reduced in resolution in width and height by a factor of two relative to the G component (i.e. this is a _420 format), the $\tau\_{ijk}\[level]$ values accessed by texel filtering are reconstructed as follows:$$\begin{aligned} \tau\_R'(i, j) & = \tau\_R(\left\lfloor{i\times 0.5}\right\rfloor, \left\lfloor{j\times 0.5}\right\rfloor)\[level] \\\ \tau\_B'(i, j) & = \tau\_B(\left\lfloor{i\times 0.5}\right\rfloor, \left\lfloor{j\times 0.5}\right\rfloor)\[level] \end{aligned}$$

    xChromaOffset and yChromaOffset have no effect if chromaFilter is VK_FILTER_NEAREST for explicit reconstruction.

• If the chromaFilter member of the VkSamplerYcbcrConversionCreateInfo structure is VK_FILTER_LINEAR:
  • If the format’s R and B components are reduced in resolution in just width by a factor of two relative to the G component (i.e. this is a _422 format):
    • If xChromaOffset is VK_CHROMA_LOCATION_COSITED_EVEN:$$\tau\_{RB}'(i,j) = \begin{cases} \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)\[level], & 0.5 \times i = \left\lfloor{0.5 \times i}\right\rfloor\\\ 0.5\times\tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)\[level] + \\\ 0.5\times\tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor + 1,j)\[level], & 0.5 \times i \neq \left\lfloor{0.5 \times i}\right\rfloor \end{cases}$$
    • If xChromaOffset is VK_CHROMA_LOCATION_MIDPOINT:$$\tau\_{RB}'(i,j) = \begin{cases} 0.25 \times \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor - 1,j)\[level] + \\\ 0.75 \times \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)\[level], & 0.5 \times i = \left\lfloor{0.5 \times i}\right\rfloor\\\ 0.75 \times \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)\[level] + \\\ 0.25 \times \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor + 1,j)\[level], & 0.5 \times i \neq \left\lfloor{0.5 \times i}\right\rfloor \end{cases}$$
  • If the format’s R and B components are reduced in resolution in width and height by a factor of two relative to the G component (i.e. this is a _420 format), a similar relationship applies. Due to the number of options, these formulae are expressed more concisely as follows:$$\begin{aligned} i\_{RB} & = \begin{cases} 0.5 \times (i) & \textrm{xChromaOffset = COSITED}\\*\textrm{EVEN} \\\ 0.5 \times (i - 0.5) & \textrm{xChromaOffset = MIDPOINT} \end{cases}\\\ j*{RB} & = \begin{cases} 0.5 \times (j) & \textrm{yChromaOffset = COSITED}\\*\textrm{EVEN} \\\ 0.5 \times (j - 0.5) & \textrm{yChromaOffset = MIDPOINT} \end{cases}\\\ \\\ i*{floor} & = \left\lfloor i\_{RB} \right\rfloor \\\ j\_{floor} & = \left\lfloor j\_{RB} \right\rfloor \\\ \\\ i\_{frac} & = i\_{RB} - i\_{floor} \\\ j\_{frac} & = j\_{RB} - j\_{floor} \end{aligned}$$$$\begin{aligned} \tau\_{RB}'(i,j) = & \tau\_{RB}( i\_{floor}, j\_{floor})\[level] & \times & ( 1 - i\_{frac} ) & & \times & ( 1 - j\_{frac} ) & + \\\ & \tau\_{RB}( 1 + i\_{floor}, j\_{floor})\[level] & \times & ( i\_{frac} ) & & \times & ( 1 - j\_{frac} ) & + \\\ & \tau\_{RB}( i\_{floor}, 1 + j\_{floor})\[level] & \times & ( 1 - i\_{frac} ) & & \times & ( j\_{frac} ) & + \\\ & \tau\_{RB}( 1 + i\_{floor}, 1 + j\_{floor})\[level] & \times & ( i\_{frac} ) & & \times & ( j\_{frac} ) & \end{aligned}$$

Implicit Reconstruction

Implicit reconstruction takes place by the samples being interpolated, as required by the filter settings of the sampler, except that chromaFilter takes precedence for the chroma samples.

If chromaFilter is VK_FILTER_NEAREST, an implementation may behave as if xChromaOffset and yChromaOffset were both VK_CHROMA_LOCATION_MIDPOINT, irrespective of the values set.

The sample coordinates are adjusted by the downsample factor of the component (such that, for example, the sample coordinates are divided by two if the component has a downsample factor of two relative to the luma component):

Sampler Y′C_BC_R Conversion

Sampler Y′C_BC_R conversion performs the following operations, which an implementation may combine into a single mathematical operation:

• Sampler Y′C_BC_R Range Expansion
• Sampler Y′C_BC_R Model Conversion

Sampler Y′C_BC_R Range Expansion

Sampler Y′C_BC_R range expansion is applied to color component values after all texel input operations which are not specific to sampler Y′C_BC_R conversion. For example, the input values to this stage have been converted using the normal format conversion rules.

The input values to this stage may have been converted using sRGB to linear conversion if ycbcrDegamma is enabled.

Sampler Y′C_BC_R range expansion is not applied if ycbcrModel is VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY. That is, the shader receives the vector C'_rgba as output by the Component Swizzle stage without further modification.

For other values of ycbcrModel, range expansion is applied to the texel component values output by the Component Swizzle defined by the components member of VkSamplerYcbcrConversionCreateInfo. Range expansion applies independently to each component of the image. For the purposes of range expansion and Y′C_BC_R model conversion, the R and B components contain color difference (chroma) values and the G component contains luma. The A component is not modified by sampler Y′C_BC_R range expansion.

The range expansion to be applied is defined by the ycbcrRange member of the VkSamplerYcbcrConversionCreateInfo structure:

• If ycbcrRange is VK_SAMPLER_YCBCR_RANGE_ITU_FULL, the following transformations are applied:$$\begin{aligned} Y' &= C'*{rgba}\[G] \\\ C\_B &= C'*{rgba}\[B] - {{2^{(n-1)}}\over{(2^n) - 1}} \\\ C\_R &= C'\_{rgba}\[R] - {{2^{(n-1)}}\over{(2^n) - 1}} \end{aligned}$$

  These formulae correspond to the full range encoding in the Quantization schemes chapter of the Khronos Data Format Specification.

  Should any future amendments be made to the ITU specifications from which these equations are derived, the formulae used by Vulkan may also be updated to maintain parity.

• If ycbcrRange is VK_SAMPLER_YCBCR_RANGE_ITU_NARROW, the following transformations are applied:$$\begin{aligned} Y' &= {{C'*{rgba}\[G] \times (2^n-1) - 16\times 2^{n-8}}\over{219\times 2^{n-8}}} \\\ C\_B &= {{C'*{rgba}\[B] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \\\ C\_R &= {{C'\_{rgba}\[R] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \end{aligned}$$

  These formulae correspond to the narrow range encoding in the Quantization schemes chapter of the Khronos Data Format Specification.

• n is the bit-depth of the components in the format.

The precision of the operations performed during range expansion must be at least that of the source format.

An implementation may clamp the results of these range expansion operations such that Y′ falls in the range [0,1], and/or such that C_B and C_R fall in the range [-0.5,0.5].

Sampler Y′C_BC_R Model Conversion

The range-expanded values are converted between color models, according to the color model conversion specified in the ycbcrModel member:

VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY

The color components are not modified by the color model conversion since they are assumed already to represent the desired color model in which the shader is operating; Y′C_BC_R range expansion is also ignored.

VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_IDENTITY

The color components are not modified by the color model conversion and are assumed to be treated as though in Y′C_BC_R form both in memory and in the shader; Y′C_BC_R range expansion is applied to the components as for other Y′C_BC_R models, with the vector (C_R,Y′,C_B,A) provided to the shader.

VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_709

The color components are transformed from a Y′C_BC_R representation to an R′G′B′ representation as described in the BT.709 Y′C_BC_R conversion section of the Khronos Data Format Specification.

VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_601

The color components are transformed from a Y′C_BC_R representation to an R′G′B′ representation as described in the BT.601 Y′C_BC_R conversion section of the Khronos Data Format Specification.

VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_2020

The color components are transformed from a Y′C_BC_R representation to an R′G′B′ representation as described in the BT.2020 Y′C_BC_R conversion section of the Khronos Data Format Specification.

In this operation, each output component is dependent on each input component.

An implementation may clamp the R′G′B′ results of these conversions to the range [0,1].

The precision of the operations performed during model conversion must be at least that of the source format.

The alpha component is not modified by these model conversions.

Texel Output Operations

Texel output instructions are SPIR-V image instructions that write to an image. Texel output operations are a set of steps that are performed on state, coordinates, and texel values while processing a texel output instruction, and which are common to some or all texel output instructions. They include the following steps, which are performed in the listed order:

• Validation operations
  • Format validation
  • Type validation
  • Coordinate validation
  • Sparse validation
• Texel output format conversion

Texel Output Validation Operations

Texel output validation operations inspect instruction/image state or coordinates, and in certain circumstances cause the write to have no effect. There are a series of validations that the texel undergoes.

Texel Format Validation

If the image format of the OpTypeImage is not compatible with the VkImageView’s format, the write causes the contents of the image’s memory to become undefined:.

Texel Type Validation

If the Sampled Type of the OpTypeImage does not match the SPIR-V Type, the write causes the value of the texel to become undefined:. For integer types, if the signedness of the access does not match the signedness of the accessed resource, the write causes the value of the texel to become undefined:.

Integer Texel Coordinate Validation

The integer texel coordinates are validated according to the same rules as for texel input coordinate validation.

If the texel fails integer texel coordinate validation, then the write has no effect.

Sparse Texel Operation

If the texel attempts to write to an unbound region of a sparse image, the texel is a sparse unbound texel. In such a case, if the VkPhysicalDeviceSparseProperties::residencyNonResidentStrict property is VK_TRUE, the sparse unbound texel write has no effect. If residencyNonResidentStrict is VK_FALSE, the write may have a side effect that becomes visible to other accesses to unbound texels in any resource, but will not be visible to any device memory allocated by the application.

Texel Output Format Conversion

If the image format is sRGB, a linear to sRGB conversion is applied to the R, G, and B components as described in the sRGB EOTF section of the Khronos Data Format Specification. The A component, if present, is unchanged.

Texels then undergo a format conversion from the floating-point, signed, or unsigned integer type of the texel data to the VkFormat of the image view. If the number of components in the texel data is larger than the number of components in the format, additional components are discarded.

Each component is converted based on its type and size (as defined in the Format Definition section for each VkFormat). Floating-point outputs are converted as described in Floating-Point Format Conversions and Fixed-Point Data Conversion. Integer outputs are converted such that their value is preserved. The converted value of any integer that cannot be represented in the target format is undefined:.

If the VkImageView format has an X component in its format description, undefined: values are written to those bits.

If the underlying VkImage format has an X component in its format description, undefined: values are also written to those bits, even if result format conversion produces a valid value for those bits because the VkImageView format is different.

Normalized Texel Coordinate Operations

If the image sampler instruction provides normalized texel coordinates, some of the following operations are performed.

Projection Operation

For Proj image operations, the normalized texel coordinates (s,t,r,q,a) and (if present) the D_ref coordinate are transformed as follows:

Derivative Image Operations

Derivatives are used for LOD selection. These derivatives are either implicit (in an ImplicitLod image instruction in a mesh, task, compute, or fragment shader) or explicit (provided explicitly by shader to the image instruction in any shader).

For implicit derivatives image instructions, the derivatives of texel coordinates are calculated in the same manner as derivative operations. That is:

Partial derivatives not defined above for certain image dimensionalities are set to zero.

For explicit LOD image instructions, if the optional SPIR-V operand Grad is provided, then the operand values are used for the derivatives. The number of components present in each derivative for a given image dimensionality matches the number of partial derivatives computed above.

If the optional SPIR-V operand Lod is provided, then derivatives are set to zero, the cube map derivative transformation is skipped, and the scale factor operation is skipped. Instead, the floating-point scalar coordinate is directly assigned to λ_base as described in LOD Operation.

If the image or sampler object used by an implicit derivative image instruction is not uniform across the quad and quadDivergentImplicitLod is not supported, then the derivative and LOD values are undefined:. Implicit derivatives are well-defined when the image and sampler and control flow are uniform across the quad, even if they diverge between different quads.

If quadDivergentImplicitLod is supported, then derivatives and implicit LOD values are well-defined even if the image or sampler object are not uniform within a quad. The derivatives are computed as specified above, and the implicit LOD calculation proceeds for each shader invocation using its respective image and sampler object.

Cube Map Face Selection and Transformations

For cube map image instructions, the (s,t,r) coordinates are treated as a direction vector (r_x,r_y,r_z). The direction vector is used to select a cube map face. The direction vector is transformed to a per-face texel coordinate system (s_face,t_face), The direction vector is also used to transform the derivatives to per-face derivatives.

Cube Map Face Selection

The direction vector selects one of the cube map’s faces based on the largest magnitude coordinate direction (the major axis direction). Since two or more coordinates can have identical magnitude, the implementation must have rules to disambiguate this situation.

The rules should have as the first rule that r_z wins over r_y and r_x, and the second rule that r_y wins over r_x. An implementation may choose other rules, but the rules must be deterministic and depend only on (r_x,r_y,r_z).

The layer number (corresponding to a cube map face), the coordinate selections for s_c, t_c, r_c, and the selection of derivatives, are determined by the major axis direction as specified in the following two tables.

Cube Map Coordinate Transformation

Cube Map Derivative Transformation

The partial derivatives of the Cube Map Coordinate Transformations can be computed as:

The other derivatives are simplified similarly, resulting in

Scale Factor Operation, LOD Operation and Image Level(s) Selection

LOD selection can be either explicit (provided explicitly by the image instruction) or implicit (determined from a scale factor calculated from the derivatives). The LOD must be computed with mipmapPrecisionBits of accuracy.

Scale Factor Operation

The magnitude of the derivatives are calculated by:

• m_ux = |∂s/∂x| × w_base
• m_vx = |∂t/∂x| × h_base
• m_wx = |∂r/∂x| × d_base
• m_uy = |∂s/∂y| × w_base
• m_vy = |∂t/∂y| × h_base
• m_wy = |∂r/∂y| × d_base

where:

• ∂t/∂x = ∂t/∂y = 0 (for 1D images)
• ∂r/∂x = ∂r/∂y = 0 (for 1D, 2D or Cube images)

and:

• w_base = image.w
• h_base = image.h
• d_base = image.d

(for the baseMipLevel, from the image descriptor).

For corner-sampled images, the w_base, h_base, and d_base are instead:

• w_base = image.w - 1
• h_base = image.h - 1
• d_base = image.d - 1

A point sampled in screen space has an elliptical footprint in texture space. The minimum and maximum scale factors (ρ_min, ρ_max) should be the minor and major axes of this ellipse.

The scale factors ρ_x and ρ_y, calculated from the magnitude of the derivatives in x and y, are used to compute the minimum and maximum scale factors.

ρ_x and ρ_y may be approximated with functions f_x and f_y, subject to the following constraints:

The minimum and maximum scale factors (ρ_min,ρ_max) are determined by:

• ρ_max = max(ρ_x, ρ_y)
• ρ_min = min(ρ_x, ρ_y)

The ratio of anisotropy is determined by:

• η = min(ρ_max/ρ_min, max_Aniso)

where:

• sampler.max_Aniso = maxAnisotropy (from sampler descriptor)
• limits.max_Aniso = maxSamplerAnisotropy (from physical device limits)
• max_Aniso = min(sampler.max_Aniso, limits.max_Aniso)

If ρ_max = ρ_min = 0, then all the partial derivatives are zero, the fragment’s footprint in texel space is a point, and η should be treated as 1. If ρ_max ≠ 0 and ρ_min = 0 then all partial derivatives along one axis are zero, the fragment’s footprint in texel space is a line segment, and η should be treated as max_Aniso. However, anytime the footprint is small in texel space the implementation may use a smaller value of η, even when ρ_min is zero or close to zero. If either VkPhysicalDeviceFeatures::samplerAnisotropy or VkSamplerCreateInfo::anisotropyEnable are VK_FALSE, max_Aniso is set to 1.

If η = 1, sampling is isotropic. If η > 1, sampling is anisotropic.

The sampling rate (N) is derived as:

• N = ⌈η⌉

An implementation may round N up to the nearest supported sampling rate. An implementation may use the value of N as an approximation of η.

LOD Operation

The LOD parameter λ is computed as follows:

where:

and maxSamplerLodBias is the value of the VkPhysicalDeviceLimits feature maxSamplerLodBias.

Image Level(s) Selection

The image level(s) d, d_hi, and d_lo which texels are read from are determined by an image-level parameter d_l, which is computed based on the LOD parameter, as follows:

where:

and:

baseMipLevel and levelCount are taken from the subresourceRange of the image view.

minLod_imageView must be less or equal to level_base + q.

If the sampler’s mipmapMode is VK_SAMPLER_MIPMAP_MODE_NEAREST, then the level selected is d = d_l.

If the sampler’s mipmapMode is VK_SAMPLER_MIPMAP_MODE_LINEAR, two neighboring levels are selected:

δ is the fractional value, quantized to the number of mipmap precision bits, used for linear filtering between levels.

(s,t,r,q,a) to (u,v,w,a) Transformation

The normalized texel coordinates are scaled by the image level dimensions and the array layer is selected.

This transformation is performed once for each level used in filtering (either d, or d_hi and d_lo).

where:

• width_scale = width_level
• height_scale = height_level
• depth_scale = depth_level

for conventional images, and:

• width_scale = width_level - 1
• height_scale = height_level - 1
• depth_scale = depth_level - 1

for corner-sampled images.

and where (Δ_i, Δ_j, Δ_k) are taken from the image instruction if it includes a ConstOffset or Offset operand, otherwise they are taken to be zero.

Operations then proceed to Unnormalized Texel Coordinate Operations.

Unnormalized Texel Coordinate Operations

(u,v,w,a) to (i,j,k,l,n) Transformation and Array Layer Selection

The unnormalized texel coordinates are transformed to integer texel coordinates relative to the selected mipmap level.

The layer index l is computed as:

• l = clamp(RNE(a), 0, layerCount - 1) + baseArrayLayer

where layerCount is the number of layers in the image subresource range of the image view, baseArrayLayer is the first layer from the subresource range, and where:

The sample index n is assigned the value 0.

Nearest filtering (VK_FILTER_NEAREST) computes the integer texel coordinates that the unnormalized coordinates lie within:

where:

• shift = 0.0

for conventional images, and:

• shift = 0.5

for corner-sampled images.

Linear filtering (VK_FILTER_LINEAR) computes a set of neighboring coordinates which bound the unnormalized coordinates. The integer texel coordinates are combinations of i₀ or i₁, j₀ or j₁, k₀ or k₁, as well as weights α, β, and γ.

where:

• shift = 0.5

for conventional images, and:

• shift = 0.0

for corner-sampled images, and where:

where the number of fraction bits retained is specified by VkPhysicalDeviceLimits::subTexelPrecisionBits.

Cubic filtering (VK_FILTER_CUBIC_EXT) computes a set of neighboring coordinates which bound the unnormalized coordinates. The integer texel coordinates are combinations of i₀, i₁, i₂ or i₃, j₀, j₁, j₂ or j₃, k₀, k₁, k₂ or k₃, as well as weights α, β, and γ.

where:

where the number of fraction bits retained is specified by VkPhysicalDeviceLimits::subTexelPrecisionBits.

Integer Texel Coordinate Operations

Integer texel coordinate operations may supply a LOD which texels are to be read from or written to using the optional SPIR-V operand Lod. If the Lod is provided then it must be an integer.

The image level selected is:

If d does not lie in the range [baseMipLevel, baseMipLevel + levelCount) or d is less than minLodInteger_imageView, then any values fetched are zero if the robustImageAccess2 feature is enabled, otherwise are undefined:, and any writes (if supported) are discarded.

Image Sample Operations

Wrapping Operation

If the used sampler was created without VK_SAMPLER_CREATE_NON_SEAMLESS_CUBE_MAP_BIT_EXT, Cube images ignore the wrap modes specified in the sampler. Instead, if VK_FILTER_NEAREST is used within a mip level then VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE is used, and if VK_FILTER_LINEAR is used within a mip level then sampling at the edges is performed as described earlier in the Cube map edge handling section.

The first integer texel coordinate i is transformed based on the addressModeU parameter of the sampler.

where:

j (for 2D and Cube image) and k (for 3D image) are similarly transformed based on the addressModeV and addressModeW parameters of the sampler, respectively.

Texel Gathering

SPIR-V instructions with Gather in the name return a vector derived from 4 texels in the base level of the image view. The rules for the VK_FILTER_LINEAR minification filter are applied to identify the four selected texels. Each texel is then converted to an RGBA value according to conversion to RGBA and then swizzled. A four-component vector is then assembled by taking the component indicated by the Component value in the instruction from the swizzled color value of the four texels. If the operation does not use the ConstOffsets image operand then the four texels form the 2 × 2 rectangle used for texture filtering: