HDR video reconstruction by converted tone mapping

An encoder comprising:

• a processor circuit and a memory circuit, wherein the memory is arranged to store instructions for the processor circuit,
• wherein the processor circuit is arranged to encode an input high dynamic range image as encoded data,
• wherein the input high dynamic range image has a high dynamic range,
• wherein the encoded data comprises a matrix of pixel colors of a lower dynamic range image and a metadata of the lower dynamic range image,
• wherein the lower dynamic range is lower than the high dynamic range,
• wherein the metadata comprises a luma mapping function,
• wherein the luma mapping function is arranged to calculate high dynamic range pixel lumas of the input high dynamic range image by applying the luma mapping function to pixel lumas of the lower dynamic range image,
• wherein the processor circuit is arranged to receive the luma mapping function from a connectable or comprised inverse tone mapping system,
• wherein the inverse tone mapping system is arranged to derive an up-grading function,
• wherein the up-grading function is based on analyzed properties of a master low dynamic range image,
• wherein the up-grading function is arranged to calculate the input high dynamic range image from the master low dynamic range image by applying the up-grading function to lumas of the master low dynamic range image,
• wherein the inverse tone mapping system is arranged to invert the up-grading function so as to obtain the luma mapping function;
• a mapping splitting circuit,
• wherein the mapping splitting circuit is arranged to compose the luma mapping function into a first data item and a second data item,
• wherein the first data item is a stretched luma mapping function,
• wherein the stretched luma mapping function is defined by mapping a clipping point of the luma mapping function onto an endpoint,
• wherein the clipping point is where the luma mapping function reaches a maximum output value,
• wherein the endpoint has as coordinates a maximum of an input value and the maximum output value,
• wherein the clipping point corresponds to a horizontal scaling factor,
• wherein the mapping splitting circuit is arranged to map each point of the luma mapping function having an input coordinate less than the input coordinate of the clipping point to a stretched input coordinate by multiplying the input coordinate of each such point by a horizontal scaling factor, and maintaining the output coordinate of each such point,
• wherein the second data item is a scale factor,
• wherein the scale factor is equal to the reciprocal of the horizontal scaling factor;
• and
• a formatter circuit, wherein the formatter circuit is arranged to output the stretched luma mapping function and the scaling value as metadata of the lower dynamic range image.