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-rw-r--r--chapters/image.adoc134
1 files changed, 63 insertions, 71 deletions
diff --git a/chapters/image.adoc b/chapters/image.adoc
index 690480c..6f1d3cc 100644
--- a/chapters/image.adoc
+++ b/chapters/image.adoc
@@ -13,40 +13,34 @@
Resizes a tensor. Resize is only allowed in the H and W dimensions.
-The height dimension is scaled by factor (scale_y_n/scale_y_d).
-The width dimension is scaled by factor (scale_x_n/scale_x_d).
-
The NEAREST_NEIGHBOR mode returns the value of the input tensor closest to the
calculated sample position for both floating-point and integer data formats.
Floating-point BILINEAR mode returns a bilinearly interpolated output value
based on the four closest input sample positions.
-For integer BILINEAR interpolation mode, the output value must
-be scaled by 1/(scale_y_n * scale_x_n) in a following operation to
-complete the interpolation (for example with a RESCALE operator).
+For integer BILINEAR interpolation mode, the output value is calculated by using
+the shift value along with the other parameters to create a fixed point scaling
+factor for each input. These values are then summed to create the value for
+output, which has 2 * shift fractional bits. To convert back to the original
+integer size, the output value must be rescaled.
The following examples show practical uses of the parameters:
* For approximate uniform input sampling between (0, 0) and (IH-1, IW-1) set
-** scale_y_n/scale_y_d = (OH-1)/(IH-1) as integer ratios
-** scale_x_n/scale_x_d = (OW-1)/(IW-1) as integer ratios
-** offset_x = 0, offset_y = 0, border_x = 0, border_y = 0
-
-* For power of two upscale [OH-1,OW-1] = (1<<k) * [IH-1, IW-1],
-sampling between (0,0) and (IH-1,IW-1), set:
-** scale_y_n = (1<<k), scale_y_d = 1, offset_y = 0, border_y = 0
-** scale_x_n = (1<<k), scale_x_d = 1, offset_x = 0, border_x = 0
-
-* For power of two upscale [OH,OW] = (1<<k) * [IH,IW],
-sampling range approximately (-0.5, -0.5) to (IH-0.5, IW-0.5), set:
-** scale_y_n = 2<<k, scale_y_d = 2, offset_y = -(1<<k)+1, border_y = (1<<k)-1
-** scale_x_n = 2<<k, scale_x_d = 2, offset_x = -(1<<k)+1, border_x = (1<<k)-1
-
-The output dimensions can be derived from the input dimensions by inverting
-the scale as described in the pseudocode. The [border_y, border_x] values
-adjust the output size to allow fractional sampling beyond integer
-input position (IH-1,IW-1).
+stride_y = ( (IH-1) * (1<<shift) ) / (OH-1),
+stride_x = ( (IW-1) * (1<<shift) ) / (OW-1),
+offset_x=0, offset_y=0, border_x=0, border_y=0.
+
+* For power of two upscale by factor (1<<k) the following parameters can
+be used for fixed point upscales:
+** For upscale [OH-1,OW-1] = (1<<k) * [IH-1, IW-1] set
+shift=k, stride_y=1, stride_x=1, offset_x=0, offset_y=0,
+border_x=0, border_y=0.
+** For upscale [OH,OW] = (1<<k) * [IH,IW] set
+shift=(k+1), stride_y=2, stride_x=2, offset_x=-(1<<k)+1, offset_y=-(1<<k)+1,
+border_x=1<<(k-1), border_y=1<<(k-1). This samples approximately
+the input area (-0.5, -0.5) to (IH-0.5, IW-0.5).
*Arguments:*
@@ -54,9 +48,11 @@ input position (IH-1,IW-1).
|Argument|Type|Name|Shape|Description
|Input|in_t*|input|[N,IH,IW,C]|Input tensor
-|Attribute|int16_t *|scale|[4]|[scale_y_n, scale_y_d, scale_x_n, scale_x_d]
-|Attribute|int16_t *|offset|[2]|[offset_y, offset_x]
+|Attribute|int32_t* |output_size|[2]|[OH,OW]
+|Attribute|resize_t*|stride|[2]|[stride_y, stride_x]
+|Attribute|resize_t*|offset|[2]|[offset_y, offset_x]
|Attribute|int32_t* |border|[2]|[border_y, border_x]
+|Attribute|int32_t |shift|-|Shift value (must be zero if resize_t is float)
|Attribute|mode_t|mode|-|BILINEAR or NEAREST
|Output|out_t*|output|[N,OH,OW,C]|Output tensor
|===
@@ -65,61 +61,57 @@ input position (IH-1,IW-1).
[source,c++]
----
+// Derive the output dimensions from the input dimensions
+OH = idiv((IH-1)*(1<<shift) - offset_y, stride_y) + 1 + border_y;
+OW = idiv((IW-1)*(1<<shift) - offset_x, stride_x) + 1 + border_x;
// Ensure the image size is supported by GPU APIs and that for integer
// implementations, position * stride does not overflow int32_t.
ERROR_IF(max(OH,OW,IH,IW) >= 16384);
-ERROR_IF(scale_y_n <= 0 || scale_y_d <=0 || scale_x_n <=0 || scale_x_d <=0);
-// if in_t=int8_t ensure that an int32_t accumulator can be used
-ERROR_IF(scale_y_n > (1<<11) || scale_x_n > (1<<11));
-// set a consistent lower limit of 1/16 downscale to simplify implementations
-ERROR_IF(scale_y_d >= 16 * scale_y_n || scale_x_d >= 16 * scale_x_n);
-ERROR_IF(offset_y < -scale_y_n || offset_y >= 16*scale_y_n);
-ERROR_IF(offset_x < -scale_x_n || offset_x >= 16*scale_x_n);
-ERROR_IF(border_y < -16*scale_y_n || border_y >= scale_y_n);
-ERROR_IF(border_x < -16*scale_x_n || border_x >= scale_x_n);
-ERROR_IF(OH != idiv_check((IH-1)*scale_y_n - offset_y + border_y, scale_y_d) + 1);
-ERROR_IF(OW != idiv_check((IW-1)*scale_x_n - offset_x + border_x, scale_x_d) + 1);
+ERROR_IF(stride_x <= 0 || stride_y <= 0);
+if (is_floating_point(resize_t)) {
+ // The shift attribute is not used for floating point
+ ERROR_IF(shift != 0);
+ ERROR_IF(stride_x > IW || stride_y > IH);
+} else {
+ // if in_t=int8_t ensure that an int32_t accumulator can be used
+ ERROR_IF(shift < 1 || shift > 11);
+ // set a consistent lower limit of 1/16 downscale
+ // independent of the shift value to simplify implementations
+ ERROR_IF(stride_x >= (16 << shift));
+ ERROR_IF(stride_y >= (16 << shift));
+ // offset range is similarly limited to maximum 16 pixels irrespective
+ // of shift. Both stride and offset fit in int16_t when shift=11.
+ ERROR_IF(offset_x <= (-16 << shift) || offset_x >= (16 << shift));
+ ERROR_IF(offset_y <= (-16 << shift) || offset_y >= (16 << shift));
+}
for_each(0 <= n < N, 0 <= oy < OH, 0 <= ox < OW; 0 <= c < C) {
- out_t acc;
- resize_t dx, dy;
-
- int32_t y = oy * scale_y_d + offset_y;
- int32_t x = ox * scale_x_d + offset_x;
- int16_t iy = floor(y / scale_y_n);
- int16_t ix = floor(x / scale_x_n);
-
+ unit = (is_floating_point(resize_t)) ? 1.0 : (1 << shift);
+ y = oy * stride_y + offset_y;
+ x = ox * stride_x + offset_x;
if (is_floating_point(resize_t)) {
- dy = ((resize_t)y / (resize_t)scale_y_n) - iy;
- dx = ((resize_t)x / (resize_t)scale_x_n) - ix;
+ iy = (int32_t)apply_floor(y); dy = y - (resize_t)iy;
+ ix = (int32_t)apply_floor(x); dx = x - (resize_t)ix;
} else {
- dy = y - iy * scale_y_n;
- dx = y - ix * scale_x_n;
+ iy = y >> shift; dy = y - (iy<<shift);
+ ix = x >> shift; dx = x - (ix<<shift);
}
- // Note that -1 <= iy < IH and -1 <= ix < IW
- int16_t iy0 = apply_max(iy, 0);
- int16_t iy1 = apply_min(iy+1, IH-1);
- int16_t ix0 = apply_max(ix, 0);
- int16_t ix1 = apply_min(ix+1, IW-1);
+ iy0 = apply_max(iy, 0);
+ iy1 = apply_min(iy+1, IH-1);
+ ix0 = apply_max(ix, 0);
+ ix1 = apply_min(ix+1, IW-1);
+ REQUIRE(ix0 <= ix1 && iy0 <= iy1);
if (mode==BILINEAR) {
- in_t v00 = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy0,ix0,c]);
- in_t v01 = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy0,ix1,c]);
- in_t v10 = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy1,ix0,c]);
- in_t v11 = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy1,ix1,c]);
- acc = v00 * (scale_y_n - dy) * (scale_x_n - dx);
- acc += v01 * (scale_y_n - dy) * dx;
- acc += v10 * dy * (scale_x_n - dx);
- acc += v11 * dy * dx;
+ v00 = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy0,ix0,c]);
+ v01 = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy0,ix1,c]);
+ v10 = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy1,ix0,c]);
+ v11 = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy1,ix1,c]);
+ out_t acc = v00 * (unit - dy) * (unit - dx) + v01 * (unit - dy) * dx;
+ acc = acc + v10 * dy * (unit-dx) + v11 * dy * dx;
tensor_write<out_t>(output, [N,OH,OW,C], [n,oy,ox,c], acc);
} else if (mode==NEAREST) {
- int32_t iy, ix;
- if (is_floating_point(resize_t)) {
- iy = (dy >= 0.5) ? iy1 : iy0;
- ix = (dx >= 0.5) ? ix1 : ix0;
- } else {
- iy = (2*dy >= scale_y_n) ? iy1 : iy0;
- ix = (2*dx >= scale_x_n) ? ix1 : ix0;
- }
- in_t v = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy,ix,c]);
+ iy = (dy >= unit/2) ? iy1 : iy0;
+ ix = (dx >= unit/2) ? ix1 : ix0;
+ v = tensor_read<in_t>(input, [N,IH,IW,C], [n,iy,ix,c]);
tensor_write<out_t>(output, [N,OH,OW,C], [n,oy,ox,c], v);
}
}
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