ppdiffusers/pipelines/paint_by_example/pipeline_paint_by_example.py

# Copyright 2022 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import inspect
from typing import Callable, List, Optional, Union

import numpy as np
import paddle
import PIL

from paddlenlp.transformers import CLIPFeatureExtractor

from ...models import AutoencoderKL, UNet2DConditionModel
from ...pipeline_utils import DiffusionPipeline
from ...schedulers import DDIMScheduler, LMSDiscreteScheduler, PNDMScheduler
from ...utils import logging
from ..stable_diffusion import StableDiffusionPipelineOutput
from ..stable_diffusion.safety_checker import StableDiffusionSafetyChecker
from .image_encoder import PaintByExampleImageEncoder

logger = logging.get_logger(__name__)  # pylint: disable=invalid-name


def prepare_mask_and_masked_image(image, mask):
    """
    Prepares a pair (image, mask) to be consumed by the Paint by Example pipeline. This means that those inputs will be
    converted to ``paddle.Tensor`` with shapes ``batch x channels x height x width`` where ``channels`` is ``3`` for the
    ``image`` and ``1`` for the ``mask``.

    The ``image`` will be converted to ``torch.float32`` and normalized to be in ``[-1, 1]``. The ``mask`` will be
    binarized (``mask > 0.5``) and cast to ``torch.float32`` too.

    Args:
        image (Union[np.array, PIL.Image, paddle.Tensor]): The image to inpaint.
            It can be a ``PIL.Image``, or a ``height x width x 3`` ``np.array`` or a ``channels x height x width``
            ``paddle.Tensor`` or a ``batch x channels x height x width`` ``paddle.Tensor``.
        mask (_type_): The mask to apply to the image, i.e. regions to inpaint.
            It can be a ``PIL.Image``, or a ``height x width`` ``np.array`` or a ``1 x height x width``
            ``paddle.Tensor`` or a ``batch x 1 x height x width`` ``paddle.Tensor``.


    Raises:
        ValueError: ``paddle.Tensor`` images should be in the ``[-1, 1]`` range. ValueError: ``paddle.Tensor`` mask
        should be in the ``[0, 1]`` range. ValueError: ``mask`` and ``image`` should have the same spatial dimensions.
        TypeError: ``mask`` is a ``paddle.Tensor`` but ``image`` is not
            (ot the other way around).

    Returns:
        tuple[paddle.Tensor]: The pair (mask, masked_image) as ``paddle.Tensor`` with 4
            dimensions: ``batch x channels x height x width``.
    """
    if isinstance(image, paddle.Tensor):
        if not isinstance(mask, paddle.Tensor):
            raise TypeError(f"`image` is a paddle.Tensor but `mask` (type: {type(mask)} is not")

        # Batch single image
        if image.ndim == 3:
            assert image.shape[0] == 3, "Image outside a batch should be of shape (3, H, W)"
            image = image.unsqueeze(0)

        # Batch and add channel dim for single mask
        if mask.ndim == 2:
            mask = mask.unsqueeze(0).unsqueeze(0)

        # Batch single mask or add channel dim
        if mask.ndim == 3:
            # Batched mask
            if mask.shape[0] == image.shape[0]:
                mask = mask.unsqueeze(1)
            else:
                mask = mask.unsqueeze(0)

        assert image.ndim == 4 and mask.ndim == 4, "Image and Mask must have 4 dimensions"
        assert image.shape[-2:] == mask.shape[-2:], "Image and Mask must have the same spatial dimensions"
        assert image.shape[0] == mask.shape[0], "Image and Mask must have the same batch size"
        assert mask.shape[1] == 1, "Mask image must have a single channel"

        # Check image is in [-1, 1]
        if image.min() < -1 or image.max() > 1:
            raise ValueError("Image should be in [-1, 1] range")

        # Check mask is in [0, 1]
        if mask.min() < 0 or mask.max() > 1:
            raise ValueError("Mask should be in [0, 1] range")

        # paint-by-example inverses the mask
        mask = 1 - mask

        # Binarize mask
        mask[mask < 0.5] = 0
        mask[mask >= 0.5] = 1

        # Image as float32
        image = image.cast(paddle.float32)
    elif isinstance(mask, paddle.Tensor):
        raise TypeError(f"`mask` is a paddle.Tensor but `image` (type: {type(image)} is not")
    else:
        if isinstance(image, PIL.Image.Image):
            image = [image]

        image = np.concatenate([np.array(i.convert("RGB"))[None, :] for i in image], axis=0)
        image = image.transpose(0, 3, 1, 2)
        image = paddle.to_tensor(image).cast(paddle.float32) / 127.5 - 1.0

        # preprocess mask
        if isinstance(mask, PIL.Image.Image):
            mask = [mask]

        mask = np.concatenate([np.array(m.convert("L"))[None, None, :] for m in mask], axis=0)
        mask = mask.astype(np.float32) / 255.0

        # paint-by-example inverses the mask
        mask = 1 - mask

        mask[mask < 0.5] = 0
        mask[mask >= 0.5] = 1
        mask = paddle.to_tensor(mask)

    masked_image = image * mask

    return mask, masked_image


class PaintByExamplePipeline(DiffusionPipeline):
    r"""
    Pipeline for text-guided image inpainting using Stable Diffusion. *This is an experimental feature*.

    This model inherits from [`DiffusionPipeline`]. Check the superclass documentation for the generic methods the
    library implements for all the pipelines (such as downloading or saving, running on a particular device, etc.)

    Args:
        vae ([`AutoencoderKL`]):
            Variational Auto-Encoder (VAE) Model to encode and decode images to and from latent representations.
        text_encoder ([`CLIPTextModel`]):
            Frozen text-encoder. Stable Diffusion uses the text portion of
            [CLIP](https://huggingface.co/docs/transformers/model_doc/clip#transformers.CLIPTextModel), specifically
            the [clip-vit-large-patch14](https://huggingface.co/openai/clip-vit-large-patch14) variant.
        tokenizer (`CLIPTokenizer`):
            Tokenizer of class
            [CLIPTokenizer](https://huggingface.co/docs/transformers/v4.21.0/en/model_doc/clip#transformers.CLIPTokenizer).
        unet ([`UNet2DConditionModel`]): Conditional U-Net architecture to denoise the encoded image latents.
        scheduler ([`SchedulerMixin`]):
            A scheduler to be used in combination with `unet` to denoise the encoded image latents. Can be one of
            [`DDIMScheduler`], [`LMSDiscreteScheduler`], or [`PNDMScheduler`].
        safety_checker ([`StableDiffusionSafetyChecker`]):
            Classification module that estimates whether generated images could be considered offensive or harmful.
            Please, refer to the [model card](https://huggingface.co/runwayml/stable-diffusion-v1-5) for details.
        feature_extractor ([`CLIPFeatureExtractor`]):
            Model that extracts features from generated images to be used as inputs for the `safety_checker`.
    """
    _optional_components = ["safety_checker"]

    def __init__(
        self,
        vae: AutoencoderKL,
        image_encoder: PaintByExampleImageEncoder,
        unet: UNet2DConditionModel,
        scheduler: Union[DDIMScheduler, PNDMScheduler, LMSDiscreteScheduler],
        safety_checker: StableDiffusionSafetyChecker,
        feature_extractor: CLIPFeatureExtractor,
        requires_safety_checker: bool = False,
    ):
        super().__init__()

        self.register_modules(
            vae=vae,
            image_encoder=image_encoder,
            unet=unet,
            scheduler=scheduler,
            safety_checker=safety_checker,
            feature_extractor=feature_extractor,
        )
        self.vae_scale_factor = 2 ** (len(self.vae.config.block_out_channels) - 1)
        self.register_to_config(requires_safety_checker=requires_safety_checker)

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.run_safety_checker
    def run_safety_checker(self, image, dtype):
        if self.safety_checker is not None:
            safety_checker_input = self.feature_extractor(self.numpy_to_pil(image), return_tensors="pd")
            image, has_nsfw_concept = self.safety_checker(
                images=image, clip_input=safety_checker_input.pixel_values.cast(dtype)
            )
        else:
            has_nsfw_concept = None
        return image, has_nsfw_concept

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.prepare_extra_step_kwargs
    def prepare_extra_step_kwargs(self, generator, eta):
        # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
        # eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
        # eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
        # and should be between [0, 1]

        accepts_eta = "eta" in set(inspect.signature(self.scheduler.step).parameters.keys())
        extra_step_kwargs = {}
        if accepts_eta:
            extra_step_kwargs["eta"] = eta

        # check if the scheduler accepts generator
        accepts_generator = "generator" in set(inspect.signature(self.scheduler.step).parameters.keys())
        if accepts_generator:
            extra_step_kwargs["generator"] = generator
        return extra_step_kwargs

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.decode_latents
    def decode_latents(self, latents):
        latents = 1 / 0.18215 * latents
        image = self.vae.decode(latents).sample
        image = (image / 2 + 0.5).clip(0, 1)
        # we always cast to float32 as this does not cause significant overhead and is compatible with bfloa16
        image = image.transpose([0, 2, 3, 1]).cast("float32").numpy()
        return image

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion_image_variation.StableDiffusionImageVariationPipeline.check_inputs
    def check_inputs(self, image, height, width, callback_steps):
        if (
            not isinstance(image, paddle.Tensor)
            and not isinstance(image, PIL.Image.Image)
            and not isinstance(image, list)
        ):
            raise ValueError(
                "`image` has to be of type `paddle.Tensor` or `PIL.Image.Image` or `List[PIL.Image.Image]` but is"
                f" {type(image)}"
            )

        if height % 8 != 0 or width % 8 != 0:
            raise ValueError(f"`height` and `width` have to be divisible by 8 but are {height} and {width}.")

        if (callback_steps is None) or (
            callback_steps is not None and (not isinstance(callback_steps, int) or callback_steps <= 0)
        ):
            raise ValueError(
                f"`callback_steps` has to be a positive integer but is {callback_steps} of type"
                f" {type(callback_steps)}."
            )

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.prepare_latents
    def prepare_latents(self, batch_size, num_channels_latents, height, width, dtype, generator, latents=None):
        shape = [batch_size, num_channels_latents, height // self.vae_scale_factor, width // self.vae_scale_factor]
        if isinstance(generator, list) and len(generator) != batch_size:
            raise ValueError(
                f"You have passed a list of generators of length {len(generator)}, but requested an effective batch"
                f" size of {batch_size}. Make sure the batch size matches the length of the generators."
            )

        if latents is None:
            if isinstance(generator, list):
                shape = [
                    1,
                ] + shape[1:]
                latents = [paddle.randn(shape, generator=generator[i], dtype=dtype) for i in range(batch_size)]
                latents = paddle.concat(latents, axis=0)
            else:
                latents = paddle.randn(shape, generator=generator, dtype=dtype)
        else:
            if latents.shape != shape:
                raise ValueError(f"Unexpected latents shape, got {latents.shape}, expected {shape}")

        # scale the initial noise by the standard deviation required by the scheduler
        latents = latents * self.scheduler.init_noise_sigma
        return latents

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion_inpaint.StableDiffusionInpaintPipeline.prepare_mask_latents
    def prepare_mask_latents(
        self, mask, masked_image, batch_size, height, width, dtype, generator, do_classifier_free_guidance
    ):
        # resize the mask to latents shape as we concatenate the mask to the latents
        # we do that before converting to dtype to avoid breaking in case we're using cpu_offload
        # and half precision
        mask = paddle.nn.functional.interpolate(
            mask, size=(height // self.vae_scale_factor, width // self.vae_scale_factor)
        )
        mask = mask.cast(dtype)

        masked_image = masked_image.cast(dtype)

        # encode the mask image into latents space so we can concatenate it to the latents
        if isinstance(generator, list):
            masked_image_latents = [
                self.vae.encode(masked_image[i : i + 1]).latent_dist.sample(generator=generator[i])
                for i in range(batch_size)
            ]
            masked_image_latents = paddle.concat(masked_image_latents, axis=0)
        else:
            masked_image_latents = self.vae.encode(masked_image).latent_dist.sample(generator=generator)
        masked_image_latents = 0.18215 * masked_image_latents

        # duplicate mask and masked_image_latents for each generation per prompt, using mps friendly method
        if mask.shape[0] < batch_size:
            if not batch_size % mask.shape[0] == 0:
                raise ValueError(
                    "The passed mask and the required batch size don't match. Masks are supposed to be duplicated to"
                    f" a total batch size of {batch_size}, but {mask.shape[0]} masks were passed. Make sure the number"
                    " of masks that you pass is divisible by the total requested batch size."
                )
            mask = mask.tile([batch_size // mask.shape[0], 1, 1, 1])
        if masked_image_latents.shape[0] < batch_size:
            if not batch_size % masked_image_latents.shape[0] == 0:
                raise ValueError(
                    "The passed images and the required batch size don't match. Images are supposed to be duplicated"
                    f" to a total batch size of {batch_size}, but {masked_image_latents.shape[0]} images were passed."
                    " Make sure the number of images that you pass is divisible by the total requested batch size."
                )
            masked_image_latents = masked_image_latents.tile([batch_size // masked_image_latents.shape[0], 1, 1, 1])

        mask = paddle.concat([mask] * 2) if do_classifier_free_guidance else mask
        masked_image_latents = (
            paddle.concat([masked_image_latents] * 2) if do_classifier_free_guidance else masked_image_latents
        )

        # aligning device to prevent device errors when concating it with the latent model input
        masked_image_latents = masked_image_latents.cast(dtype)
        return mask, masked_image_latents

    def _encode_image(self, image, num_images_per_prompt, do_classifier_free_guidance):
        # dtype = self.image_encoder.dtype

        if not isinstance(image, paddle.Tensor):
            image = self.feature_extractor(images=image, return_tensors="pd").pixel_values

        # image = image.cast(dtype)
        image_embeddings = self.image_encoder(image)

        # duplicate image embeddings for each generation per prompt, using mps friendly method
        bs_embed, seq_len, _ = image_embeddings.shape
        image_embeddings = image_embeddings.tile([1, num_images_per_prompt, 1])
        image_embeddings = image_embeddings.reshape([bs_embed * num_images_per_prompt, seq_len, -1])

        if do_classifier_free_guidance:
            uncond_embeddings = self.image_encoder.uncond_vector
            uncond_embeddings = uncond_embeddings.tile([1, image_embeddings.shape[0], 1])
            uncond_embeddings = uncond_embeddings.reshape([bs_embed * num_images_per_prompt, 1, -1])

            # For classifier free guidance, we need to do two forward passes.
            # Here we concatenate the unconditional and text embeddings into a single batch
            # to avoid doing two forward passes
            image_embeddings = paddle.concat([uncond_embeddings, image_embeddings])

        return image_embeddings

    @paddle.no_grad()
    def __call__(
        self,
        example_image: Union[paddle.Tensor, PIL.Image.Image],
        image: Union[paddle.Tensor, PIL.Image.Image],
        mask_image: Union[paddle.Tensor, PIL.Image.Image],
        height: Optional[int] = None,
        width: Optional[int] = None,
        num_inference_steps: int = 50,
        guidance_scale: float = 5.0,
        num_images_per_prompt: Optional[int] = 1,
        eta: float = 0.0,
        generator: Optional[Union[paddle.Generator, List[paddle.Generator]]] = None,
        latents: Optional[paddle.Tensor] = None,
        output_type: Optional[str] = "pil",
        return_dict: bool = True,
        callback: Optional[Callable[[int, int, paddle.Tensor], None]] = None,
        callback_steps: Optional[int] = 1,
    ):
        r"""
        Function invoked when calling the pipeline for generation.

        Args:
            example_image (`paddle.Tensor` or `PIL.Image.Image` or `List[PIL.Image.Image]`):
                The exemplar image to guide the image generation.
            image (`paddle.Tensor` or `PIL.Image.Image` or `List[PIL.Image.Image]`):
                `Image`, or tensor representing an image batch which will be inpainted, *i.e.* parts of the image will
                be masked out with `mask_image` and repainted according to `prompt`.
            mask_image (`paddle.Tensor` or `PIL.Image.Image` or `List[PIL.Image.Image]`):
                `Image`, or tensor representing an image batch, to mask `image`. White pixels in the mask will be
                repainted, while black pixels will be preserved. If `mask_image` is a PIL image, it will be converted
                to a single channel (luminance) before use. If it's a tensor, it should contain one color channel (L)
                instead of 3, so the expected shape would be `(B, H, W, 1)`.
            height (`int`, *optional*, defaults to self.unet.config.sample_size * self.vae_scale_factor):
                The height in pixels of the generated image.
            width (`int`, *optional*, defaults to self.unet.config.sample_size * self.vae_scale_factor):
                The width in pixels of the generated image.
            num_inference_steps (`int`, *optional*, defaults to 50):
                The number of denoising steps. More denoising steps usually lead to a higher quality image at the
                expense of slower inference.
            guidance_scale (`float`, *optional*, defaults to 7.5):
                Guidance scale as defined in [Classifier-Free Diffusion Guidance](https://arxiv.org/abs/2207.12598).
                `guidance_scale` is defined as `w` of equation 2. of [Imagen
                Paper](https://arxiv.org/pdf/2205.11487.pdf). Guidance scale is enabled by setting `guidance_scale >
                1`. Higher guidance scale encourages to generate images that are closely linked to the text `prompt`,
                usually at the expense of lower image quality.
            num_images_per_prompt (`int`, *optional*, defaults to 1):
                The number of images to generate per prompt.
            eta (`float`, *optional*, defaults to 0.0):
                Corresponds to parameter eta (η) in the DDIM paper: https://arxiv.org/abs/2010.02502. Only applies to
                [`schedulers.DDIMScheduler`], will be ignored for others.
            generator (`torch.Generator`, *optional*):
                One or a list of [torch generator(s)](https://pytorch.org/docs/stable/generated/torch.Generator.html)
                to make generation deterministic.
            latents (`paddle.Tensor`, *optional*):
                Pre-generated noisy latents, sampled from a Gaussian distribution, to be used as inputs for image
                generation. Can be used to tweak the same generation with different prompts. If not provided, a latents
                tensor will ge generated by sampling using the supplied random `generator`.
            output_type (`str`, *optional*, defaults to `"pil"`):
                The output format of the generate image. Choose between
                [PIL](https://pillow.readthedocs.io/en/stable/): `PIL.Image.Image` or `np.array`.
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether or not to return a [`~pipelines.stable_diffusion.StableDiffusionPipelineOutput`] instead of a
                plain tuple.
            callback (`Callable`, *optional*):
                A function that will be called every `callback_steps` steps during inference. The function will be
                called with the following arguments: `callback(step: int, timestep: int, latents: paddle.Tensor)`.
            callback_steps (`int`, *optional*, defaults to 1):
                The frequency at which the `callback` function will be called. If not specified, the callback will be
                called at every step.

        Returns:
            [`~pipelines.stable_diffusion.StableDiffusionPipelineOutput`] or `tuple`:
            [`~pipelines.stable_diffusion.StableDiffusionPipelineOutput`] if `return_dict` is True, otherwise a `tuple.
            When returning a tuple, the first element is a list with the generated images, and the second element is a
            list of `bool`s denoting whether the corresponding generated image likely represents "not-safe-for-work"
            (nsfw) content, according to the `safety_checker`.
        """
        # 1. Define call parameters
        if isinstance(image, PIL.Image.Image):
            batch_size = 1
        elif isinstance(image, list):
            batch_size = len(image)
        else:
            batch_size = image.shape[0]
        # here `guidance_scale` is defined analog to the guidance weight `w` of equation (2)
        # of the Imagen paper: https://arxiv.org/pdf/2205.11487.pdf . `guidance_scale = 1`
        # corresponds to doing no classifier free guidance.
        do_classifier_free_guidance = guidance_scale > 1.0

        # 2. Preprocess mask and image
        mask, masked_image = prepare_mask_and_masked_image(image, mask_image)
        height, width = masked_image.shape[-2:]

        # 3. Check inputs
        self.check_inputs(example_image, height, width, callback_steps)

        # 4. Encode input image
        image_embeddings = self._encode_image(example_image, num_images_per_prompt, do_classifier_free_guidance)

        # 5. set timesteps
        self.scheduler.set_timesteps(num_inference_steps)
        timesteps = self.scheduler.timesteps

        # 6. Prepare latent variables
        num_channels_latents = self.vae.config.latent_channels
        latents = self.prepare_latents(
            batch_size * num_images_per_prompt,
            num_channels_latents,
            height,
            width,
            image_embeddings.dtype,
            generator,
            latents,
        )

        # 7. Prepare mask latent variables
        mask, masked_image_latents = self.prepare_mask_latents(
            mask,
            masked_image,
            batch_size * num_images_per_prompt,
            height,
            width,
            image_embeddings.dtype,
            generator,
            do_classifier_free_guidance,
        )

        # 8. Check that sizes of mask, masked image and latents match
        num_channels_mask = mask.shape[1]
        num_channels_masked_image = masked_image_latents.shape[1]
        if num_channels_latents + num_channels_mask + num_channels_masked_image != self.unet.config.in_channels:
            raise ValueError(
                f"Incorrect configuration settings! The config of `pipeline.unet`: {self.unet.config} expects"
                f" {self.unet.config.in_channels} but received `num_channels_latents`: {num_channels_latents} +"
                f" `num_channels_mask`: {num_channels_mask} + `num_channels_masked_image`: {num_channels_masked_image}"
                f" = {num_channels_latents+num_channels_masked_image+num_channels_mask}. Please verify the config of"
                " `pipeline.unet` or your `mask_image` or `image` input."
            )

        # 9. Prepare extra step kwargs. TODO: Logic should ideally just be moved out of the pipeline
        extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)

        # 10. Denoising loop
        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
        with self.progress_bar(total=num_inference_steps) as progress_bar:
            for i, t in enumerate(timesteps):
                # expand the latents if we are doing classifier free guidance
                latent_model_input = paddle.concat([latents] * 2) if do_classifier_free_guidance else latents

                # concat latents, mask, masked_image_latents in the channel dimension
                latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
                latent_model_input = paddle.concat([latent_model_input, masked_image_latents, mask], axis=1)

                # predict the noise residual
                noise_pred = self.unet(latent_model_input, t, encoder_hidden_states=image_embeddings).sample

                # perform guidance
                if do_classifier_free_guidance:
                    noise_pred_uncond, noise_pred_text = noise_pred.chunk(2)
                    noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

                # compute the previous noisy sample x_t -> x_t-1
                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample

                # call the callback, if provided
                if i == len(timesteps) - 1 or ((i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0):
                    progress_bar.update()
                    if callback is not None and i % callback_steps == 0:
                        callback(i, t, latents)

        # 11. Post-processing
        image = self.decode_latents(latents)

        # 12. Run safety checker
        image, has_nsfw_concept = self.run_safety_checker(image, image_embeddings.dtype)

        # 13. Convert to PIL
        if output_type == "pil":
            image = self.numpy_to_pil(image)

        if not return_dict:
            return (image, has_nsfw_concept)

        return StableDiffusionPipelineOutput(images=image, nsfw_content_detected=has_nsfw_concept)